Master’s Thesis In the joint international graduate program Advanced Materials Science (AMS) Within the “Elitenetzwerk Bayern” (ENB) Offered by Technische Universität München (TUM) Ludwig-Maximilans-Universität München (LMU) Universität Augsburg (UA) Magnetic properties of high quality single crystals of the electron underdoped cuprate superconductor Nd 2-x Ce x CuO 4+δ Submitted by Alma Gabriela Dorantes Palacios Completed at the Walther-Meißner-Institute (WMI), Bayerische Akademie der Wissenschaften External supervisors: Prof. Dr. Andreas Erb and Dr. Mark Kartsovnik University supervisors: P.D. Dr. Jan Minar and Prof. Dr. Hubert Ebert October 2013, Munich
Transcript
Master’s Thesis In the joint international graduate program
Advanced Materials Science (AMS)
Within the “Elitenetzwerk Bayern” (ENB)
Offered by
Technische Universität München (TUM)
Ludwig-Maximilans-Universität München (LMU)
Universität Augsburg (UA)
Magnetic properties of high quality single crystals of the electron underdoped
cuprate superconductor Nd2-xCexCuO4+δ
Submitted by
Alma Gabriela Dorantes Palacios
Completed at the
Walther-Meißner-Institute (WMI), Bayerische Akademie der Wissenschaften
External supervisors: Prof. Dr. Andreas Erb and Dr. Mark Kartsovnik
University supervisors: P.D. Dr. Jan Minar and Prof. Dr. Hubert Ebert
2.3 Phase diagram of the electron doped and hole doped cuprate superconductors. ............................................ 12
2.3.1 Hole doped side of the phase diagram ....................................................................................................... 13
2.3.2 Electron doped side of the phase diagram. ................................................................................................ 15
Chapter 3: Growth of electron-doped single crystals ............................................................................................ 17
3.1 The Traveling Solvent Floating Zone (TSFZ) method .......................................................................................... 17
3.2 Crystal growth equipment: the mirror furnace. ................................................................................................. 21
3.3 The stages of the crystal growth. ....................................................................................................................... 23
3.3.1 Preparation of the source materials for crystal growth. ............................................................................ 24
Chapter 4: Post-growth treatment of the crystals ................................................................................................ 26
4.1 The annealing treatment of the grown crystals. ................................................................................................ 26
4.2 The role of oxygen in the electron-doped superconducting cuprates. ............................................................... 27
4.3 Optimization of the annealing process. ............................................................................................................. 29
5.2.1 General setup ............................................................................................................................................. 34
5.2.2 Measurements: AC and DC susceptibility ................................................................................................... 35
Theoretical background support ......................................................................................................................... 75
The present work deals with the improvement of the post-growth annealing treatment of the electron-
underdoped cuprate superconductor Nd2-xCexCuO4+δ (NCCO) in order to optimize superconducting (SC)
transition temperature and with a study of its magnetic properties. Particular attention was paid to the
estimation of the SC volume fraction of the high quality single crystals. The latter was investigated to
inquire in the relation between the antiferromagnetic (AF) state and SC state of the electron-doped
cuprate superconductors and try to observe if there exists an intrinsic phase separation or a microscopic
coexistence of these two states. The results indicated that a SC transition is achievable under the correct
annealing conditions even for very underdoped samples and that bulk superconductivity is present. In
addition there appears to be a break in the monotonic doping dependence of the transition temperature
Tc between samples with 12% and 13% Ce doping, which could signify a first evidence of the so-called
1/8 anomaly in the electron-doped cuprate superconductors.
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Chapter 1: Introduction
High-temperature superconductors (HTSC) are materials that become superconducting at unusually high
temperatures. More than 20 years have passed since the discovery of these remarkable and fascinating
materials and today, not only are many fundamental questions still unanswered, but new inquiries keep
appearing with every single day.
The first challenge was to try and find an explanation for conventional superconductors, which took the
efforts of numerous scientists. Work by Cooper in 1956 and Bardeen, Cooper, and Schrieffer (BCS) [1] in
1957 procured the model description of elemental superconductors and made it possible to understand
superconductivity as a macroscopic and quantum phenomenon [2].
This theory describes how electrons can pair up in a way that changes their quantum properties. A
particular type of electron-phonon attractive interaction is possible below the so-called transition
temperature (Tc). The repulsive Coulomb interaction between electrons is dominated by the electron-
phonon attraction. This allows the formation of a virtual electron pair which can move effectively and
unperturbed through the lattice as a single particle, the so-called the Cooper pair [1, 3]. The Cooper pair
has long range phase coherence. An electron moves through the lattice, the phonon-electron attraction
is strong enough to deform the lattice in a way that a second electron can feel this effect and it is drawn
to the other electron to form a Cooper pair. The shape of the wave function is an s-wave [3, 4].
Not long after these conclusions, new types of superconducting materials were discovered, such as
organic superconductors and heavy-fermions. They presented an unusual superconducting behaviour.
But yet another breakthrough came along in 1986 by Bednorz and Müller with the discovery of a cuprate
material with a remarkably high superconducting transition temperature. The cuprate La2-xBaxCuO4
(LBCO) showed an onset temperature of 34 K. The compound La2CuO4 is an insulator and the appearance
of superconductivity by Ba doping was a surprise [5]. In the next year another cuprate compound was
discovered, with an even higher transition temperature. The Y-Ba-Cu-O system shocked the scientific
community with Tc≈ 92 K [6].
The BCS theory did not comprehend such high temperature behaviour and new investigations
commenced to try and explain what seemed to be a completely different superconductivity mechanism.
Many cuprate systems were, and still are, the subject of study but to this date the origin and mechanism
of superconductivity (SC) in cuprates has not been unanimously outlined. The s-wave function model
which applies to conventional superconductors does not agree with the behaviour of cuprates. Because
of this reason, a model which predicts a d-wave function due to antiferromagnetic (AF) fluctuations has
been proposed [4].
The copper-oxide based high temperature superconductors (HTSC) are a group of compounds which structurally belong to the perovskites family1. The main structural features are the planes of copper and oxygen ions, with a copper ion at every corner of a square and an oxygen ion along each side. Between
1 For a better comparison with the crystal structure of the cuprates, an illustration of the perovskites system is
these planes, different types of elements such as lanthanum, strontium, yttrium, bismuth and thallium can be introduced. Other examples, and with more relevance to this thesis, are Nd2-xCexCuO4 and Pr2-
xCexCuO4. For these compound the Ce element is the charge carrier donor to the copper oxide layers and is normally referred as charge reservoir [3, 7]. The conductivity capabilities of these compounds are directly related to the charge carrier concentration provided by hole or electron- doping to the CuO2 layers. The charge carriers move from copper ion to copper ion along the CuO2 layers by weak coupling [8]. Thus, the cuprate type superconductors present a highly anisotropic conductivity which happens mainly in the plane parallel to the CuO2 layers [4, 9]. The discovery of superconductor capabilities in cuprates opened a new field for research and prospective applications. Superconducting cuprates originate from an insulating parent compound called the Mott insulator [10]. Charger carriers are introduced to the system by doping and the dopant concentration x determines the physical properties of these High Tc materials. First cuprates to be discovered and highly studied were La2-xBaxCuO4 (LBCO) and YBa2Cu3O7-δ (YBCO). These cuprates belong to the p-type or hole-doped cuprates. It was in 1989 that superconductivity was discovered in the electron-doped systems (Nd, Pr, Sm)2-xCexCuO4 (LnCCO) [11]. To this date, it is generally accepted that the superconductivity phenomena is due to the strong electron repulsion and the layered nature of the cuprates. But a true understanding of how the charge carriers pair up and develop such physical properties is still to be resolved. Due to the many proposals and theories which have developed to try to explain this phenomenon, an intense review of the basic mechanism which gives place to the formation of Cooper pairs is not part of this thesis. It should only be mentioned that there are two main theories which can still be addressed. Dating from the very beginning of the discovery of the superconducting cuprates , P.W. Anderson proposed the resonating valence-bond theory [12]. The bonds between the oxygen atoms provide the means for electron sharing and the formation of a coherent superconducting phase is more favourable with increasing doping. This means that the closer the carrier concentration is to the Mott insulator parent compound, the more it should resemble it. The second theory addresses the antiferromagnetic (AF) inherent characteristic of the Mott insulator and its relation to spin fluctuations [13]. The movement of the electrons has an effect which is perceived by the spin arrangement in the lattice causing a deformation in the long-range ordering and thus inducing superconductivity [14]. These two approaches are the subject of exhaustive debate. Furthermore, the outstanding physical properties of the cuprates cannot be explained without the proper distinction between the properties caused by the material itself, such as impurities, inhomogeneities etc., and intrinsic factors of the copper-oxide materials caused by their own nature [15]. Concerning the issues arising from material specifications, the phase diagram of the cuprates which correlates transition temperature Tc and doping level x needs further investigation. But the different boundaries and borders between phases cannot be completely fixed and this complicates the interpretation of the phase diagram. The Mott insulator parent compound has a doping of x= 0. Coulomb repulsion causes a split of the conduction band of these compounds, an energy gap opens up and thus the material behaves as an insulator. The parent compounds also share a characteristic antiferromagnetic ordering at the copper
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sites. As the dopant concentration increases from x=0, p-type or n-type compounds, the commensurate AF state continues to be present, until a certain doping concentration x is achieved and a superconducting transition is first observed. With increasing x, the temperature to observe superconductivity raises, and for a special x a maximum value of Tc is recognized, this is the optimal doping xc. At higher carrier concentration Tc goes back to 0 K. So the superconducting transition occurs within a particular range of x-values. Surrounding the SC state different types of metallic states are found [16]. Moreover, a definite barrier between the AF state and the SC state is not clear. In the hole-doped side of the phase diagram the AF state seems to vanish quite early according to doping, but in the electron-doped side this state persists way further into the SC state [17, 18]. It is a current question of whether the AF state has a fixed finish line or if it manages to coexist with the SC state [19]. Another example which concerns this question is the observation of Quantum Oscillations2 in optimally electron-doped cuprates [20]. At optimal doping xc the evidence of this phenomenon was outstanding, while it showed a sudden and abrupt disappearance if the sample material was underdoped. It was not understood if this experience was due to sample quality or to coexistence of the two states. The first step to be able to describe the physical properties of these compounds is to be able to distinguish between intrinsic and extrinsic effects such as material specific issues. This is why the investigation of the phase diagram of the superconducting cuprates is of major importance. The hole-doped compounds have received much attention while on the other hand; the electron-doped half of the family has been relatively overlooked. Within these scarce investigations, the scientific community focused on the optimally doped and overdoped compounds. In the electron-doped cuprates the particular underdoped regime presents quite a list of obstacles in terms of their proper preparation. This is the main reason why they were ignored as research objects for some time [21]. But they also present many advantages which makes them an exemplary system to approach the issues of the possible coexistence of the AF and SC states. An advantage of the electron-doped cuprates is that almost the complete phase diagram is synthesis accessible. From the undoped antiferromagnetic insulator Ln2CuO4+δ (with Ln = Pr, Nd, Sm, Eu) to high carrier concentrations in the overdoped metallic regime can be achieved by doping with tetravalent Ce [21]. Nowadays it is possible to achieve high quality crystals even in the underdoped regime, thanks to a novel technique, the Traveling Solvent Floating Zone method, which will be described in further sections of this thesis. The focus of this thesis is to address the particular underdoped regime of the electron-doped cuprates by studying low-temperature magnetic properties of high-quality Nd2−xCexCuO4+δ crystals. The growth parameters of the high-quality single crystals comprise the first part in this work, with special focus on the optimization of the post-growth annealing treatment of the samples. The second part of this work focuses on the estimation of SC volume fraction and its spatial homogeneity. Depending on whether or not there is a SC/AF phase separation at low temperatures, the SC volume fraction will change with Ce concentration or stay constant. The aim of the present work is a quantitative estimation of the SC volume fraction as a function of x in the underdoped region.
2 Description of Quantum Oscillations meaning and further explanation is not covered in this thesis. It should only
be mentioned that the observance of this phenomenon allows determining Fermi liquid behavior in a material.
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Chapter 2: The cuprate superconductors
2.1 General overview of the cuprate superconductors If a superconducting material possesses CuO2 layers within its structure, it belongs to the cuprate superconductor family. Among the cuprate superconductors are the 214 compounds who have the general formula Ln2-xAxCuO4 (Ln= rare earth metal, A= Ca, Sr, Ba, Ce, etc.). Depending on their chemical composition, they are divided into two families, hole-doped cuprates and electron-doped cuprates. The first 214 compounds were discovered in 1986 by Bednorz and Müller [5] as they decided to work with transition metal oxides since they showed evidence of polaronic3 effect, a good sign of strong electron-phonon interaction [22]. They have in common some main aspects; the nature of the parent compound with a particular spin order and the presence of CuO2 planes in their crystal structure, which is responsible for the conduction phenomena. If the electron concentration in the CuO2 planes of an undoped cuprate is one electron per unit cell, the compound can behave as a Mott insulator, which is the parent compound of the 214 copper oxide superconductors [17]. In a normal insulator the electrons can’t move because the conduction band contains two electrons per unit cell. If all orbitals are filled, then conduction would contradict the Pauli Exclusion Principle. According to this, the parent compounds of the copper oxide superconductors should behave like a metal since they only have one electron-occupancy. However, the motion of electrons between atoms will be resisted by a strong Coulomb repulsion. In a Mott insulator the electrons repel each other and a metal-insulator transition occurs [13, 22]. At low temperatures the Mott insulators have an antiferromagnetic order. The long-range AF order is disturbed if the electron concentration per unit cell is modified upon charge carrier doping. Eventually, at a particular dopant concentration x, the AF order vanishes and superconducting state is achieved [11, 17]. The limits of the AF order and SC state border are not defined and it seems as if they overlap. As mentioned before, the conductivity mechanism in the cuprates takes place in the CuO2 due to the correlation between the Cu sites and the inter-layer elements acting as chare reservoirs. The conductivity is highly anisotropic, the charge carriers move along the CuO2 layers. Each copper is bound to four oxygen ions with an approximate distance of 1.9 Å. The Cu-O bonding is a covalent bond between the copper 3dxy and oxygen 2py orbitals [9]. It has been suggested that there is a direct relation between the number of CuO2 layers which are close to each other in the crystal structure and the value of Tc [7]. A good example is Tl2Ca2Ba2Cu3O10 which has three adjacent CuO2 planes and a Tc= 125 K. A big variety of cuprate oxides have been studied, a few examples are listed below in Figure 21. Until recently the main focus was given to the family of hole-doped cuprates.
