In-plane electronic anisotropy ofunderdoped ‘122’ Fe-arsenidesuperconductors revealed bymeasurements of detwinned single crystalsI R Fisher1,2, L Degiorgi3 and Z X Shen1,2
1 Geballe Laboratory for Advanced Materials and Department of Applied Physics, Stanford University,CA 94305, USA2 Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory,2575 Sand Hill Road, Menlo Park, CA 94025, USA3 Laboratorium fur Festkorperphysik, ETH - Zurich, CH-8093 Zurich, Switzerland
Received 8 June 2011Published 22 September 2011Online at stacks.iop.org/RoPP/74/124506
AbstractThe parent phases of the Fe-arsenide superconductors harbor an antiferromagnetic groundstate. Significantly, the Neel transition is either preceded or accompanied by a structuraltransition that breaks the four-fold symmetry of the high-temperature lattice. Borrowinglanguage from the field of soft condensed matter physics, this broken discrete rotationalsymmetry is widely referred to as an Ising nematic phase transition. Understanding the originof this effect is a key component of a complete theoretical description of the occurrence ofsuperconductivity in this family of compounds, motivating both theoretical and experimentalinvestigation of the nematic transition and the associated in-plane anisotropy. Here we reviewrecent experimental progress in determining the intrinsic in-plane electronic anisotropy asrevealed by resistivity, reflectivity and angle-resolved photoemission spectroscopymeasurements of detwinned single crystals of underdoped Fe-arsenide superconductors in the‘122’ family of compounds.
(Some figures in this article are in colour only in the electronic version)
Contents
1. Introduction 12. Methods to detwin single crystals in situ 3
2.1. Uniaxial stress 32.2. In-plane magnetic fields 5
The various closely related families of Fe-pnictide andchalcogenide superconductors are well known, and weshall not belabor an unnecessary introduction. Severalrecent reviews (Johnston 2010, Mazin 2010, Paglioneand Greene 2010), and early seminal papers describe theoccurrence of superconductivity in materials which havecommonly become known as ‘1111’ (for example LaFeAsO
(Kamihara et al 2008)), ‘122’ (for example BaFe2As2 (Rotteret al 2008a, 2008b)), ‘111’ (LiFeAs (Tapp et al 2008) andNaFeAs (Parker et al 2009)) and ‘11’ (for example Fe(Se,Te)(Hsu et al 2008)). With the apparent exception of LaFePOand LiFeAs, all of these families comprise a stoichiometricparent compound that exhibits an antiferromagnetic (AFM)ground state. And in all cases, the antiferromagnetism iseither accompanied or preceded in temperature by a structuraltransition that breaks a discrete rotational symmetry of the
Rep. Prog. Phys. 74 (2011) 124506 I R Fisher et al
high-temperature crystal lattice. Borrowing language from thefield of soft condensed matter physics, this broken rotationalsymmetry (from C4 to C2) is widely referred to as an Isingnematic phase transition (Fradkin et al 2010). It is the purposeof this short review to draw together results of recent resistivity,reflectivity and angle-resolved photoemission spectroscopy(ARPES) measurements that reveal the associated in-planeelectronic anisotropy that develops as the materials are cooledthrough this structural transition. Our discussion is limitedsolely to the ‘122’ family of compounds, for which the majorityof the measurements have thus far been performed. It willclearly be important to extend these measurements to otherfamilies in the near future in order to establish generic features.A necessary prerequisite for obtaining such results has been thedevelopment of techniques to detwin crystals in situ, whichwe will briefly review. Several groups have contributed to theemerging story, and we will try to describe each set of resultsaccurately, acknowledging that we are best acquainted withmeasurements from our own collaborations.