3 Polaron: quasiparticle composed of a charge surrounded by a cloud of phonons.
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Figure 2.1: Comparison of hole-doped and electron-doped studied copper oxide superconductors with their Tc and other examples of conventional superconductors. Many combinations can be synthesized by modifying parameters like the number of planes per unit cell, atoms separating the nearby planes, as well as the structure, composition, and size of the charge reservoir [9].
The cuprates with general formula Ln2CuO4 can crystallize in two different types of structure. In the so-called T structure, mainly found for the hole-doped cuprates, the Ln element contains two-dimensional sheets of CuO6 octahedra and the charge carriers are electron vacancies. Half of the oxygens are in the planes O(1) and the other half are between the planes O(2) [11, 23]. The electron-doped cuprates crystallize in the T’ structure, in this case the Ln element has CuO4 planes. Figure 2.1(b) shows that, in the T structure, above and below each copper ion there is an O atom, these particular oxygens in the c direction are called apical oxygens. Both structures are said to derive from the perovskites family and they both crystallize in the I4/mmm space group. A contrasting image of both types of structures is shown in Figure 2.2 (a) and (b). In the undoped parent compound of the prototypical system La2-xSrxCuO4 the Cu ions have a 2+ valence in their 3d9 configuration and O has a fully occupied 2p states. Upon doping, a La ion with a 3+ valence is by replaced the Sr2+, the 2p band of the oxygen receives fewer electrons and the holes enter this band. The out-of plane oxygens inhibit fluctuations of electron band onto a Cu site and stabilize the presence of holes in the plane [24]. It should be remarked that the Cu-O octahedral is not ideal; the Cu-O distance in the c axis is 2.4 Å making the in-plane bonds much stronger. In the case of the Nd2-xCexCuO4, the apical oxygens are shifte away from the Cu sites, so electrons can enter the 3d band of the Cu and fill in a hole.
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Ln2-x
CexCuO
4 La2-x
SrxCuO
4
Figure 2.2: (Left) T’ type unit cell, typically seen in (Nd1-xCex)2CuO4 electron-doped compounds. (Right)T’ unit cell, seen in the family of the hole-doped superconductors La2-xSrxCuO4 . Notice that the main difference between these two structures is the absence of apical oxygen in the electron-doped cuprate. The shift of the adjacent CuO2 layers in the diagonal results in an doubled in-plane unit cell. Modified from [25].
The hole-doped and the electron-doped cuprates present many interesting physical properties which derive from their structural differences. These differences have played a role as an advantage to study certain compounds and to overlook others. For example, the hole-doped materials have been the topic of interest in research for many years. Amongst these beneficial features one can mention their high stoichiometry, a controllable synthesis and access to the most interesting parts of the phase diagram etc. However not all the phase diagram is accessible by synthesis and even though it should be expected that the physical properties of the hole-doped compounds show similarities to the electron-doped ones, this is not completely the case. In fact, many differences of great importance are present. One important motivation for this thesis is the lack of research and available information on many of the physical properties and behaviour of the electron-doped cuprates. To begin this approach, the main focus of this work is related to the underdoped regime of the electron-doped Nd2-xCexCuO4.
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2.2 Electron-doped compounds
2.2.1 General structure features.
The electron-doped superconductors have the formula Ln2-xCexCuO4, where Ln stands for the lanthanides Pr, Nd or Sm. They crystallize in in the T’ structure already shown in Figure 2.2 (left) with a space group I4/mmm [26]. Common features within the electron and hole-doped 214 families of cuprates superconductors are the role of the CuO2 in their electronic properties and their highly anisotropic character. But obvious differences are seen in their crystal structure. The T’ phase differs from the T structure in the absence of the apical oxygens. The coordination number CN is reduced to 4, so the Cu atom is surrounded by only four oxygen ions O(1). The adjacent CuO2 layers are shifted along the in-plane diagonal [25] . Thus, the position of the oxygen atoms of the charge reservoirs O(2) is also different from the T structure, which results in an expansion of the in-plane unit cell [18]. The O(2) of the T structure shift and they are now referred as O(3) in the T’ structure, and they have the same x, y coordinate positions as O(1) with z = ¼ or ¾ . The Ln element is coordinated to four O(1) and four O(3) atoms, but with slightly different Ln–O distances to the hole-doped compounds. The lattice parameters are a= 3.95 Å and c = 12.07 Å [23]. The electron-doped compound of interest in this thesis is the Nd2-xCexCuO4 (NCCO). Electronic and magnetic properties, along with a description of the phase diagram are discussed in the next section.
2.2.2 Nd2-xCexCuO4 (NCCO)
Superconductivity was discovered in the Nd2-x-ySrxCeyCuO4 compound in 1988 and suddenly there was a lot of interest in the Nd2-xRxCuO4 system [27]. The material was expected to behave as an n-type conductor material, it surprisingly showed a superconducting transition at 28 K. Furthermore, if the Ce concentration was modified to higher values, the Tc would react in direct proportion [10]. Later on, in 1989, the Nd2-xCexCuO4 compound with x= 0.16 was reported to have a Tc=24 K and most interestingly, the copper oxidation state in the compound was lower than 2+ [9]. The Cu-O bond is a covalent bond formed between the orbitals orbitals of the oxygen. The
highest occupied level is the antibonding half of the orbital. The orbitals of the copper and
the orbitals of the oxygen interact to form a π full orbital [9]. In contrast to the Sr3+ doping in the
hole-doped cuprates, the Nd3+ is replaced by Ce4+ and the CuO2 planes automatically have an excess of electrons and the conductivity becomes electron type, electrons enter the upper half of the
band
as Nd ions are replaced by Ce ions, and the energy of the highest occupied state is increased [27]. Figure 2.3 shows the molecular orbitals of an isolated CuO4.
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Figure 2.3: Molecular orbital energy levels of an isolated CuO4 square. Notice the upper level vacancy where electrons can be accepted upon doping. To form a π orbital, the energy of the oxygen orbitals is raised and the energy of the copper orbitals is lowered [9].
Another important feature is the behaviour of Ce. The oxidation state of Ce in CeO2 is in an intermediate state of approximately 3.5+ due to hybridization with th 2p band of the oxygen [24]. The holes in the neighbouring oxygen compensate this lower valence and thus the copper sites behave as if the net charge of Ce were the formal 4+. The T’ structure of the Nd2-xCexCuO4 favours the addition of an electron into the 3d hole of the Cu ion because of the absence of the apical oxygen, the CuO2 plane gets richer in electrons with doping as some Cu2+ convert into Cu+ [24]. This lack of the apical oxygen is of major importance for the electron-doped cuprates. They do not superconduct in their as- grown state and they must undergo a post growth annealing treatment to achieve an appropriate oxygen doping. This topic is one of the two main objectives for this thesis, thus further details and explanations will be given in Chapter 4. As it has been mentioned, the appearance of the SC state is doping dependent. In the electron-doped cuprates it has been reported that a superconducting phase exists between x= 0.13 and x= 0.18 [25]. Previous studies at the Walther-Meißner Institute determined that the Tc(x) relation shows a maximum Tc around xc,opt= 0.145, where Tc, opt=25 K [21]. This short description of the Nd2-xCexCuO4 only provides a first enlightening of the general behaviour of the electron-doped cuprates, but the relation between these points and the wide variety of unusual physical properties they depict has yet to be investigated. Among the many intriguing subjects which surround these compounds, the possible coexistence of the AF state and the SC state is a big debate. The apparent asymmetry between the superconducting dome of the hole-doped and the electron-doped cuprates is also a matter of concern. This is why a better understanding of the phase diagram of the superconducting cuprates is an approaching method to solve some of the mentioned questions. For this work, the focus is placed on the underdoped regime of the phase diagram of Nd2-xCexCuO4 in an attempt to observe how the AF state merges into the SC state.
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2.3 Phase diagram of the electron doped and hole doped cuprate
superconductors. A general phase diagram of the cuprate superconductors is shown in Figure 2.4, electron-doped and hole-doped regimes are visible. The pink area indicates the range where superconductivity is observed. The blue coloured area indicates the region of long-range commensurate antiferromagnetic order. Since both types of superconductors originate from a Mott insulator parent compound, the presence of the AF order is a similarity between the two regimes, although the extension of the latter on each side of the diagram is highly asymmetric. To illustrate how the AF ordering happens in the Mott insulators refer to the Appendix 1, Figure A2. The Néel temperature (TN)4 recorded for both type of materials shows rather high values. For the hole-doped parent compounds TN is between 250 K and 400 K, while for the electron-doped compounds it shows a value of around 250 K.
Figure 2.4: Schematic of the phase diagram of hole- and electron-doped superconductors obtained from experiments performed on La2-xSrxCuO4 and Nd2-xCexCuO4 respectively [10] . The AF state is found below TN, the latter decreases with increasing doping. Various phase transitions and ordering phenomena are possible. They depend on the charge carrier concentration and the temperature. Below the temperature T* there is a particular state where anomalous properties are seen, often referred as a pseudogap. On the hole-doped side of the diagram the AF and SC regions are clearly separated from each other. For the electron-doped cuprates, it is not quite clear whether the AF and SC states coexist and, if yes, then to which extent.
Along with the AF and SC areas, other electronic states are visible in the phase diagram, although the analysis of such additional states is beyond the scoop of this thesis. It is more important to stress that these phase transitions are not completely fixed and only certain points in the diagram can be defined. In Figure 2.4 a dashed line which corresponds to the temperature T* is visible. Near the insulating state there is a regime which presents many peculiarities and it seems to contain parts of the other existing states. This area is often called the pseudogap. Above the pseudogap a strange metal phase covers a large range of temperature and in the overdoped regime the Fermi liquid phase is present.
4 Néel Temperature is the temperature above which an antiferromagnetic or ferrimagnetic material becomes
paramagnetic.
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After mentioning the general features that both types of cuprate superconductors share in terms of their
carrier concentration and temperature dependence, the differences between them should be
highlighted. Symmetry in the phase diagram exists only for a very short region close to the zero doping.
To probe the many discrepancies in the physical properties of these materials, different systems in both
sides of the phase diagram have been investigated. Figure 2.5 shows the corresponding cuprate
compounds on each side of the phase diagram.
Figure2.5: Generic phase diagram of the cuprate superconductors with examples of notable compounds which have
been probed to investigate different features and phase transitions. The arrows indicate the doping regimes which
are accessible by synthesis of the specific compounds [25].
2.3.1 Hole doped side of the phase diagram
Due to the many compounds which have been tested in this regime, Tc and TN values can vary. But a
general case accepts that the AF order is destroyed at x=0.02 dopant concentration. Superconducting
state is achieved between 0.05< xc,opt < 0.27 with a maximum Tc at xc,opt≈0,16 and a critical hole content
psh≈ 0.05-0.06, where psh is the fraction of doped holes per Cu atom [28]. The d-wave like shape of the
order parameter for these materials has been confirmed by ARPES measurements [3]. By muon
spectroscopy (µSR) it has been pointed out that for the La2-xSrxCuO4 system the AF state persists up to
0.05< psh< 0.1. Neutron scattering measurements state that this persistence has a short range order [28,
29]. These findings present a new picture of magnetic order inhomogeneity; this is today commonly
referred as “stripe ordering”. This charge and stripe order has been directly associated with a curious
phenomenon which appears at x= 1/8. The “1/8 anomaly” is nothing other than the sudden and
unexpected suppression of superconductivity. A schematic diagram which illustrates this type of
commensurate order in the CuO2 can be seen in figure 2.6 [29].
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Figure 2.6: Idealized diagram of the stripe order in real space. The charges are ordered in a stripe arrangement and
between them there regions of locally AF order. a) Diagram of vertical stripes. b) Diagram of horizontal stripes. c)
Diagram of horizontal spin ladder. Arrows indicate the orientation of magnetic moments on undoped Cu sites and
empty circles represent Cu sites in hole-doped stripes. This representation is called the “bond-centered” model [29].
But what exactly is meant by a stripe ordering, and how does it supress conductivity?
It can be viewed as a spatial correlation between spins and holes. It is a coupled, dynamical modulation
of spin and charge, where stripes of hole-doped copper sites are separated by equidistant walls of
undoped copper sites which maintain the antiferromagnetic order. This should be consistent with
Coulomb repulsion. It should be remarked that the stripe alignment is not yet defined, but so far the
bond-centered model is generally accepted as a good description of the arrangement. This model
describes the alignment as either horizontally or vertically arranged [29].
The stripe order can be described as domain walls pinned to a certain level of commensurability, which
would result in static correlations and possible long-range order. In this case the AF state becomes
dominant, thus insulating properties predominate and superconductivity is supressed [30].
The 1/8 anomaly has also been associated with structural phase transition. This is the case for the La2-
xBaxCuO4 system [31]. The tetragonal-to-orthorhombic transition is TTO = 180 K with maximal lattice
distortion at 35 K [32]. Other studies compared the low-temperature orthorhombic (LTO) and the low-
temperature tetragonal (LTT) structures and it was stated that a horizontal stripe alignment was
favoured in the LTT structure5 [30]. This pattern does not appear along the c axis.
This sudden suppression of superconductivity and other features such as a linear temperature
dependence of the normal state behaviour still require a general agreement on their physical origin and
impact on the superconductivity. And although many systems have been probed, the hole-doped regime
reaches a limit in terms of achievable doping, which impedes further explorations over-doped regimes
[30].
5 A comparison of the LTO and LTT possible stripe arrangement is shown in the Appendix 1, Figure A3.
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2.3.2 Electron doped side of the phase diagram.
As mentioned before the electron-doped side of the phase diagram shares some qualitative features
with its hole-doped counterpart, but quantitative differences are of main importance. The first and
maybe most evident difference can be seen at first glance; the much larger extension of the AF state. It
even merges into the superconducting dome, which is limited to a more narrow doping range.
Superconductivity has been observed to set in at x=0.13. The maximum Tc is observed at xc,opt= 0.145
[25]. No structural phase transitions have been reported. Resistivity behaves ≈T2 near optimal doping,
showing a reminiscent behaviour of a Fermi liquid, and the registered values for Tc are considerably
lower compared to the p-doped cuprates. They also present lower critical magnetic fields, Hc2 (T=
0)│B˪layers ≈10 T compared to Hc2 (T= 0)│B˪layers ≈ 50 T for p-type materials. The suppression of
superconductivity in n-type cuprates is possible in simpler experimental conditions to test the normal
state properties [18, 33].
It is also visible that the spacing between the AF and SC states is not as definite as for the hole-doped counterparts. The AF state seems to possess more stability which allows its persistence into larger concentrations of Ce doping. Since the AF state does not disappear within a defined and abrupt limit as it does in the hole-doped cuprates, it seems as if doping with electrons has a different effect on the electronic properties of these materials. The doping dependence of the Tc for Nd2-xCexCuO4 is depicted in Figure 2.7.
Figure 2.7: Derived superconducting dome of Nd2-xCexCuO4 from AC susceptibility experiments performed at the
Walther-Meißner Institute [25]. The vertical bars denote the width of the transition. Notice how below x= 0.13 there
is no evidence of SC transition.
From figure 2.7 one can observe that at x= 0.13 the superconductivity sets in, but with a rather broad
transition as depicted by the vertical bars. Below this dopant concentration the Tc decreases and a SC
transition is no longer observed. This doping range, the underdoped regime, has not been as fully
studied as the optimally and overdoped regime, although it is in this area where the AF state and the SC
have an unusual and possible coexistent relation. The lack of further experimentation has been due to
difficulties on sample preparation. Details on this matter are discussed in further sections of this thesis.
16
There are other unresolved issues for the electron-doped cuprates which might find some explanation if further investigations are performed in this area of the phase diagram. Although they will not be covered in this thesis, it can be worth to mention them. For example there is no general consensus on the symmetry of the order parameter. It is still debated if the true nature of the Cooper pair should follow that of an s-wave or d-wave [34, 35]. Another unresolved controversy is the nature of the pseudogap. The physical origins of the anomalies observed in this area are not understood. Within the subject of this work, one can mention the problematic that the exact dopant concentration x where the AF state vanishes has not been determined yet: the question of coexistence of the AF phase with the SC phase. From the Figures 2.4 and 2.7 one can appreciate a slight merging of the AF regime into the SC one. Particular observation of Figure 2.7 leads to the belief that below x =0.13 a SC transition cannot be fulfilled. Hence, a closer examination of underdoped Nd2-xCexCuO4 samples should be conducted. Particular points of interest are x= 0.10 to x= 0.13. High quality crystal samples are necessary to achieve this goal.
17
Chapter 3: Growth of electron-doped single crystals
3.1 The Traveling Solvent Floating Zone (TSFZ) method
After discussing the many characteristics of the HTSC cuprates, specifically for the electron-doped group of materials, a motivation for this thesis has been set in order to approach one of the unresolved issues concerning these compounds. For such a task, materials with specific qualities are needed. High purity, dopant homogeneity and accessibility to the whole range of the doping regime are only the basic parameters. Furthermore, since the superconductivity properties of these materials are highly anisotropic, oriented single crystals are needed.
Research and advances on the growth of single crystals for the YBa2CuO7 and La2-xSrxCuO4 systems have been conducted with great enthusiasm and progress [36, 37]. Intrinsic properties of the compounds to be grown such as stoichiometry and congruent melting are advantageous to achieve successful crystal growth.
Unfortunately the electron-doped Ln2-xCexCuO4+δ (Ln= Pr, Nd, Sm, Eu…) family does not benefit from such characteristics. Not only is the crystal growth a very demanding process in technique, ability and equipment, but the post-growth annealing treatment still lacks on definite parameters. The true impact and mechanism of the annealing treatment are not entirely resolved, but it is accepted that it is directly related to elimination of the oxygen surplus in the chemical formula. Nevertheless these materials are drawing attention to serve as sample set for investigations because they are solid solutions with a tetragonal crystal structure and gradual doping to the parent compound yields access to almost all the phase diagram [21].
Classical methods in crystal growing include growth from a crucible. A crystal grower will encounter three main obstacles when attempting to synthesize electron-doped HTSC single crystals from a CuO rich melt in a crucible6. Variation of the distribution of the dopant is unavoidable; this is evaluated from the
distribution coefficient parameter. It is the ratio of the concentration of a component A in two phases
[ ] [ ] , and it is dependent on the growth kinetics and the transport processes [25]. The
final crystals may show higher concentration of Ce in the center or on the surface of the crystal [38].
Another issue is the lack of inert crucible materials. The sample melts are notoriously aggressive to the crucibles7; they deteriorate and produce impurities in the final crystal which interfere or suppress superconductivity. Phase diagrams of Nd2CuO4 and Pr2CuO4 are shown below in Figure 3.1.
6 Nd2-xCexCuO4/CuO ratio x=70/30. This mixture is molten in a crucible at T > T(x) of the liquidus line. Then it is
slowly cooled down to the eutectic temperature. 7 Commercially available crucibles such as Pt, Al2O3 and Y stabilized ZrO2 have been used.
18
Figure 3.1: A) Phase diagram of Nd2CuO4 in air. B) Phase diagram of Pr2CuO4 in air [38, 39]. Eutectic and peritectic points are between 1000-1200°C. Eutectic point is the lowest temperature at which a mixture of chemical compounds or elements with a single chemical composition solidifies. Peritectic point is the temperature at which a liquid and a solid phase of fixed proportions react to yield a single solid phase. Peritectic reactions happen at the interface between the two reactants and can generate a diffusion barrier.
The phase diagrams demonstrate that the compounds Nd2-xCex CuO4 and Pr2-xCex CuO4 show incongruent melting 8 thus the growth is limited to a certain area between peritectic (TP) and eutectic point (TE) [21].
The peritectic point for the superconducting phase of the Ln2-xCexCuO4 compounds sits at temperatures above 1200°C, while the eutectic point is found around 1000°C. This restricts the growing to a very narrow range in temperature.
The final shape of the crystal is also a matter to consider. Depending on the application or experiment desired to perform on the crystal, some specific requirements might be needed. For example in the case of neutron scattering experiments, bulky crystals are imperative.
Methods such as Czochralski and flux growth are alternatives which do not fulfill all the parameters to obtain optimal single crystals, despite the popularity of both methods. While Czochralski method produces crystals of useful size and quality, it can only deal with materials which melt congruently. Flux growth might then seem as a good option. The materials, with a very high melting temperature, are dissolved in a solvent or “flux” of a third off stoichiometric composition, the crystal is grown below the melting temperature of the mixture and by means of very slow cooling rate, it solidifies before room temperature. However the crystals yielded by this technique result very small with eventual presence of flux impurities, not to mention that the extraction of the crystal from the flux is a complicated and chemically aggressive process if decantation is not possible [40].
In 1952 Keck and Golay [41] used a tantalum heater adapted to a process where the material to be crystallized was suspended in space, the floating zone process. They used this method to grow ultra-pure silicon single crystals. They patented the floating zone method and it has evolved into what today is known as the Traveling Solvent Floating Zone (TSFZ) technique. A lot of improvement in terms of
8A solid phase decomposes before melting, or exhibits a phase transition below the melting point.
A B
19
equipment and procedure control was made, and crystals with 200 mm diameter can be achieved nowadays [42].
For the formation of a TSFZ system, three key elements are needed. A small CuO-rich flux pellet9 and polycrystalline feed material, i.e. the feed rod and the seed rod. They are located in a growth apparatus which consists of an isolated chamber with four halogen lamps as radiation source and an ellipsoidal mirror set. The growth region is isolated by a quartz tube where atmosphere is controlled. Visibility of the interface is possible. This apparatus is called Mirror Furnace10.
To help describe the complicated growth procedure, a scheme of the TSFZ set-up of the growing materials and a general phase diagram of the Ln2-xCexCuO4 compounds is shown in Figure 3.2. Additionally the stages of growth are depicted in Figure 3.3.
Figure 3.2: Illustration of the working principle of the TSFZ technique and its relation to the compositional phase
diagram of the Ln2-xCexCuO4 HTSC [25].
The feed rod and the seed rod are mounted in the mirror furnace in such a way that their tips meet at the focal point of the ellipsoidal mirrors. The flux pellet with composition between xP and xE is settled on top of the seed rod and below the feed rod. This will become the solvent zone, called “floating zone”. The process starts by melting this region, thus it becomes a vertical solvent zone which is contained due to surface tension and adhesion between the corresponding rods. While working at temperatures between TP and TE, and once equilibrium has established, the polycrystalline 214 phase is constantly dissolved into the melt at the feed rod-melt interface. Then it “travels” to the lower liquid-solid interface, this motion is depicted by black arrows in Figure 3.2 in the flux area, the liquid flux x.
After traveling the melting zone it crystallizes at the lower interface. The zone is moved upwards by moving the mirrors and simultaneously the rods are rotated either in the same sense or opposite directions [21, 25, 40, 42, 43].
9 The flux can also be produced if the feed rod is melted above Tx’ and then follow the liquidus line (green arrow in
Figure 3.2) until reaching the peritectic point. This version is depicted in Figure 3.3 left side. 10
Examples of different types and old versions of the mirror furnace are depicted in the Appendix 2, Figures B1 and B2. Consider that the apparatus can also be classified according to other parameters, such as shape of mirrors, source of heater etc. The one utilized for this thesis will be described in the following section.
20
Fig.3.3. Left: nucleation stages for the growth of single crystal in the mirror furnace by the TSFZ method. Here the
flux is obtained by melting the feed rod (see footnote 9). Right: illustration of the buoyancy and convection patterns
due to high temperature gradients in the molten zone. a) Convection for counter-rotation. b) Marangoni convection
(thermo-capillary convection) [42].
It should be noted to the reader that this technique requires high ability and skills to properly control the system. Critical parameters which can be accessed before and throughout the growth process are the correct adjusting of the rods, corresponding rotation rate, pulling rate, temperature management and composition of the molten zone.
A correct set up assures the proper contact between the growing elements. Rotation of the rod is deeply relevant since it affects the convection pattern shown in Figure 3.3 right side, correct stirring of the melt, and final shape and defect presence in the crystal. The pulling rate controls the growth rate and the diameter of the final crystal. The temperature is evidently of tremendous importance. If temperature is too high the melt is unstable and surface tension would be too low to maintain a stable molten zone, plus the composition would vary according to the phase diagram [42].
The multiple benefits obtained from this method make it incomparably better than other techniques. [42, 44]
The need of a crucible is suppressed.
Congruent and incongruent melting mixtures can be crystallized.
Starting materials are the sole source of the growth process. Presence of impurities is highly reduced.
Homogeneous distribution of Ce dopant along the crystal (dependent on oxygen partial pressure po2, flux composition x, temperature and growth velocity).
The final shape of the crystal is a several centimeters long bulky rod. In contrast with the plate like form obtained from crucible method.
No need to separate the grown crystals from the solvent by chemically aggressive methods or decantation.
Accelerated growth rate. The molten zone is constantly stirred.
After this short overview of the growing method and having listed its multiple benefits, it is clear that the TSFZ is the right method to grow high quality single crystals for the 214 HTSC cuprates. In the next section a description of the real experimental set up and technique will be made. It will become evident that the appropriate equipment, correct preparation of growing materials and high skills from the experimentalist are the three minimal prerequisites to grow high quality single crystals.
21
3.2 Crystal growth equipment: the mirror furnace.
The particular machinery used for the growth of single crystals is a mirror furnace. Figure 3.4 shows an illustration of the main body of a typical four-mirror furnace. They can be classified according to different parameters (see footnote 10) but for the purpose of this thesis, the working furnace is an image furnace from CSI Corporation (Japan), type FZ-T-10000-H-VI-VP, four half ellipsoidal-mirror type. This is important since uniform heating of only a small volume of the material is necessary, which cannot be achieved with every available furnace.
Image furnaces use focused light, they are energy efficient and the working temperature range is quite large. Additionally, visual control of the growth area is possible. A small disadvantage is that temperature measurements parallel to the growth process are not feasible [45].
Four ellipsoidal mirrors with halogen projector lamps are located on first focus. They are used to create a uniform temperature around the sample which minimizes the radial thermal stress. This is normally a problem by furnaces with one or two mirrors. The arrangement of the mirrors sits on the horizontal plane; each mirror faces the next with a 90°C angle around the vertical axis.
Fig.3.4. Sketch of the main body parts of the four-mirror furnace charged with the growing elements. Mirror stage
and upper shaft can be moved up and down, this capability is used to regulate the growth rate, control the size of
the molten zone and grown crystal. To control the rotation of the feed and seed rods, both upper and lower shaft
can be rotated, the stirring of the molten zone improves the uniformity of the temperature field and favors the
material transport in the solvent [46] .
The feed rod and the seed rod are mounted at the center of the furnace, connected to the upper and
lower shaft, along the vertical axis of the setup. Sample housing is made of a transparent quartz tube,
which isolates the growing elements and allows to work under the desired atmosphere and pressure.
A real picture of the working setup is shown in Figure 3.5.
22
Figure 3.5: Actual view of the opened 4-mirror furnace with a mounted set of rods for crystal growth inside the
quartz tube. Right: operating mode of the furnace. The radiation is focused on one point in the center where the flux
pellet sits. The second focus of all the mirrors overlaps at this point. Only a small area should be heated and the
temperature gradient happens in vertical direction. As the temperature increases, the pellet melts and the rods are
joint together [25].
The temperature of the molten zone is a critical parameter. It depends on the material capacity of radiation absorption. Some materials are transparent and cannot absorb IR radiation; therefore they cannot be directly grown by the mirror furnace technique.
Specifications of the image furnace are listed below.
Model FZ-T-10000-H-VI-VP
Type of lamp Halogen
Number of lamps 4
Power lamp range 300-1500 W
Max temperature 2200°C
Max crystal growth length 100 mm
Growth speed range 0.18-18 mm/hr
Rotation rate 5-60 rpm
Max pressure 9.5 atm
Max vacuum 5x10-5 Torr
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3.3 The stages of the crystal growth.
After proper preparation of the feed and seed rods, and the flux pellet, they are staged in the corresponding shafts and sample holders inside the furnace. Description of the preparation of the growing elements will be discussed separately.
In the beginning the top of the flux pellet and the bottom of the feed rod are not in contact. The temperature ramp commences and they start to melt independently. By lowering the upper shaft, the feed rod is brought down and connected to the flux. Uniform temperature in the horizontal plane is of high relevance at this point.
To achieve contact with the seed rod, the flux is elevated once it has “bonded” with the feed rod. The upper shaft is pulled and the solvent zone is separated. The same procedure of melting is performed but this time for the top of the seed rod and the bottom of the flux. After reaching stability, they are brought into contact and the molten zone can further be adjusted to grow a crystal. From this point on, the rods might be rotated, first in the same direction and after the solvent is stable, in opposite direction.
In Figure 3.6 the stages of initial growth are clarified.
Figure 3.6: Beginning of growing procedure. Melting and joining the feed rod, flux pellet and seed rod. As soon as
the floating zone can be preserved, the growing zone must be carefully treated. Static stability, shape of the floating
zone and interfaces, and growth angle are the parameters which define the success of the crystal growth [47].