Before going any further, we should emphasize that theorigin and significance of the structural transition has beenwidely discussed from the very earliest days after the basicproperties of the ‘1111’ family of Fe-superconductors weredetermined. From a theoretical perspective, it was quicklyappreciated that spin fluctuations might play a key role indriving the nematic transition (Fang et al 2008, Ma et al2008, Xu et al 2008, Mazin et al 2009). Within a local-moment Heisenberg model of a square lattice with nearestand next-nearest neighbor superexchange J1 and J2 in theregime J2 0.5J1, both quantum and thermal fluctuationscontribute a biquadratic term to the effective spin Hamiltonianwhich breaks the perfect frustration of the square lattice, andintroduces an Ising nematic order parameter (Chandra et al1990, Fang et al 2008, Xu et al 2008). The applicability ofsuch a local moment description has of course been questioned(Johannes and Mazin 2009), and it has also been suggested thatif such a model is used then biquadratic terms must be includedin the effective spin Hamiltonian irrespective of the effectsof frustration, and that these terms are close in magnitude tothe bilinear contribution (Yaresko et al 2009). Within a moreitinerant framework, a Pomerancuk type of instability mightlead to better nesting of electron and hole pockets (Zhai et al2009), while interaction between elliptical electron pocketsalso naturally leads to the presence of a biquadratic term inthe effective Hamiltonian, presaging nematic order (Ereminand Chubukov 2010, Fernandes et al 2011). Alternatively,the orbital degeneracy associated with partial filling of dxz
and dyz states has inspired pictures in which the orbitaldegree of freedom plays an equally important role (Chenet al 2009, Lv et al 2009, Kruger et al 2009, Basconeset al 2010, Laad et al 2010, Valenzuela et al 2010, Yanagiet al 2010, Kontani et al 2011). And finally, combinedspin, charge and orbital order has also been described in thecontext of perfect nesting within a unified ‘valley densitywave’ formalism (Cvetkovic and Tesanovic 2009, Kang andTesanovic 2011). At this stage it is unclear which of thesepictures provides the best description of the actual material,motivating detailed quantitative measurements of the in-planeelectronic anisotropy that develops in the nematic state.
Figure 1. Twin formation in underdoped Fe-arsenidesuperconductors. (a) Schematic diagram illustrating the Fe–Asplane of BaFe2As2 in the tetragonal state, with the crystal axeslabeled. Fe and As are shown as red and purple spheres,respectively. (b) The structural phase transition corresponds to astretching/contraction of the Fe–Fe distance along the orthorhombica- and b-axes, respectively. Twin boundaries separate regions forwhich the a and b crystal axes are oriented in opposite directions.The actual difference in the a and b lattice parameters is much lessthan illustrated in the diagram. (c), (d) Optical images of a singlecrystal of Ba(Fe1−xCox)2As2 with x = 0.025 at a temperature aboveand below the structural phase transition, respectively. The imagescorrespond to a region of the sample approximately 100 µm across,and were taken using almost crossed polarizers, such that theobserved contrast reflects the different birefringence of the two twinorientations. Both images reveal the same surface morphology.Twin domains (regions of light or dark intensity) run diagonallyfrom top left to bottom right, and from bottom left to top right inpanel (d).
Measurement of the in-plane electronic anisotropy is ofcourse hampered by twin formation (figure 1). On coolingthrough the critical temperature associated with the structuraltransition, Ts, the materials tend to form dense structural twins,
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corresponding to alternation of the orthorhombic a- and b-axes (Tanatar et al 2009). For probes which cannot distinguishthe a and b orthorhombic directions, this effect obscures anyin-plane anisotropy measured on length scales greater thanthe average twin dimension, which can be as small as a fewmicrometers. Even so, experiments performed using twinnedcrystals have yielded several key results which reveal a large in-plane anisotropy in the AFM state. In terms of the magneticproperties, early inelastic neutron scattering experiments forCaFe2As2 revealed an anisotropic spin-wave dispersion thatcan be best fit by a J1a−J1b−J2 model (Zhao et al 2009), whereJ1a and J1b, the nearest neighbor exchange constants along theorthorhombic a- and b-axes, differ both in magnitude and sign.Similar measurements of Ba(Fe1−xCox)2As2 have revealedanisotropic magnetic excitations even for the optimally dopedcomposition (Lester et al 2010, Li et al 2010), and morerecent measurements for BaFe2As2 have shown the presenceof anisotropic spin fluctuations for temperatures well aboveTN (Harriger et al 2010), although in both cases the overallC4 symmetry of the crystal lattice is not broken because theanisotropic spin wave dispersion is centered at (0, π ) and(π , 0) in the 1-Fe unit cell notation. In terms of the electronicstructure, analysis of quasiparticle interference observed viascanning tunnelling microscopy (STM) measurements alsoindicates a large anisotropy in the electronic dispersion in theAFM state (Chuang et al 2010). In addition, a polarization-dependent laser ARPES study on twinned BaFe2As2 incombination with first-principle calculations suggested a two-fold electronic structure in the SDW state (Shimojima et al2010), and another ARPES study of crystals of CaFe2As2 forwhich the incident beam size was comparable to the size ofthe structural twins, revealed evidence for a large electronicanisotropy below the Neel temperature TN (Wang et al 2010).These various observations have motivated several groups tofind ways to detwin crystals in order to study the in-planeelectronic anisotropy by other techniques, and for temperaturesspanning Ts.