24
3.3.1 Preparation of the source materials for crystal growth.
The preparation of the polycrystalline feed rods is a delicate procedure which requires special attention. The characteristics of the feed rod play an influential role on the stability and formation of the molten zone, and to maintain such stability for the duration of the growth process.
A high quality feed rod must be straight and uniform in diameter and density, and it must have homogeneous compact composition. If the density of the rod were not adequate, too much liquid flux would penetrate the feed rod and the interface would be uncertain.
The feed rods are prepared from powders of Nd and Ce oxides and CuO with purity of 99.99%. They are mixed according to the desired stoichiometric composition of the 214 compound. The correct phase is obtained in a solid state pre-reaction which enhances homogeneity. It’s a five step calcination process, between each step the powders are homogenized by grinding. The temperatures used are 900°C, 920°C, 950°C and 980°C twice, each event with duration of 10 hours in air.
After the pre-reaction the powders are ready to be packed in a rubber tube which has the required diameter and length. This is firstly done by hand, which requires extra care from the experimentalist11. For a better compact state, the rod is pressed in a hydrostatic press at 2,000 kg/cm2. Then it’s prepared for the next stage, sintering.
The purpose of the sintering is to eliminate any remaining porosity from the powders. This is done at temperatures near the melting point. If any porosity is found in the feed rod, there is high probability of bubble formation in the melt zone or penetration of the melt into the feed rod. Bubbles in the rod can join together and then collapse, which puts the stability of the molten zone in high danger. another side effect can occur when the bubbles stay in place and form defects in the crystal [43].
The sintering process is performed in a rotational lifter12 in O2 at temperatures of 1050°C, 1100°CC and 1200°C for 5 hours each. The bar is rotated inside the alumina tube to obtain the straight and uniform density rod. It is also lifted up and down continuously for temperature regularity.
Finally the flux material is also prepared from a combination of powders, further pre-reacted and annealed at 1010°C for 10 hours in air. The correct calculation of the composition is vital to grow a single and uniform crystal. Size and volume are also important matters which plays a role in the stability of the molten zone and the interface.
To conclude this small survey of the Traveling Solvent Floating Zone, a picture of the actual growth of a 214 phase material is shown in Figure 3.7.
11
Refer to Appendix 2 Figure B3 for a describing picture of the packing procedure. 12
An outline of the rotational lifter is available in the Appendix 2 Figure B4.
25
Figure 3.7: Picture taken from an actual growth process of Nd1.85Ce0.15CuO4. a) Picture taken at the initial stage of
the process, as the feed rod, flux pellet and seed rod are brought into contact by careful melting. b) Picture taken
after 7 days of successful growth. The feed rod has 6 mm diameter and the floating zone has 4.5 mm diameter. c)
The final crystal after demounting from the furnace [25].
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Chapter 4: Post-growth treatment of the crystals
4.1 The annealing treatment of the grown crystals. So far it has been assumed that the synthesis of a superconducting electron doped cuprate is limited to the crystal growth. However, a detail which was briefly mentioned before is now the most important parameter to make the 214 compounds superconducting.
An electron-doped crystal in its as-grown state is not superconducting13; even at optimal doping. They are antiferromagnetic insulators with a Néel temperature, TN, between 125-160 K. The superconducting transition appears only after an appropriate temperature treatment has been performed on them.
As it was reviewed in previous chapters, it is known that the T’ crystal structure of the electron-doped cuprates has empty sites at the apical oxygen position. On the other hand, instrumental analysis on as grown crystals by EXAFS14 and other techniques proved that a fraction of these sites are randomly occupied by oxygen; resulting in a surplus composition in the chemical formula Nd2-xCexCuO4+δ, where δ is the excess in the oxygen content. This feature is quite particular of the electron-doped cuprates, it implies that not only is the superconductivity of the compound dependent on the rare earth doping, but also on the presence of oxygen as a co-dopant [21, 25]. To eliminate this interference, a post-treatment of the as-grown crystals is imperative: a reduction process at high temperatures, 850-1080°C, in an inert atmosphere for several hours or even days. This strategy successfully removes a small fraction of the surplus oxygen atoms. It has been calculated that the amount of removed oxygen is no greater than 0.1% and 2%, still the role of this minimal has radical consequences [10]. It is very interesting that such a small amount of oxygen difference in the annealed samples can have such a severe impact on its physical properties. Not only is this step mandatory to actually produce a superconducting transition, it also defines the starting point of Tc, and the width of the transition [48, 49].
However, the microscopic mechanism of oxygen reduction and its effect on the asymmetry of the cuprates phase diagram and superconductivity is still unanswered and the real oxygen content is difficult to estimate because the observed data is very close to the detection limit.. From single crystal neutron diffraction it was concluded that the O(3) occupancy is about 0.1 in as- grown undoped samples and that this content can be lowered up to 0.04 with the annealing treatment. No change in the in-plane oxygen position was found [10]. The surplus in oxygen is negatively correlated with the Ce concentration[48]. A graphic representation of this relation is depicted in Figure 4.1.
13
NCCO crystals grown in a low oxygen atmosphere (pO2=0.03 bar) show superconducting transition at Tc=10 K even if they are not annealed. But the growing procedure at this low pressure complicates the control of the system, so the standard synthesis method requires high oxygen content during growth, resulting in a δ surplus. 14
EXAFS: Extended X-ray absorption fine structure spectroscopy.
27
Figure 4.1: Representation of the relation Tc vs. doping for electron doped cuprate. Optimal doping is found at the dashed lines. Arrows indicate the increase of Ce content and corresponding decrease of oxygen as a function of charge carrier presence. Image modified from [48].
4.2 The role of oxygen in the electron-doped superconducting cuprates. The earliest ideas which tried to explain the role of the reduction step assumed that the as grown samples were completely stoichiometric [11]. If this were true, it would mean that the temperature treatment reduces the total oxygen content to less than 4 in the chemical formula Nd2-xCexCuO4, and thus creates mobile electrons in the CuO2 layers. Under the view of a basic electron doping model, the removal of one oxygen is equivalent to the addition of two electrons. If the appropriate density of charge carriers is achieved, the sample may become superconducting at low temperature. This explanation was easily accepted considering that for some hole-doped compounds, the oxygen content would also be adjusted for this reason. But the real change in oxygen concentration due to the reduction is actually really small, and so is the additional electron carriers gained in the process. The Ce doping provides a larger amount of carriers, so it seems as though this step should not be necessary for a superconductivity transition [50]. Thermogravimetric analysis (TGA) proved that the reduction process removes oxygen from the compounds and evidence from neutron scattering also indicated that there is an excess of oxygen content in as-grown samples not only in Ce doped compounds [51]. Currently many theories attempt to grasp the origin and effects of the role of oxygen in the n-doped cuprates. The three most widespread ideas propose that the loss of oxygen content can have the following foundation or consequence [10, 48, 49]:
It should decrease impurity and scattering centers in the apical position in the T’ structure.
It should suppress the long range antiferromagnetic order in the CuO2 places.
It should have an influence on the charge carrier concentration by appearance or disappearance of an epitaxial impurity phase.
The first proposition is maybe the most extensively accepted. This picture has been supported by neutron diffraction and Hall-effect measurements [48, 50, 52]. A small amount of randomly doped apical oxygen localizes the electrons which were introduced by doping and inhibits superconductivity. If the excess of oxygen is then removed, the mobility of electrons is restored and the superconducting state appears [21, 53]. The presence of apical oxygen is considered as a scattering center and a source of Cooper pair breaking. This is directly related to disorder in the structure, which has a dominant role in the physical properties of the cuprates at low temperature. With this argument in mind, Pr2-xCexCuO4 overdoped films were submitted to irradiation to induce disorder and compare the results with oxygenated samples. The
28
results concluded that adding oxygen to overdoped samples changes the carrier concentration, proved by an decrease in Tc, and it causes disorder [48]. The mechanism of impurity scattering was not followed, but it was speculated that the O(3) removal can be related to a decline in disorder. Despite the experimental proof that a loss in oxygen up to ≈0.06 per formula was plausible, recent Raman spectroscopy, infrared-transmission and ultrasound studies have come forward with new information. This concerns the second theory of the role of the reduction procedure. It was found that a certain Raman mode, originally linked to the O(3) position, did not change regardless of the annealing procedure [10, 54]. Surprisingly, they observed departure of the oxygen in the CuO2
plane, for high Ce doping. The effect of the new defect site created by the departure of O(1) is the elimination of the antiferromagnetic order and escalation of the electron mobility. Since the antiferromagnetic state is much more stable in the underdoped regime, this effect is not seen at low Ce concentration and thus, the superconductivity should not appear [49]. So far these two theories seem to consider that both O(1) and O(3) can be removed, and at the same time play different and somehow contradicting roles in the superconducting transition of the n-doped cuprates. However one last factor is not yet mentioned: partial decomposition of Ln2-xCexCuO4 caused by annealing and the appearance of an epitaxial impurity phase, a cubic (Nd,Pr)2O3
15. Proposed by a research group in Stanford University [53] this interpretation of the observed data starts with the assumption of Cu vacancies in the CuO2 in as grown samples. Figure 4.2 shows the T’ structure of Nd2-xCexCuO4 with Cu vacancies and the T’ structure of a reduced sample where the secondary phase is present.
Figure 4.2: (a) Crystal structures of an as-grown Nd2-xCexCuO4+δ with random Cu vacancies. (b) A deoxygenated T’ structure where Cu atoms have migrated so the Nd2O3 secondary phase remains. Modified from [53, 55].
The formation of this secondary phase should follow the chemical equation that reads
( ) ( ( )) (1)
Where Ln is the rare earth element, f is the impurity phase volume fraction, and α and β are the exceeding oxygen content in as-grown and reduced samples, respectively.
15
Typical features of the secondary phase are 60 Å wide perpendicular to the CuO2 planes and 1μm parallel to the same plane. Volume fraction is about 1%.
29
The proposed mechanism for the formation of Ln2O3 phase says that during annealing some Cu atoms migrate to fill the alleged Cu vacancies in the CuO2 planes; this is so to say a “self-fixing” process of the defect sites. In figure 4.2 (a) and (b) there is a comparison of T’ structure with Cu vacancies and a T’ structure which contains a Cu-free plane; a plane which in theory was occupied by Cu before the reduction process. The effect of a lower Cu vacancy density should remove breaking sites and favor superconductivity. It was concluded that the removal of oxygen by heat treatment causes a phase separation of the material into a Cu-perfect T’ phase and a Cu-free secondary phase. A connection between the apparition of this phase and the superconducting behavior of Nd2-xCexCuO4 was made, the secondary phase was attributed as one reason of SC transition [49, 53, 55]. During the performance of this thesis, the annealing process was conceived as a mean to eliminate apical oxygen, i.e. the δ oxygen surplus in the chemical formula Nd2-xCexCuO4+δ. The appearance of a secondary phase was not dismissed but its role was not directly attributed as a positive contributor for the SC transition.
4.3 Optimization of the annealing process. These three theories attempt to explain the effects of the post-growth treatment. But since no final consensus has been concreted, the details of the effect of the oxygen reduction are still an open question, although change and contribution to the electron concentration is one inevitable consequence. After all two effects can be certain: in terms of the structure it reduces tension in the crystal and disorder in the rare earth sublattice and it gets rid of the exceeding oxygen. For a general view, the chemical reaction which describes the decomposition of the undoped Nd2CuO4 is described as follows
( ) ( ) (2)
Interestingly enough, from past experiments it has been found that the highest Tc in the NCCO compounds is found when the annealing procedure pushes the system to the limit conditions, almost at the point of decomposition. Obviously this makes it rather complicated to find a “recipe” for the proper conditions.
In order to determine accurate and effective annealing conditions, the phase stability diagram must be taken into account. A doping dependent annealing phase diagram can be seen in Figure 4.3. Doped samples decompose to different products as shown in equation (2).
30
Figure 4.3: Stability diagram of (Nd,Pr)2-xCexCuO4. The solid line marks the barrier between a stable cuprate and its decomposition by-products. Modified from [21, 25], where the samples were annealed in a flow of pure Ar 4.8 (O2≤3 ppm) for 20 h.
The final goal of the process is to obtain a superconducting sample with a sharp transition, from which the superconducting volume fraction can be estimated. In other words, the aim is to achieve the maximum superconducting capability of each sample according to its carrier concentration.
The quality of the electron-doped crystal after the treatment, that is to say the effectiveness of the process, depends on several parameters. They are listed below
Ce doping content
Temperature range and cooling rate
Sample size and shape
Time of annealing
Another point to consider is if the reduction step is reversible. It should be mentioned that the impurity phase Ln2O3 appears with reduction and disappears with intended reoxygenation, according to recent studies [49, 53].
The Ce concentration x is relevant in terms of how susceptible is the sample to the formation of a secondary phase within some temperature range, a tendency which is depicted in Figure 4.3 with the stability diagram. The lower the Ce concentration x is, the lower is the limit in temperature that can be applied to a sample without causing a dramatic and possibly irreversible deoxygenation. After this point the applied cooling rate is also very important. Samples should be brought back to room temperature at a slow rate to avoid freezing defects and causing stress in the crystal structure.
Size and shape effects are a highly discussed topic. Many different annealing sequences have been tried out, but not many of these experiments were performed on single crystals but on thin films or polycrystalline samples where the oxygen diffusion mechanism might have a different mechanism [48, 50]. For single crystal samples, it has been reported [52] that bigger samples (650-850 mg) need up to 50 hours annealing time to achieve a superconducting transition compared to small samples (120-200 mg).
The time-temperature relation indicates that for higher temperatures, less time is needed for the same doping range. And a connection between Tc and annealing T indicates that if a sample is reduced at relatively low temperatures, the corresponding Tc will be higher. On the other hand Tc seems to be independent of time [52].
31
All these criteria are considered for the present work. In some cases the results obtained by our experiments were consistent with the literature and could help to develop a better sequence in the annealing process. However, not all the data collected from the literature should be considered as imminently true because these experiments were carried out on optimally and over-doped. So there is no reliable data on under-doped single crystals.
This is one of the main goals of this thesis, to obtain electron-underdoped single crystals by the TSFZ method, to subject the samples to the post-growth annealing treatment to observe if a superconducting transition exists and, in case of appearance of such transition, to try and establish a confident and reproducible route to perform such treatment on future samples.
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Chapter 5: Sample characterization techniques
5.1 Back-reflection X-ray Laue technique Before any annealing process can be performed on the crystals, they need to be brought to a proper size and orientation for the further measurements. The correct orientation is necessary due to the anisotropy character of the electron conduction, which happens mainly in the CuO2 plane. As they have a tetragonal crystal structure, the c-axis must be found and the sample is then cut according to that position. This is important for the magnetic characterization since the c-axis is placed parallel to the magnetic field.