Before describing the methods used to detwin single crys-tals, and the resulting in-plane anisotropy that measurement ofthese detwinned samples reveals, we briefly comment on theseparation of the structural and magnetic transitions. For theparent ‘122’ compounds, initial measurements indicated thatthe tetragonal-to-orthorhombic structural transition occurredat the same temperature as the Neel transition (Goldman et al2008, Huang et al 2008, Zhao et al 2008). More recently,high resolution resonant x-ray diffraction measurements forBaFe2As2 indicate that for this compound Ts occurs 0.75 Kabove TN (Kim et al 2011). Substitution on the Fe site, forexample by Co which has been widely studied, results in asuppression of both Ts and TN, but significantly TN is sup-pressed more rapidly, resulting in a progressive separation ofthe two transitions. The temperature difference monotonicallyincreases with increasing concentration of the substituent, atleast until the top of the superconducting dome (Ni et al 2008a,Chu et al 2009, Lester et al 2009, Nandi et al 2010, Ni et al2010). The origin of the splitting of TN and Ts with chemi-cal substitution is at present not clear, but consideration of theeffect of crystal-quality on the splitting of the transitions in
CeFeAsO (Jesche et al 2010) implies that this effect might, atleast in part, be associated with the strong in-plane disorderintroduced by partial substitution on the Fe site.
2. Methods to detwin single crystals in situ
For all of the known families of Fe-arsenide and chalcogenidesuperconductors, the structural transition occurs below roomtemperature, and it is therefore necessary to detwin singlecrystals in situ. Two distinct methods have been employedthus far; application of uniaxial stress (either compressive (Chuet al 2010b, Ying et al 2011, Dusza et al 2011a, Yi et al2011) or tensile (Tanatar et al 2010, Kim et al 2011)) andapplication of an in-plane magnetic field (Chu et al 2010a,Xiao et al 2010). The former method is superior, at least forthe materials considered to date, resulting in almost completedetwinning. The latter method results in only a modest changein the relative twin domain populations for Ba(Fe1−xCox)2As2,but has several other advantages that warrant a briefdescription.
2.1. Uniaxial stress
BaFe2As2 and closely related compounds form natural crystalfacets along (1 0 0) and equivalent planes, referenced to thetetragonal structure. The orthorhombic a- and b-axes areoriented at 45 to the tetragonal a-axes (figure 1), so in orderto apply uniaxial stress along the orthorhombic a/b directions,crystals must be cut into rectilinear bars with the tetragonala-axis oriented at 45 to the edges of the sample. Singlecrystal x-ray diffraction can be used to confirm the orientationof the crystal axes with respect to the cut edges, with typicalerrors of 2 or less. Application of uniaxial stress at 45
to the tetragonal a-axis favors one twin orientation over theother upon cooling through the structural transition; if theuniaxial stress is compressive, the shorter b-axis is favoredin the direction of the applied stress, whereas the longera-axis is favored for the case of tensile stress. Experimentalmanifestations of detwinning devices from various groupsbased on this simple concept are shown in figure 2. Theextent to which the crystals have been detwinned can bemonitored in situ by either x-ray diffraction (figure 3) oroptical imaging using polarized light (figure 4). For the caseof the cantilever beam device, it is possible to obtain anorder of magnitude estimate of the stress required to fullydetwin the crystals based on the deflection of the cantilever.Typical values are in the range 5–10 MPa, comparable topressures used to mechanically detwin La2−xSrxCuO4 (Lavrovet al 2001).
It is important to appreciate that uniaxial stress also has aneffect for temperatures above Ts. Specifically, although underambient conditions the lattice has a four-fold symmetry aboveTs, application of uniaxial stress fundamentally breaks thissymmetry. Under such conditions, a finite in-plane anisotropyis anticipated in all physical properties, where the anisotropynow refers to directions parallel and perpendicular to theapplied stress. Indeed, any nematic order parameter that wedefine (for example (ρb −ρa)/(ρb +ρa), where ρa and ρb refer
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Figure 2. Examples of experimental methods to mechanicallydetwin single crystals in situ. (a) A mechanical cantilever can beused to apply compressive stress. An order of magnitude estimate ofthe force applied to the crystal can be estimated from the curvatureof the cantilever. From Chu et al (2010b). Reprinted withpermission from AAAS. Extensions of this basic idea include (b)attaching a post to the crystal to allow cleaving the strained crystalin situ for ARPES measurements, and (c) incorporating thedetwinning device close to a reference metal for optical reflectivitymeasurements. (d) Equivalently, tensile stress provides analternative means to mechanically detwin the crystals. Reprintedwith permission from Blomberg et al (2011). Copyright 2011 by theAmerican Physical Society. The elegant design shown in panel (e)enables both compressive and tensile stress to be applied, with theadditional advantage that the sample is able to be cleaved in situ forsurface sensitive measurements like ARPES. Reprinted withpermission from Kim et al (2011). Copyright 2011 by the AmericanPhysical Society. Apparently the applied stress is transmittedthrough the entire crystal to the exposed surface.