The as-grown crystal is aligned by using the Back-reflection X-ray Laue technique. The basic principle of the technique relies on the use of white radiation16. The fixed single crystal is placed on a goniometer in front of a film (respectively S and H in Figure 5.1). The radiation source (C in figure 5.1) is behind the film. The beam goes through the collimator and by interaction with the sample it is diffracted in the opposite direction and a spot pattern is recorded on the film. By the use of a Greninger chart17, each spot in the pattern can be indexed and thus the orientation of the crystal is obtained [56].
Figure 5.1: Components and basic set up of the Back-reflection variant of the Laue method. The X-ray tube produces
white radiation. The beam is narrowed by the collimator (C). (H) is a photographic holder. (S) is the sample. (B)
Goniometer holder [57].
16
White radiation= radiation with flat spectrum. 17
The Greninger chart is used to convert the positions of the spots on the Laue photograph to a stereographic projection. The chart is superimposed on the photograph and the coordinates are transposed to a Wulff net.
33
Figure 5.2: Basic operation of the Back-reflection Laue technique. The array of spots is placed on the surface of an
imaginary cone. The axis of the cone is the zone axis. The symmetry of the crystal is obtained by the Laue pattern.
Depending on the beam direction, it shows the corresponding symmetry operation, e.g. three-fold symmetry for a
cubic crystal along [ ] Image modified from [40].
The position and intensity of the spots depend on the set of different planes which compose the crystal. One plane zone responds to a suitable wavelength λ because all the lattice planes are parallel to a common direction. This particular λ is sorted out from the full spectrum beam and the reflection fulfills the Bragg law.
The use of this technique also provides certainty of the high quality of the crystal. In the presence of multiple grains the Laue pattern shows doubled, deformed or split spots, respectively, instead of a sharp array of spots.
After the growth of the crystal in the mirror furnace, the crystal rod is cut into smaller cylinders. One small rod is used to determine the crystal orientation. Several surface zones and faces are examined because the real area of the crystal is much larger than the actual capacity of the beam. The determining parameter to find is the orientation of the c-axis. This assures the delimitation of a high quality single crystal within the small rod. The crystals are afterwards cut in a High-Precision wire-saw18. Different shape can be achieved and precision up to 0.1 mm is possible. A full detail of size and shape of the samples used in this study is given in Chapter 6 Table 6.1.
An example of a Laue picture taken from an as grown sample of Nd1.855Ce0.145CuO4 (NCCO 14.5%) is shown in Figure 5.3. It is possible to see that the Laue pattern is not completely straight. That means that the four-fold rotation is somehow rotated to the right. In the case of the present study, this misalignment can be disregarded, since the direction of a-b plane is not a major concern.
18
Access to the precision wire-saw and polishing machine is available at the Physic Department in the Crystal laboratory at the Technical University of Munich.
34
Figure 5.3: Laue picture of an NCCO crystal. The c-axis is perpendicular to the upper surface of the sample. The
picture was taken with a 10 s collecting time and accelerating voltage of 8kV and current of 25 mA.
Pictures of real samples used for this study can be seen in Appendix 3 figures C3-C5. Pictures of the Pb
reference samples are also shown.
5.2 Magnetic properties measurements. Superconducting Quantum
Interference Device (SQUID)
5.2.1 General setup
The superconducting quantum interference device (SQUID)19 used in an extremely sensitive magnetometer, is a loop of superconductor containing two Josephson junctions20. It is used to determine the magnetic properties of a material. It is very sensitive for AC and DC magnetic measurements and it can resolve flux increments of approximately 10-10 G or tiny voltages down to 10-15 V [58, 59].
The magnetometer21 consists of a SQUID sensor connected to a superconducting coil, i.e. the flux transformer and its main goal is to measure a small magnetic flux in the sample. The magnetic field is transmitted to the SQUID by the flux transformer; the latter is a superconducting circuit containing two coils in series, the input coil and detection or pickup coils. The flux generated in the sample placed in the detection coils couples by means of the pickup coil with the SQUID sensor and, it is thus detected.
19
There are two types of SQUIDs: rf and dc. The difference relies on how the current is biased and on the number of junctions it uses. rf SQUID uses one junction and dc SQUID uses two junctions. 20
Josephson junction is a device which consists of two weakly coupled superconductors. DC or AC current crosses the weak link in the absence of applied voltage. If the two junctions are identical the current divides in two equal parts and it passes through each junction and finally recombines at the other side. The junctions are marked with an X in Figure 5.4. 21
A schematic of the system setup is shown in figure B5 in Appendix 2.
35
Figure 5.4: Simple schematic of the SQUID input circuit. ΔB is the change in applied field; ΔI is the change in current
in the superconducting circuit. Modified from [60].
In order to obtain such sensitive measurements from the setup, it must be cooled down to very low
temperatures. This is only achieved by immersion in liquid He at 4.2 K.
Various magnetic properties can be tested with this system. The magnetic measurements performed for
this thesis were AC and DC magnetometry, i.e. AC and DC susceptibility measurements.
5.2.2 Measurements: AC and DC susceptibility
AC susceptibility
In AC susceptibility measurements, an oscillating magnetic field is applied to a sample in order to measure its resulting AC magnetic moment “m”. The AC field is superimposed on the DC field and the sample is centered within a coil while exposed to this external field, thus making the moment time-dependent. The time dependent field induces a current in the pickup coils.
If the AC field is small, the AC magnetization signal can be expressed as [61]
( ⁄ ) ( )
Where HAC is the amplitude of the driving field, ω is the driving frequency and χ=dM/dH is the slope of the magnetization curve, called magnetic susceptibility. The latter is a quantity which describes how magnetic a material is and its corresponding response to an applied magnetic field H.
As the frequency increases the magnetization signal starts to lag behind the driving field, thus it presents a phase shift ϕ. This is the imaginary or out-of-phase component. Often the AC susceptibility is referred to as complex susceptibility as it presents both real and imaginary parts χ’ and χ” respectively. Both quantities are very sensitive to thermodynamic phase changes so they are used to test transition temperatures in superconducting materials, which is the case of this work. It should be remarked that the sensitivity is limited to the slope in M(H) and not to the absolute value. Above the transition temperature, a superconducting material presents a zero or close to zero susceptibility. In the superconducting state, the sample should become perfectly diamagnetic, thus completely expelling the magnetic flux from the inside. In the presence of a magnetic field, the superconducting material develops shielding currents which expel the field and in a perfect superconductor it shows χ’=-1. The χ” corresponds to dissipative processes in the sample[58, 62].
36
For the study of superconductors, and for comparison of different materials, a typical measurement is χ’ vs. T, which can yield the onset temperature Tc, onset, which is the point where the magnetic susceptibility starts decreasing drastically due to SC transition. The transition temperature Tc can be defined as the midpoint of the transition width or the full drop of the susceptibility signal.
The imaginary component χ” peaks at the SC transition, in the interval where fluctuations of magnetic flux, vortex motion, are significant. It can deliver information on structural details of the material, such as intragranular and intergranular responses, satellite peaks to the main transition are sometimes referred to as intergranular or intragranular loss peaks [60, 63].
For this study the AC susceptibility was used to determine whether a sample presented superconductivity and for the estimation of a transition temperature Tc from χ’. Structural stability upon annealing was traced by close examination of the χ”. If more than one peak could be observed it was taken as indication of sample inhomogeneity, which during the course of this thesis it has been referred as decomposition.
DC susceptibility
DC magnetometry determines the absolute value of the magnetization of a sample. A constant magnetic field is applied and the magnetic moment of the sample is measured and depicted in a magnetization curve. There are different techniques to measure the DC susceptibility: by force, torque or induction.
For the latter, the sample is moved in a series of steps relative to a set of superconducting pickup coils wound in a gradiometer configuration22, from the lowest point of the scan length in upward direction. Every step delivers a voltage data coming from the moving magnetic moment of the sample. When the sample reaches the end of the scanning range distance, it is returned to the starting point and reset to near zero volts [58]. The final result is depicted in a longitudinal moment (emu23) vs. temperature curve.
For a further comprehension of the actual measurement mechanics, Figure 5.5 shows the experimental setup for AC and DC susceptibility measurements. However, this setup can be used for other types of analysis as well.
22
The gradiometer configuration means that the coils are wound in opposite directions. 23
Emu here: a magnetic moment unit in the CGS system.
37
Figure 5.5: Typical experimental setup for susceptibility measurement. a) AC susceptibility setup. b) Close-up view of
the coils. c) Oscillation setup for DC magnetization measurements. From [60].
DC magnetization measurements were performed during this work with the aim of obtaining an estimation of the superconducting volume fraction of the samples. The DC susceptibility of a lead sample was measured and used as a reference, i.e. the maximal superconducting contribution which can be obtained for a specific volume in a perfect superconductor. The magnitude of the signal from the sample was compared to the one of the reference and thus the percentage of the superconducting volume fraction was estimated.
The Nd2-xCexCuO4 crystals were annealed at different time durations and temperatures and the evolution in the superconducting volume fraction was followed. Due to difference in sample shape and size, a reference sample was made for each crystal of the Nd2-xCexCuO4 crystals of interest to match the dimensions and volume.
There are two distinct ways to measure the magnetization in both AC and DC measurements. In the beginning the sample is cooled down from high temperature, this process can be performed in the presence or absence of magnetic field, field-cooled (FC) and zero field-cooled (ZFC) respectively. The measurements for this thesis were done with a ZFC sequence.
To understand the main differences of these experiments the reader can consider a thick-wall hollow cylinder of perfectly diamagnetic material with a hole that is either open or closed to the outside [23]. During a FC experiment a sample is cooled down below its transition temperature in the presence of a magnetic field and the magnetization is measured. The observed effect, also known as the Meissner effect, is characterized by flux expulsion from the cavity but not from the hole. For the ZFC condition, the sample is cooled down to low temperature in the absence of an external magnetic field. Once the sample is at 2 K, a magnetic field is applied and the magnetization is measured as temperature increases. In this case, the flux is excluded from the open hole; the circulating currents shield the superconductor, and the hole. This phenomenon is called diamagnetic shielding.
In both types of experiments the superconducting fraction achieves to expel the magnetic flux, but in the case of ZFC it excludes more than in the FC one. The difference is the trapped flux, since for the FC the magnetic field is trapped in the open hole while surface currents shield the superconductor at the closed cavity [23].
38
If a sample is composed of a mixture of superconducting a non-superconducting material then the FC magnetization signal is less negative than the ZFC signal. The FC signal can yield the Meissner fraction, which is the ratio of FC to an ideal diamagnetic ZFC magnetization signal [64]. When a material has no pinning sites and H < Hc1 then the magnetic susceptibility χ= -1, FC=ZFC. The more defects a material has, the smaller is its Meissner fraction, since the vortexes are pinned at the defects.
In terms of the estimation of the superconducting volume fraction, the ZFC measurement provides a signal which shows the maximum possible superconducting regions of the sample, while the FC measurement shows the minimum contributors.
For the purposes of this thesis, the ZFC measurements provide enough information to estimate the SC volume fraction of the samples. If further studies need to be done on this subject, they should be completed with the information from FC experiments.
39
Chapter 6: Results
6.1 The Nd2-xCexCuO4+δ (NCCO) single crystals and the annealing
sequences. One of the aims of this work was to optimize of the annealing process of the NCCO crystals, in order to obtain the best transition from the AF state to the superconducting state. The second main goal was to estimate the superconducting volume fraction of the samples. A specific feature of the study is the doping of the samples; which covered the underdoped regime up to the optimal doping. The doping percentage of different NCCO samples ranged from 10, 12, 13, 14.5 and 15%.
As crystallographic orientation it was chosen the c-direction perpendicular to the upper surface of every crystal.
Different annealing sequences were performed depending on the doping percentage of the samples24.
Table 6.1 presents a summary of the samples of interest. It describes their physical dimensions, masses and their corresponding annealing sequences. The annealing time in table 6.1 is the overall time; if a detailed explanation on the annealing profile is required, it will be given in the following sections. The weights presented in table 6.1 are the ones of the as-grown cut-out crystals.
It should be remarked that the samples listed below are those whose progress was successfully followed. No standard size or shape was defined; hence, for the calculation of the superconducting volume fraction, a set of identical reference samples25 was made by hand from lead.
For the actual annealing treatment the as grown crystals were placed in a polycrystalline crucible made out of the same material. See figure C1 in the Appendix 3. This was done in order to avoid contamination from the sample container and to protect the crystal surface. The annealing program was performed as follows:
Heating rate 300C°/h up to desired temperature.
Dwell time 20 hours26.
Cooling rate 100°C/h.
The atmosphere in the furnace was a flow of pure Ar 4.8 (O2< 3 ppm). A cooling rate of 100°C/h was chosen to allow the crystal metallic sublattice to relax and to avoid freezing of strain and disorder created at high temperature.
For reversibility experiments, i.e. to try and restore the as grown state, the sample was annealed in O2 flow at 900°C and then further annealing cycles in Ar were performed without intermediate cooling to room temperature. These samples a re-labeled as “reox”.
24
See Figure 4.3 in Chapter 4, stability curve of electron doped cuprates. 25
It was not possible to achieve a perfect similarity for all samples, therefore an error range should be considered. If the crystal had a highly irregular shape, no reference was made. 26
The annealing processes were performed in cycles of 20 hours unless specified differently.
40
Table 6.1: Overview of NCCO crystals and overall annealing profile.
Sample Size /mm3 Mass /mg Volume /cm3 Annealing profile
NCCO 10%
N10A 2x2x0.6 15.38 2.4 x10-3 900°C, 40 h
N10B 2.3x2.3x1.1 40.53 5.8 x10-3 900°C, 40 h
NCCO 12%
N1227 1.9x3.0x1.0 20.9 8.9 x10-3 910°C, 60 h
N12reox 910°C, 80 h
N12A 1.5x3.2x1.1 27.6 5.2 x10-3 910°C, 60 h
N12B 1.4x3.45x1.1 30.0 5.3 x10-3 910°C, 100 h
NCCO 13%
N13 1.0x3.0x1.0 22.4 5.2 x10-3 860-950°C, 20 h
N13reox 935°C, 120 h
N13A 2.0x2.9x0.7 26.1 4.1 x10-3 935°C, 100 h
N13B 2.2x2.7x0.7 25.8 4.2 x10-3 935°C, 60 h
NCCO 14,5%
N14.5A 2.2x2.4x0.3 8.7 1.6 x10-3 935°C, 80 h
N14.5C128 1.5x3.0x0.5 14.5 2.3 x10-3 935°C, 100 h
N14.5C2 3.0x3.3x0.5 31.8 4.9 x10-3 935°C, 100 h
N14.5C3 3.0x3.0x1.0 57.3 9.0x10-3 935°C, 80 h
NCCO 15%
N15A29 2.0x2.45x0.4 13.5 2.0 x10-3 935°C, 60 h
N15B30 B=4.3x4.2x2.8 H=0.8
38.2 7.5 x10-3 935°C, 60 h
N15C 4.0x4.1x1.0 96.1 16.4 x10-3 950°C, 20 h
The evolution of oxygen loss was documented by weighting the samples before and after each annealing program. Hence it was possible to calculate the δ oxygen content31 and the approximate percentage of oxygen loss caused by the post growth treatment. Table 6.2 shows the δ oxygen per formula for individual annealing events. Where δ1 corresponds to the first anneal cycle, δ2 to the second cycle and so on; if applicable. The final δtotal corresponds to the addition of all intermediate δ values, it can be viewed as the oxygen surplus content that the NCCO crystal had in its as-grown state. For some samples the mass difference was not measured until several annealing processes had been performed.
To calculate δ it was assumed that the difference in mass ΔW would correspond only to oxygen loss. The amount of oxygen moles would be normalized to the moles of the annealed sample.
27
The actual shape was a half ellipsoidal cylinder; a picture can be seen in figure C4 in Appendix 3. 28
The samples N14.5C1-C3 were cut from a big crystal which received 60 hours of annealing. Further annealing was performed separately. 29
N15A was cut from a big crystal which had received 20 hours of annealing. 30
Shaped as a trapezoidal figure where B is the base and H is the maximal thickness. 31
The δ is the excess of oxygen content per chemical formula in Nd2-xCexCuO4+δ.
41
⁄
ΔWba is the mass difference of the sample before and after annealing. OMw is the molar mass of oxygen
(16 g/mol) and Molesa are the mass of the sample after annealing in moles.
Table 6.2: Summary of δ evolution throughout annealing treatment
Difference in mass was only measured after annealing in O2. The mass of the as grown sample is taken as W1. 33
Difference in mass was measured after 80 hours of annealing.
42
6.2 The AC susceptibility of the crystals and first observation of
superconducting transition. AC susceptibility was taken as a preliminary check-up point to continue with the annealing process of the
samples. AC susceptibility reveals information about SC shielding currents in the sample but it fails to
describe the actual superconducting volume fraction.
However, once a clear transition temperature was observed in AC susceptibility, it was possible to
determine the subsequent conditions for the reduction treatment. Due to demagnetization effects the
curves for AC susceptibility, χ’ vs. T, will be displayed in a normalized form to their respective low
temperature values. The χ” vs. T curves are normalized to the highest registered peak. The DC volume
susceptibility curves are not normalized to low temperature to allow the visual evolution of the SC
volume fraction by increase or decrease in the signal magnitude. Measurements were done in an
external field H= 100 Oe applied parallel to the c-axis.
The first sample of NCCO 13% (N13) was taken as a reference to establish the maximum annealing
temperature for the 10, 12, 14.5 and 15% samples. N13 was annealed different runs of 20 hours at
temperatures ranging from 860°C to 950°C. The temperature where it showed the best SC phase
transition was taken as the ideal annealing condition. In order to take a transition signal as optimal, the
AC first susceptibility (χ’) should present a sharp transition. The imaginary part of the AC susceptibility
(χ”) was used to determine if a sample would be past the stability state. The presence of a satellite peak
was taken as evidence of NCCO decomposition and formation of a secondary phase.
The NCCO samples with less than 13% Ce content would be annealed at lower temperature to avoid
rapid decomposition. In the case of 14.5% and 15% Ce content, the temperature range was the same as
for NCCO 13% in order to obtain a better understanding of the evolution and gradual increase of the
Tc,ac,dc and SC volume fraction in the regime close to optimal doping.
0 5 10 15 20 25 30 35 40 45
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
' a
c/
' ac (
3K
)
Temperature (K)
N13-900°C
N13-920°C
N13-925°C
N13-930°C
N13-935°C
N13-940°C
N13-945°C
N13-950°C
Nd1.87Ce0.13CuO4+
(a)
0 5 10 15 20 25 30 35
0.0
0.2
0.4
0.6
0.8
1.0
Nd1.87Ce0.13CuO4+
" a
cnorm
aliz
ed
Temperature (K)
N13-900°C
N13-920°C
N13-925°C
N13-930°C
N13-935°C
N13-940°C
N13-945°C
(b)
Figure 6.1: Normalized χ’ac (a) and χ’’ac (b) transition curves of N13 single crystal annealed at different temperatures.
43
The transition curves corresponding to the annealing of N13 are plotted in Figure 6.1. No transition was
detected by AC magnetization for annealing temperatures below 920°C.
In Figure 6.1 (a) the χ’ac susceptibility is plotted. A close observation reveals that, for 920° and 925°C, the
superconducting phase transition first appears approximately at 12 K and 16 K respectively, and it
saturates at 3 K. The main difference between these two curves is the 4 K step in the onset temperature
Tc,onset. Both curves are broad and present a tendency to higher values in the magnetization at low
temperature. For the χ”ac susceptibility, neither of these two processes results a saturated
magnetization. This feature was an indicator that further annealing would yield a higher Tc,ac. The
expected progress is observed in the curves at 930°C and 935°C in the Figure 6.1 (a). The onset
temperature Tc,onset starts between 17 K and 18 K and the saturation is at higher temperature, around 5
K. The χ’’ac curve for 930°C is very broad and asymmetric but once the annealing temperature is raised
935°C, this feature is narrowed and Tc,ac also increases.
The curves for 940°C and 945°C reflect the highest values of Tc,ac. The onset temperature lies between 19
K and 20 K. The Tc,ac was taken from the midpoint of the χ’ac curve, at a 50% drop, is Tc,ac≈ 16 K. No major
variation existed between the results of these two annealing processes, which was taken as a sign of
structure stability. Nevertheless, the sample was annealed again at 950°C to probe stability. The χ’’ac
result of this extra reduction reveals a very clear secondary peak at 8.5 K. This peculiarity, along with the
decrease in onset temperature in the χ’ac signal, was understood as a signal of sample decomposition.
Table 6.2.1: N13 onset and transition temperature for progressive annealing.
Annealing temperature Tc,onset 34 /K Tc,ac /K
920°C 12 7
925°C 16.6 9.5
930°C 17.8 11.5
935°C 17.8 13.5
940°C 19.6 16
945°C 20.2 16
950°C 18.4 13.5
Table 6.2.1: Summary of the Tc,onset and Tc,ac for the N13 annealing process. The main goal of these
successive processes was to find an optimal annealing temperature for the samples with 13% doping.
Considering 13% as the middle point in the studied doping range, this temperature was chosen as
reference to which the rest of the samples would be annealed.
The highest Tc,ac values were obtained at annealing temperature of 940°C and 945°C. Further annealing
proved to be sample destructive despite the fact that the stability curve from [21] states that, for 13%
34
Onset temperature Tconset and transition temperature Tc,ac,dc values determined by tangent method. The transition width ΔTc,ac,dc which will be introduced later on this work was also derived from this method. An illustration of the definition can be seen in Appendix 3 Figure C2.
44
doping, the sample should remain stable slightly above this temperature. Considering this result, 940°C
could have been chosen as the reference temperature for the heat treatment but 935°C was chosen
instead. It was taken into consideration that the features yielded at 940°C were not the result of one
single annealing event, but rather a summary result of all subsequent thermal treatments; whose effects
could have accumulated to give such a sharp and high transition. Additionally, a close examination of the
χ’’ac at 940°C reveals a very slight asymmetry in the curve between 9 and 12 K. So, even though the
curves demonstrate a level of stability, it was decided that in order to observe a clear evolution of the
superconducting volume fraction, they should not be annealed near to the limit of stability but rather in
a slow and constant process. For these reasons the samples with 13%, 14.5% and 15% Ce doping were
annealed in cycles of 20 hours at 935°C. The samples with 10% and 12% Ce doping were annealed at
900°C and 910°C, respectively, to avoid rapid decomposition and to allow a development of the
superconducting phase transition.
6.3 The electron-underdoped cuprate samples
6.3.1 Nd1.9Ce0.10CuO4+δ (NCCO 10)
Two samples of NCCO 10 were studied. Physical dimensions and the annealing sequence are described in
Table 6.1.
AC susceptibility measurements yielded the result, plotted in Figure 6.3.1 (a) and (b).
0 5 10 15 20 25 30 35
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
' a
c/
' ac (
2K
)
Temperature (K)
N10A 40 h
N10B 20h
N10B 40 h
Nd1.90
Ce0.10
CuO4+
(a)
0 5 10 15 20 25 30 35
0.0
0.2
0.4
0.6
0.8
1.0
'' a
c n
orm
aliz
ed
Temperature (K)
N10A 40 h
N10B 20h
N10B 40 h
Nd1.90Ce0.10CuO4+
(b)
Figure 6.3.1: Normalized χ’ac (a) and χ’’ac (b) transition curves of N10A and N10B. The annealing temperature was
900°C. N10A magnetization curve was measured only after 40 hours of annealing treatment.
From the 6.3.1 (a) it is observed that for N10B the Tc,onset suffers a decrease from ≈16 K to ≈13 K when
the sample is annealed another set of 20 hours. This Tc,onset is reproduced by N10A. However, the signal
also becomes less broad and the superconducting transition is more definite. The χ’’ac curve confirms
that the decrease in Tc,onset is accompanied by a refinement in transition, although the transition is not
complete at the lowest temperature.
45
The observation of the AC transition is the first evidence that the reduction of NCCO 10 in Ar yields
superconductivity, even with such a low level of doping. But a more reliable result can only be obtained
from DC volume susceptibility χdc35 which can be seen in figure 6.3.2.
0 5 10 15 20 25 30 35-0.15
0.00
0.15
0.30
0.45
0.60
Temperature (K)
Nd1.90
Ce0.10
CuO4+
d
cx1
0-3
N10A 40h
N10B 20h
N10B 40h
Figure 6.3.2: Volume susceptibility χdc of N10A (40 hours) and N10B (20 and 40 hours).
Two main features are important in these curves. N10B 20h presents a minima point at 4 K which shifts
to 5 K and decreases in magnitude with the second annealing process. However, the magnitudes of these
features are very small to guarantee the evidence of superconducting transition.
The second important feature concerns N10A. The susceptibility curve seems to show a SC transition
with a magnitude order of 10-4. The Tc,onset ≈10 K and Tc≈5 K36. The low temperature increase and high
temperature background may be considered as contribution from the still present paramagnetic main
parts of the sample.
An interesting remark is that both samples were annealed together and N10A has a bigger SC volume
fraction. The difference in physical characteristics may be of importance for the process of oxygen
elimination. N10A has smaller volume and surface area, and the length in the direction of the c-axis in
the crystal is also shorter than in N10B.
It should also be mentioned that to the best of our knowledge there have been no reports on
superconducting behavior for NCCO with 10% doping, and that this concentration of Ce corresponds to
the AF regime in the phase diagram of electron doped cuprates. The observance of SC transition might
hint to possible coexistence of the SC and AF states due to ordering of the phases or due to sample
inhomogeneity.
35
The volume susceptibility χdc=M/H = emu/ (Oe*cm3) = [dimensionless].
36 The transition temperature was estimated only from the negative values of the transition curve.
46
6.3.2 Nd1.88Ce0.12CuO4+δ (NCCO 12)
Four relevant samples of NCCO 12 were studied. Their characteristics are found in Table 6.1. The
behavior of their corresponding AC and DC magnetization measurements will be treated separately.
N12, eventually named N12reox, was the first sample to be analyzed. The first approach was to try and
find the annealing conditions to yield superconductivity. The original sample had an uneven shape and
after the first series of annealing, it was cut into the shape described in table 6.1. N12 was studied by AC
and DC susceptibility measurements after 20, 40 and 60 h of annealing, respectively. The result of χ’ac
and χ’ac are given in Figure 6.3.3.
0 5 10 15 20 25 30 35
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
' a
c/
' ac (
3 K
)
Temperature (K)
N12 20 h
N12 40 h
N12 60 h
Nd1.88
Ce0.12
CuO4+
(a)
0 5 10 15 20 25 30 35
0.0
0.2
0.4
0.6
0.8
1.0
'' a
c n
orm
aliz
ed
Temperature (K)
N12 20 h
N12 40 h
N12 60 h
Nd1.88Ce0.12CuO4+(b)
Figure 6.3.3: Normalized χ’ac (a) and χ’’ac (b) transition curves of N12 annealed at 910°C for 20, 40 and 60 hours.
The normalized AC magnetization curves show that, for N12 20h and N12 40h, Tc,onset has a dramatic shift
from ≈16 K to ≈22 K, respectively. The Tc,ac increases from 10 K to 20 K. This feature is then lost, when the
sample receives another cycle of annealing. The Tc,onset drops to ≈16.5 K and the Tc,ac presents a decrease
to 10 K. This behavior can be supported by observation of the χ’’ac curves in figure 6.3.3 (b). Although the
sample presents a high transition response for 40 h, it also exhibits a peak around 11 K which is either a
sign of formation of a secondary phase or the effect of the irregular shape of the sample. The low
temperature behaviour of the transition in χ’ac for N12 40 h is also slightly eerie. The final response at 60
h was expected to yield definite evidence of decomposition. It was verified with the χ’’ac N12 60h and
with comparison to the DC measurements. They are depicted in the following figure.
47
0 5 10 15 20 25 30 35
-0.020
-0.015
-0.010
-0.005
0.000
Nd1.88
Ce0.12
CuO4+
dc/g
-1 O
e-1
Temperature (K)
N12 20h
N12 40h
N12 60h
Figure 6.3.4: DC magnetization curve of N12 annealed at 20, 40 and 60 hours at 910°C . Only for this sample the DC
susceptibility is shown as the mass magnetic susceptibility χdc in the Y axis shows.
It can be seen from figure 6.3.4 that there is a drastic activation of the superconducting behavior when
the sample is annealed for 40 hours. For 20 and 40 hours, the magnitude of the signal has a difference of
2.1x10-2 g-1Oe-1. Since DC susceptibility reflects the real contribution of the superconducting fraction
from a sample, this was taken as a proof that the oxygen elimination was enough to surpass the AF state,
thus yielding superconductivity. Tc,onset for 20 h and 40 h is 11.5 K and 19 K, respectively, and Tc,dc is 7 K
and 15 K. This high-temperature superconducting state fades out for 60 h annealing, with a Tc,onset=10 K
and Tc,dc= 8 K. The whole magnitude of this transition also decreases to -3x10-4 g-1Oe-1.