to the resistivity along the a- and b-axes, or any other quantitythat represents the difference in the properties of the material inthe a and b directions) is finite for all temperatures above Ts fora crystal held under uniaxial stress. Hence, there is no longer anematic phase transition, and the associated divergent behaviorof thermodynamic quantities is consequently rounded. Thesituation is exactly analogous to the case of cooling aferromagnet in a magnetic field, for which the applied fieldresults in a finite magnetization (order parameter) for alltemperatures, and for which the divergent susceptibility at theCurie temperature is broadened. This effect can be appreciatedby considering the temperature derivative of the resistivity asa function of applied stress, shown in figure 5 for the specific
Figure 3. Single crystal x-ray diffraction provides a direct measureof the relative population of the twin orientations below thestructural transition. (a) The splitting of the (−2 − 2 2 0)T Braggpeak (referenced to the tetragonal lattice) at 40 K for a sample ofBa(Fe1−xCox)2As2 with x = 0.025 under uniaxial pressure reveals arelative volume fraction of approximately 86%, with the shorterb-axis oriented along the direction of the compressive stress. Thehigh photon energy and grazing angle of incidence ensure thatalmost the entire sample volume is probed. From Chu et al (2010b).Reprinted with permission from AAAS. (b) Spatially resolved x-raydiffraction measurements for smaller l indices can provideadditional information about the degree of detwinning in individualparts of the strained crystal. Here, the authors show diffractionpatterns for different regions of a single crystal held under tensilestress. The upper left panel shows the (2 2 0)T diffraction peak forT > Ts. The other three panels show the (4 0 0)O1 and (0 4 0)O2
diffraction peaks (referenced to the orthorhombic lattice) fordifferent regions of the strained single crystal. The upper right handpanel is for a region close to the electrical contacts, for which therelative intensity of the two peaks is comparable in intensity. Thetwo lower panels are for regions far from the electrical contacts,revealing 93% and 99% of the O1 twin orientation, respectively.Reprinted with permission from Tanatar et al (2010). Copyright2010 by the American Physical Society.
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Figure 4. Optical imaging using polarized light microcopy can alsoreveal the impact of uniaxial stress on the relative twin population.(a) An unstressed crystal of BaFe2As2 exhibits distinct twins thatrun vertically from the top to the bottom of the image. (b)Application of uniaxial stress via a cantilever detwinning device inthe direction indicated leads to a single domain in the area imaged.From Chu et al (2010b). Reprinted with permission from AAAS.
case of Ba(Fe1−xCox)2As2 with x = 0.045. Under ambientconditions, two sharp features are observed in the resistivityderivative at 58 and 68 K that match the heat capacity (Ni et al2008a, Chu et al 2009), and which correspond, respectively, tothe magnetic and structural transitions determined by x-rayand neutron scattering (Lester et al 2009). Increasing theapplied stress (in this case by adjusting the screw locatedpart way along the cantilever, shown in figure 2(a)) resultsin a progressive broadening of the feature at Ts, and a finitechange in the resistivity for temperatures above Ts. Incontrast, for temperatures below Ts, once the pressure exceedsa threshold value, there is little additional change in theresistivity, indicating that the sample is fully detwinned andthat there is little pressure dependence to the resistivity of asingle domain. Finally, from a symmetry perspective, the Neeltransition is unaffected by the application of uniaxial pressure(after all, the Neel transition occurs in the orthorhombic statefor TN < Ts), and empirically the value of TN is not affected bythe modest pressures that are exerted on the crystals in orderto detwin them (figure 5), at least for the materials consideredso far.
Figure 5. Temperature dependence of the resistivity derivativedρ/dT of a single crystal of Ba(Fe1−xCox)2As2 with x = 0.045held in a cantilever detwinning device like that shown in figure 2(a).Data are shown for a range of applied pressures, revealing the effectof uniaxial stress on the structural and magnetic phase transitions.Vertical lines indicate TN and Ts determined in the absence of stress.The black curve is for ambient conditions, with no applied stress.Colored curves indicate the resistivity as the stress is progressivelyincreased. Data are taken for current flowing in the direction of theapplied stress. Below Ts, changes in the resistivity reflectdetwinning of the crystal, which saturates beyond some value of theapplied pressure. The Neel transition is unaffected by the appliedstress, but the structural transition is rapidly broadened, affecting theresistivity well above Ts.