With this first set of results it was decided to test if, once a sample of underdoped NCCO presented clear
evidence of decomposition, it could be restored to its original state by annealing in O2 flow. Should this
attempt be effective, it should be tried to understand the evolution of the superconducting volume
fraction. Additionally, the sample was cut into a smaller and regular shape and measured in this
presumably decomposed state. As a smaller sample it was possible to calculate its physical volume and
eliminate as much influence as possible from the demagnetization factor caused by measuring in an
uneven position. For this reason, the obtained values of Tc,onset and Tc,ac,dc are not taken as definite for
N12, but rather as an indicative of a high temperature superconducting behavior in the underdoped
regime, and as reference for the subsequent NCCO 12 samples.
N12reox, after a treatment in O2, was annealed for 20, 40, 60, 80 hours. The behaviour of its AC and DC
susceptibilities is described in the following Figures 6.3.5 and 6.3.6. The volume susceptibility in DC for
N12 60 is also shown for comparison purpose.
48
0 5 10 15 20 25 30 35
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
' a
c/
' ac
(3K
)
Temperature (K)
N12reox 20h
N12reox 40h
N12reox 60h
N12reox 80h
Nd1.88
Ce0.12
CuO4+
(a)
0 5 10 15 20 25 30 35
0.0
0.2
0.4
0.6
0.8
1.0
Nd1.88
Ce0.12
CuO4+
'' a
c n
orm
aliz
ed
Temperature (K)
N12reox 20h
N12reox 40h
N12reox 60h
N12reox 80h
(b)
Figure 6.3.5: Normalized χ’ac (a) and χ’’ac (b) transition curves of N12reox annealed for 20, 40, 60 and 80 hours at
910°C.
There is a clear evolution of the Tc,onset, Tc,ac and Tc,dc according to annealing times. Tc,onset in the χ’ac (T)
curve is 15 K for 20 hours annealing and it reaches a value of 19 K for 80 hours of annealing. The width
of the transition ΔTc37 also becomes narrower with increasing annealing time, from ΔTc (20h) = 12 K to
ΔTc (80h) = 6 K. Another interesting fact is that up to 80 hours, there is no sign of sample decomposition
in χ’’ac. Between these two extremes, the processes for 40 and 60 hours present similar transitions with
the sole difference in the ΔTc, which seems to slightly refine itself from ΔTc (40h) = 7.5 K to ΔTc (60h) = 6.5
K. However, the AC susceptibility is not completely accurate to describe the SC volume fraction, thus the
DC volume susceptibility shown in Figure 6.3.6 should play a more important role to give account for the
material’s behavior.
5 10 15 20 25 30 35
-0.05
-0.04
-0.03
-0.02
-0.01
0.00
Nd1.88
Ce0.12
CuO4+
d
c
Temperature (K)
N12 60h
N12reox 20h
N12reox 40h
N12reox 60h
N12reox 80h
Figure 6.3.6: Volume susceptibility χdc curve of N12 60h and N12reox annealed for 20, 40, 60 and 80 hours at 910°C.
Increase in the magnitude of the signal is a clear sign of the evolution of the SC volume fraction, which develops
further with longer annealing time.
37
Refer to Appendix 3, Figure C2 to see an example of the calculation of the transition width ΔTc.
49
The most evident feature in figure 6.3.6 is the constant increase of the volume susceptibility with
annealing time. If N12reox 80h is taken as the maximum SC volume which can be achieved for this sample,
then the first annealing process only activated 4.9% of it, while the following treatments seemed to yield
a higher response. This behavior also matches how the ac susceptibility narrows down in transition
width. It also confirms that after 80 hours of annealing the sample does not decompose since the SC
volume does not shrink.
To determine the real SC volume fraction the volume susceptibility is compared with that of a reference
sample of lead, which has the same shape and volume. Table 6.3.1 presents a comparison of both
approaches.
Table 6.3.1. Evolution of SC volume fraction N12reox
N12reox anneal time in hours
% SC volume fraction referred to maximum sample response
% SC volume fraction referred to Pb
20 4.9% 3.6%
40 41.2% 37.7%
60 73.4% 67 .1%
80 100% 91.5 %
This data also seems to have a relation with the calculation of δ in table 6.1.2. Each δ value corresponds
to a particular annealing event and the sample did not cease losing weight with the consecutive heat
treatment, so there was still surplus in oxygen left in between effective annealing processes. However,
the loss in oxygen is not directly proportional to the increase in SC volume fraction or Tc,dc. While δ
decreases with annealing, the SC fraction increases. The first δ is of the order of 10-2, and subsequent
annealing eliminated a surplus of oxygen down to the range of 10-3, confirmed by δ1,2,3. This could mean
that, first of all, the first annealing of an as-grown sample should yield the largest value of δ content per
formula. Secondly, it seems to activate the superconductivity in the crystal, which can only improve up to
some stability point before decomposition. So a large elimination of oxygen per annealing event does
not automatically mean an immediate achievement of maximum SC volume fraction, the events in
between are most likely essential to provide the conditions for a structural arrangement from
inhomogeneous to homogeneous SC regime.
In terms of particular data, Table 6.3.2 resumes the values of Tc,onset, Tc,dc and ΔTc for N12reox.
Table 6.3.2. N12reox onset and transition temperature for progressive annealing in AC and DC susceptibility
The parameters characterizing the quality of the SC state such as Tc,onset, Tc,ac,dc, ΔTc,ac,dc and percentage of
SC volume fraction were studied in Chapter 6. Table 7.1 summarizes the global quantities of interest for
the samples with the desired Ce doping.
Table 7.1: Summary of characteristic values for the NCCO underdoped crystals.
Sample Max Tc,ac
/ K Max Tc,dc
/ K Max SC volume fraction
Max % of Oxygen loss
NCCO 10%
N10A 8 5 nd 0.050
N10B 7.5 nd -- 0.038
NCCO 12%
N12A 12 7 30.4% 0.054
N12B 17 12 85.9% --
N12reox-reann 16 11 91.5% 0.055
NCCO 13%
N13A 12 8 68.4% --
N13B 10.5 6 24.8% --
N13reox-reann 16.5 10 98.1% 0.28
NCCO 14.5%
N14.5A 22 19.5 82.6% 0.023
N14.5C1 21.5 17.5 90.1% 0.040
N14.5C2 21 17.5 100% 0.031
N14.5C3 22 18.5 99.5% 0.034
NCCO 15%
N15A 23 20 100% 1.18
N15B 21 18.5 90.2% 0.08
N15C 22.5 20.5 -- --
Table 6.2 summarizes the study of the δ oxygen surplus. The main conclusion from this table is that with
every subsequent heat treatment, the sample would constantly lose a lower percentage of weight, which
should be related to its oxygen loss. The average value of δtotal was δtotal= 5.04x10-2±0.08. Although the
actual value might not be very informative, it matches the order of magnitude which was expected in
oxygen loss for these samples, which should correspond to the original oxygen surplus of the as-grown
sample. The latter expectation comes from previous work performed at the Institute [25].
The samples of NCCO 10% showed a superconducting transition in AC but the presumably SC volume
fraction was too small to be estimated and most likely very inhomogeneous. So the possible presence of
superconductivity in the very underdoped regime of NCCO remains questionable but cannot be
completely dismissed. The connection between the physical characteristics of the sample and the
67
tentative presence of the SC region starts to formulate the question of which sample parameter can be
the most relevant for successful reduction of the oxygen surplus. From the observations in this thesis,
the samples with smaller volumes and surface areas were the one which presented a possible DC
transition.
The next two groups of samples present very captivating results. First of all, the transition in NCCO 12% is
no longer in question. While previous reports had failed to achieve a superconducting phase, the
samples treated in this study performed against prediction and not only did they yield a maximum SC
volume fraction close to 100%, but they also displayed a Tc,ac,dc much higher than it has been reported in
the literature.
As mentioned before, secondary aims appeared during this thesis. One of them was the debate if once
an underdoped sample had passed its stability state, an annealing process in O2 could regenerate the as
grown state, i.e. whether the oxygen elimination is reversible. Samples with 12% and 13% were annealed
in O2 and then annealed again in Ar. In particular, the observation of the N12reox sample demonstrated
the successful recovery of the superconducting phase. Even with the first re-annealing process, the
sample showed transition in DC magnetization and continuing processes delivered a maximum in SC
volume fraction of 91.5%, as referred to Pb. The shape of the transition curves also gave some
information on how the superconducting regions became more homogeneous during the annealing
sequences, since the ΔTc,ac,dc became narrower and sharper. The reversibility of the elimination of oxygen
agrees with similar experiments performed on optimally and overdoped samples [49]. According to this
explanation, a NCCO structure with randomly present Cu vacancies was considered. The annealing
process towards superconductivity will at some point enhance the formation of a secondary phase
Nd2O3. Hence, the subsequent oxygenation of the electron-doped cuprate should promote the random
rearrangement of the Cu vacancies and thus elimination of the phase separation. During this thesis the
reversibility of the reduction of oxygen surplus was possible but the actual reason was not attributed to
Cu vacancies, and also the presence of a secondary phase was not tested in this study. One should also
consider that the samples used in our studies and samples used in other reports from the literature are
often not comparable. A sample with Cu vacancies can be the result of specific growth conditions, and
such presence of vacancies can result in a sample which is susceptible to “easy” decomposition and
formation of a secondary phase. But such model requires the presence of Cu vacancies to yield the
epitaxial Nd2CuO3 layers. If no vacancies are found we would not expect to observe definite
decomposition of the material. The fact that our results prove that the reduction of the oxygen surplus is
reversible actually contradicts the first statement of a model with Cu vacancies: if a stable secondary
phase is formed, a simple annealing treatment in oxygen atmosphere should not be energetic enough to
promote the renewal of the random distribution of Cu vacancies in the crystal structure.
For N13reox, 60 hours of heat treatment lead to a high SC volume fraction and a homogeneous transition
which seemed to saturate with a minimum ΔTc= 7 K. The transition values of N13reox reproduced the
results of N13, something that allowed affirming that 935°C is a reliable temperature to treat NCCO
underdoped samples. N13reox remained superconducting for the next reduction processes but the
deformation of the χ”ac curve and the shrinkage of the SC volume fraction were unquestionable
indicators of progressive sample decomposition.
68
Additional samples of NCCO 13% behaved in close similarity to N13reox. Although the Tc,ac,dc values show
discrepancy and the SC volume fraction was not as high as expected, it was observed that the optimal
annealing time for NCCO 13% lies in the range of 60-80 hours.
But it can be questioned why there is such a scattering in the final Tc,ac, dc and SC volume fraction values.
The difference ΔTc,ac (N13reox-N13A) = 4.5 K, ΔTc,dc (N13reox-N13A) = 2 K and ΔSCvf (N13reox-N13A) = 30%. If
this outcome has a bigger influence from the surface area or other sample parameters, it is left to be
resolved.
Another remarkable result was encountered between NCCO 12% and NCCO 13% behaviour. If the reader
pays special attention to the maximum Tc,ac,dc and Tc,onset observed for NCCO 12% and compares them
with the results of NCCO 13%, it might be surprising that the values for the former are even higher than
the maximum Tc,ac,dc and Tc,onset of the latter. N12reox and N13reox exhibit a complete transition in AC and
DC susceptibility, and they both yield an average SC volume fraction close to 100%.
This surprising observation puts a serious question mark on the dome of the electron doped cuprates
phase diagram. First of all, and as it has already been mentioned, many reports declare that the bulk
superconductivity does not set in before 13% electron doping [10, 21, 25]. If this should be the case, a
dramatic drop in the transition values from 13% to 12% should have been observed. Secondly, a logical
trend in the Tc would be a permanent decay, plus a broadening of the transition width at lowering
doping below xc,opt.
In fact, our findings could be a first clue of the existence of symmetrical behaviour with the hole-doped
cuprates, where a sudden suppression of the superconductivity has been described at x=1/8 and it has
been explained with the formation of spin-charge stripes [10, 29, 30, 65]. This particular behaviour has
been completely denied in the electron-doped cuprates system [66]. One can also consider the absence
of the suppression of superconductivity of the 1/8 anomaly in electron-doped compounds as a direct
effect of the quality of the samples originating from different sources.
Up to date, the coexistence of the AF order with the SC order in the electron-doped cuprates has been
questioned. From spin correlation experiments, it has been stated that these two orders do not coexist
in the NCCO system and it even defined the concrete termination of the AF phase at a specific value, x=
0.134 [67]. On the other hand, the possibility of the existence of peculiar domains within the phase
diagram of the electron-doped cuprates where anomalous behaviour could be observed is not excluded.
This problematic evidently needs further explorations with the help of many other site sensitive
measurement and techniques such as NMR, spin correlation studies, magnetization experiments and
neutron scattering performed on carefully and well characterized high-quality crystals. As for
susceptibility studies, lower concentrations of Ce doping should be equally tested to complete the data
between 12-13% doping and to try and define the lower boundary for superconductivity
No definite conclusion about the possible existence of a “1/8 anomaly” can be made with these results
but it can be affirmed that NCCO 12% crystals, which were annealed at the optimal conditions of 910°C
for 60-80 hours in Ar atmosphere, proved to have a superconducting transition at high temperature with
an apparent homogenous phase bulk superconductivity.
69
A sketch of the superconducting dome observed from the results of this study is depicted in figure 7.1.
Notice the separation in the values from 13% to 12%, where the trend in the Tc should continue to
decrease, it experiences a rise and continues to drop afterwards.
0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.200
5
10
15
20
25
Tc,a
c / K
Ce content x
Overdoped
regime
(a)Nd
2-xCe
xCuO
4+
0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.200
5
10
15
20
25
Nd2-x
CexCuO
4+
Overdoped
regime
Tc,d
c /K
Ce content x
(b)
Figure 7.1: The superconducting half dome from the electron underdoped samples tested in this study. Fig. 7.1 (a)
and (b) correspond to the fit of the Tc,ac and Tc,dc respectively. The vertical lines show the error bar observed for
different samples. The dashed line represents the centre of the zone where there appears to be a break in the
tendency of the Tc. Observe that this difference is more pronounced in Tc,dc.
The last set of samples involved nearly optimal and optimal doping NCCO 14.5% and NCCO 15%. It was
attempted to see the effect of sample size on the appearance of superconductivity. Since both groups of
samples had a non-questionable transition, the effect should be more easily discernible.
N14.5A* and N15A* were the large versions of the crystals. For both cases it was observed that, in large
samples, longer annealing times are needed until superconductivity appears. This could be somehow a
very obvious effect, and it has been already discussed in other works [52]. But something was not
expected: the longer stability of the small version of the same crystals. It appeared as if once a
superconducting phase was achieved in the big sample, another cycle of annealing would easily destroy
it. In contrast with this, the small samples survived up to 100 or 120 hours of annealing with very low or
no decomposition. Data from the literature [52] states that small samples need longer times to achieve a
superconducting transition, but what we observed in this work was that the time dependence relates to
the refinement of the superconducting regimes and not to the sudden appearance of it.
Tentative discussion has been made about this observation in the corresponding section of the samples.
While for NCCO 14.5% and 15% the results were focused on the shape of the transition, the effect of
sample dimensions on the Tc,ac,dc and SC volume fraction was also visible in the underdoped samples. For
example, the smallest NCCO 10% sample unexpectedly presented a DC superconducting transition. It
was speculated that the effective oxygen diffusion in this sample should be either volume or surface
controlled.
70
There is no final consensus on the mechanism of the oxygen diffusion caused by the annealing treatment
of electron-doped cuprates. Some reports on Nd2CuO4 [68] state that the actual process can happen
along the a-b plane and the c-direction. According to this report, the chemical diffusion coefficient D in a-
b plane is 3 times larger than in c direction and the vacancy diffusion coefficient Dv should be larger in
the c direction. In this case, the vacancy is the empty site of the apical oxygen. It is stated that the
reduction process can be diffusion-controlled and/or surface controlled. In a diffusion dominated
process the rate constant of the reduction reaction is independent of the oxygen partial pressure47 [68].
So the reaction in the reverse direction, namely the oxidation reaction where there is an actual change in
the oxygen partial pressure, follows the same rate but with negative sign. If a redox reaction is surface-
controlled, the oxygen partial pressure has a substantial effect which is observed when the reaction
curves in opposite directions do not coincide with each other.
If one reflects on how the annealing affected the different samples, even for different doping
concentration, the common ground was the surface area factor. Samples from the same group with less
surface area yielded the best results. In NCCO 10% it yielded what could be taken as DC transition, in
12% and 13% it gave higher Tc,ac,dc and almost 100% of SC volume fraction, and in 14.5% and 15% the
transitions were sharp and the superconducting state seemed more stable against further heat
treatment.
To try and explain this outcome one must analyse how the annealing was executed on the samples: it
was performed in equivalent time sequences of 20 hours at temperature below the stability limit. A
model of a layered sphere might be helpful to attempt to describe the oxygen progression through the
crystal. The first event is certainly a surface dependent process. The reaction can only happen at the
surface-gas interface and it should be dependent on the oxygen partial pressure, since the dopant
concentration x has a relation to the oxygen content, samples with different doping range can react at
different rates. After the first treatment, the AC susceptibility measurements display a transition, which
comes from the first layer of the now oxygen-free structure. But most of the oxygen still resides in the
inner parts of the crystal structure. This explains why DC susceptibility shows a very low SC volume
fraction or no transition at all, since it might be too insignificant to be detected even though the AC
magnetization shows a superconducting signal.
The second reduction process of the samples, meaning the subsequent annealing cycles of 20 hours,
should be more dependent on the oxygen diffusion. The oxygen in the deeper volume of the sample
must first travel to the surface in order to escape the solid. The activation energy should be high enough
to remove the oxygen from its apical sites and to effectively transport them all the way out of the
material. But temperature and time are the same as for the first process, so the oxygen atoms which
were in the deeper volume cannot always complete their “route” and a certain fraction of them must
remain trapped in the surface of the solid. AC susceptibility now shows a transition at higher
temperature but it is not completely saturated and is still broadened. DC susceptibility continues to
47
For further specifications on the calculation of a reaction rate k which depends on the chemical diffusion coefficient D in a-b plane and c- direction, we refer to the quoted article. For general purposes, the driving force of
the diffusion in one dimension should follow Fick’s Law
. Where J is the diffusion flux, D is the diffusion
coefficient and c is the concentration.
71
evolve because evidently the SC volume fraction increased but it is still highly localized in the outer
portions of the material.
The materials response to the third annealing cycle of 20 hours could be now attributed to vacancy
diffusion. One could imagine that the remaining oxygen atoms have randomly settled down throughout
the volume of the metal sublattice, creating some sort of labyrinth pattern, where the diffused atoms
have to find a route as if they were checkers in a board game. The Tc,ac does not change greatly because
the shielding currents are strong enough, but the AC signal continues to refine and to saturate as a
response to the homogenization of the SC volume fraction. On the other hand, the DC susceptibility
signal continues to increase until it reaches the maximum SC volume fraction, and during the
intermediate annealing events the transition width also narrows down and the signal shape improves. If
the oxygen dissipates in 3D, the arrangement of the vacant oxygen apical sites constantly spreads out
and a more homogenous distribution is obtained. This process can continue up to the theoretical point
where the sample is stoichiometric.
This unsophisticated model could explain why “big” samples need more time to yield superconductivity
and also why it dramatically decomposes after achieving this superconducting state. After the first
annealing treatment, a sample with large surface area would leave behind an analogously large empty
surface. Because of this, the AC susceptibility has a high transition temperature and in DC magnetization
there is a small perceivable SC volume fraction. But as the annealing continues the oxygen fails to find an
escaping route, since a large empty surface also offers more possible sites where the oxygen can settle in
without leaving the material in the consequent heat treatment. And since the oxygen moves in all
directions it can also have enough energy to react and form some secondary phase or create
inhomogeneity in the structure.
As a clue to support this representation is the mismatch in the redox reactions. The process was proven
to be reversible for all tested samples. However one could argue that the conditions for the oxidation
reaction are different from those of the reduction reaction because the annealing in oxygen happened at
lower temperature and shorter time than the reduction process. The conditions were 900°C for 20 hours
in O2 in contrast to 935°C for multiple cycles of 20 hours. Hence, less activation energy was provided to
the system and time window for the reaction was shortened. According to the literature [68] conflicting
back and forth reaction routes are a sign that the redox reaction is surface-controlled. The crystal
structure of the compound should play an important role in the reduction of the surplus oxygen. For
other hole-doped cuprate superconductors such as YBa2Cu3O7-δ, it was found that the diffusion of the
oxygen atoms takes place in the Cu-O chains and such surface dependent reactions are not present. This
is proved by resistivity measurements, where the relaxation curves for the redox reactions are the same
in both directions but with opposite sign [64]. This is why, in order to really learn about the actual
mechanism and process of the oxygen diffusion in the electron-doped cuprates one needs to investigate
the annealing treatment with the help of other techniques like resistivity measurements to see the
response of the conductivity during the diffusion process or NMR to effectively count the different apical
oxygen vacancies etc.
A particular last experiment was performed on NCCO 15% where the samples were annealed at two
different temperatures. Those annealed at a lower temperature, 935°C, yielded maximum SC volume
72
fraction with a homogeneous and narrow transition. However the Tc,onset and Tc,ac,dc presented slightly
lower values than the sample annealed at 950°C. While for one side, this could be due to
demagnetization effects since both samples had very different dimensions, this result conflicts with the
results of Kurahashi et al. [52]. They observed that, for optimally doped NCCO, Tc,onset should be higher
for samples annealed at low temperature but the value of Tc,onset should be independent of annealing
time. Their samples also experienced decomposition after only 20 hours of annealing at low temperature
(880°C) while for the case of this work the samples were annealed up to 60 hours without any sign of
decomposition and even at higher temperature. On the other hand, pure Ar atmosphere was not used
during their annealing process and their samples sizes were much larger than the samples used for this
work, a reason why their samples did not last long.
73
Summary
This work focused on the study of the electron-underdoped cuprates Nd2-xCexCuO4+δ, with two main
goals: the formulation of a successful route for the post-growth treatment of the NCCO crystals and the
estimation of the superconducting volume fraction along with a close observation of its development
throughout the annealing events. Extensions of these two aims presented themselves along the
conduction of the thesis.
To achieve these aims, a sample set which covered the main points in the underdoped regime was
grown, samples with 10, 12, 13% Ce doping. In addition, samples within optimal doping range, 14.5 and
15% of Ce content, were studied for comparison.
Growth and shaping of the crystals was the first step during this work. The samples were synthesized
with the Traveling Solvent Floating Zone technique, a method which was described in Chapter 3 along
with the basic experimental specifications.
Once a crystal of the desired composition was obtained, the first aim was to set the standard annealing
conditions which would be followed throughout this thesis. The first experiments were set out with a
sample with 13% Ce doping because this specific doping lies in the middle point of the whole set of
samples which would be probed. After the results depicted in Chapter 6, Section 2 it was decided that
the annealing sequences should be performed according to the following pattern:
Ce doping 10%: 900°C for 20 hours dwell time.
Ce doping 12%: 910°C for 20 hours dwell time.
Ce doping 13-15%: 935°C for 20 hours dwell time.
Taking advantage of the slow pace in the annealing process for the NCCO crystals, the loss in oxygen was
also investigated by means of simple sample weighting before and after annealing. The overall picture is
presented in Table 6.1.2.
The final conclusions of this work can be listed as follows
No intrinsic phase separation effect has been found in the underdoped part of the SC dome: If
the sample is annealed long enough, the samples achieve a SC volume fraction close to 100%.
Bulk and presumably homogeneous superconductivity in NCCO 12% has been obtained which, to
the best of our knowledge, has not been reported before.
Tentative presence of superconducting phase transition in NCCO 10% has been found.
There appears to be an interruption of the monotonic Tc (x) dependence between NCCO 12%
and NCCO 13%. NCCO 12% displayed a higher transition temperature than NCCO 13.
The reduction process is reversible even in underdoped samples.
The effect of the annealing time seems to be the improvement of Tc and ΔTc. The annealing
temperature has a smaller effect for optimally doped samples, within the range of 935°C- 950°C
the Tc values did not vary greatly.
74
Samples with a lower surface area or volume are more resistant to long annealing times. They
also show better and higher transition temperatures along with a high superconducting volume
fraction. Small samples will most likely have smaller concentration gradients (Ce-doping
gradients) than bigger samples, so a sharper transition can be expected. It was noted that large
surface areas play an important role for the deoxygenation of Nd2-xCexCuO4+δ crystals.
75
Appendix 1
Theoretical background support
Figure A1: Illustration of the crystal structure of the Perovskite basic system [69].
Figure A2: Perovskite type crystal structure of La2CuO4, the Mott insulator parent compound of the hole-doped side
of the cuprate superconductors. The conducting CuO2 planes are shadowed. The arrows indicate the spin alignment
of the antiferromagnetic ground state of a Mott insulator. To the side of the crystal structure a fragment of the
CuO2 planes can be seen [15].
Figure A3: Displacement patterns in the CuO2 planes of the LTO and LTT structures. Open circles represent oxygen
atoms. Solid circles represent copper atoms. The tetragonal structure is present in the La2-xBaxCuO4 for x≥0.065 [31].
76
Appendix 2
Experimental setup depictions and machinery specifications
Figure B1: Type of mirror furnaces according to the radiation heating methods: (a) Electrical resistance heating. (b)
Heating by focused light with either an ellipsoidal mirror (top) or two parabolic mirrors (bottom). (c) Laser heating
[45].
Figure B2: Schematic illustration of different versions of the image furnace. From left to right, with one [70], two
mirrors [45] , tilting mirror type [71]. They all are equipped with halogen or Xenon arc lamp with different power as
energy source is available. The furnaces with only one or two mirrors present some disadvantages in the
temperature distribution because the illumination source does not reach the whole surface of the feed rod. The
tilting mirror type helps to control the interface shape and to stabilize the molten zone.
77
Figure B3. Sketch of the successive steps to achieve a dense preliminary packing of the rubber tube with the pre-
reacted oxide powders. This first procedure is just as critical as the following steps, since this is dependent on the
actual manual work of the experimenter [47].
Figure B4: Outline of a Rotational Lifter. The hydrostatic-pressed bar is hanged in a hook attached to the annealing
tube of 6 mm diameter. The process parameters are cycles, temperature and rotation speed. After the process is
finished the sample returns to start position and stops automatically [46]
78
Figure B5: Schematic of the actual setup of the SQUID machine [72].
79
Appendix 3
Calculation specifications and real sample examples
Figure C1: For the annealing process the NCCO crystals were placed in a NCCO polycrystalline crucible which was
mounted on a container for easier handling.
0 5 10 15 20 25 30 35 40 45
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
' a
c,d
c/
' ac,d
c
Temperature (K)
Nd2-x
CexCuO
4+
Tconset
Tcac,dc
Figure C2: Definition of onset temperature Tconset by tangent method. Tcac,dc was chosen at the half point of the
height of the transition, from onset temperature to the tangent of the saturation. If the signal showed positive
values, only the negative values were considered as part of the signal magnitude. The dashed orange lines represent
the limits taken to define the transition width ΔTcac,dc. Since for many cases the saturation did not seem to complete,
the tangent method was applied.
80
Figure C3: N13 sample. Note the shiny surface; this is a cut from the outer part of the original crystal rod. The
orange arrow indicates the orientation of the c-axis. The c-axis is perpendicular to the upper surface.
Figure C4: (a) N12reox sample. (b) N12A sample. Observe the surface in (b) the evidence of the cut by the wire saw.
The orange arrow indicates the orientation of the c-axis.
Figure C5: (a) Pb reference sample to N13. (b) Pb reference sample to N14.5A.
81
Acknowledgments
I can consider myself very fortunate to have been given the opportunity to conduct this thesis at the Walther-Meißner-Institute. The time spent at the Institute, the research and the daily sharing with the colleagues truly made this an interesting and fruitful experience. I would particularly like to thank Prof. Dr. Andreas Erb for being an enthusiastic, helpful and always approachable supervisor. For giving me confidence and great motivation to continue with this highly interesting and captivating topic, for always having a stimulating conversation to share during the day. I still have much to learn from him. I would like to also thank Dr. Mark Kartsovnik for his extensive and patient explanations about the fascinating world of superconducting materials, for always having extra time to share a tea with his students. I am also grateful to Dr. Jan Minar who maintained high interest and attention to my work. It is also important for me to thank the crystal lab at the TU Munich for helping me with crystal preparation and for their patience and nice talk. For the financial support of my Master’s studies I deeply thank the Consejo de Ciencia y Tecnología del Estado de Puebla (CONCYTEP). I want to thank the fellow students at the Institute who made this a memorable time and to my friends in Munich who were a source of encouragement for the past two years, for having turned this city into a new home. Finally I want to dedicate this work to my family and friends in Mexico, who kept supporting and encouraging me even in long distance.
82
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