2.2. In-plane magnetic fields
In 2002, Ando and coworkers demonstrated that an in-planemagnetic field can influence the relative twin population oflightly doped La2−xSrxCuO4 (Lavrov et al 2002), whichalso suffers an orthorhombic transition, but in this case at∼450 K. The effect is due to a large in-plane anisotropy ofthe susceptibility tensor, which persists well above TN (Lavrovet al 2001). Motivated by this example, similar experimentswere attempted for Ba(Fe1−xCox)2As2, revealing qualitativelysimilar effects below TN (Chu et al 2010a). In this case, thesusceptibility anisotropy has not been directly measured, buton quite general grounds it can be anticipated that the collinearAFM structure that is adopted by the ‘122’ Fe arsenides willresult in a susceptibility that is larger for fields oriented alongthe b direction (perpendicular to the orientation of the spins)than along the a direction. The resulting difference in theenergy of the two twin orientations in the presence of an in-plane field oriented along the a/b direction can be enoughto move twin boundaries, as revealed by optical imaging(figure 6). The change in the relative twin population is,however, only modest, of order 5–15% for typical laboratoryscale fields. Moreover, the effect only appears to work belowTN implying a much smaller susceptibility anisotropy aboveTN than is found for La2−xSrxCuO4.
Although the relative change in the twin populationcaused by the application of an in-plane magnetic field is
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(a) T = 40K H = 0T (b) T = 40K H = 10T
0 10 20 30 40 50distance (µm)
inte
nsity
(a.
u.)
0 10 20 30 40 50distance(µm)
H10µm
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Figure 6. Optical images of a Ba(Fe1−xCox)2As2 sample for x = 2.5%, revealing the partial detwinning effect of an in-plane magneticfield. The images were taken at T = 40 K below both Ts and TN. The initial image (a) was taken in zero field, following a zero field coolfrom above TN. The field was then swept to 10 T, at which field the second image (b) was taken. Horizontal intensity profiles, shown beloweach image, were calculated by integrating vertically over the image area after background subtraction and noise filtering. The field, whichwas oriented along the orthorhombic a/b axes, has clearly moved the twin boundaries, favoring one set of twin domains (high intensity)over the other (low intensity). For the area shown, the relative fraction of domains with a high intensity changes from 54 ± 1% to 61 ± 1%.Reprinted with permission from Chu et al (2010a). Copyright 2010 by the American Physical Society.
small, the large in-plane anisotropy of the resistivity tensorof Ba(Fe1−xCox)2As2 (described in detail below) results in asubstantial magnetoresistance for temperatures below TN if thefield is applied in the ab-plane (figure 7) (Chu et al 2010a).Rotation of the field within the ab-plane reveals a distincthysteresis, also observed in field sweeps, associated with thetwin boundary motion. This effect is thermally assisted anddisplays relaxation effects with a time constant that dependson temperature (Chu et al 2010a).
Typical laboratory-scale magnetic fields are unable tofully detwin crystals of Ba(Fe1−xCox)2As2. Nevertheless,the effect has the distinct advantage of being continuouslytunable in a straightforward manner, permitting experimentswhich explicitly probe the behavior of the twin domains. Forexample, rotation of the applied field in the ab-plane results ina hysteretic magnetoresistance (figure 8(a)). By resolving theprojection of the field separately on to the x- and y-axes, it ispossible to construct a hysteresis loop for the twin boundarymotion (figure 8(b)). This is entirely analogous to the caseof domain wall motion in a ferromagnet, but in this caseassociated with an Ising nematic system, for which B2
x − B2y
plays the equivalent role that B plays in a ferromagnet.In contrast to Ba(Fe1−xCox)2As2, Xiao et al (2010) have
demonstrated via a series of neutron scattering measurementsthat EuFe2As2 can be completely detwinned by application ofmodest in-plane magnetic fields. In this case, the field couplesto the large Eu magnetic moment, inducing a metamagnetictransition to a saturated paramagnetic state with a criticalfield a little below 1 T. Apparently the large difference inZeeman energy of the two twin orientations in the saturated
paramagnetic state is sufficient to drive a complete detwinningof EuFe2As2, but the effect is presumably restricted totemperatures below the Neel temperature of the Eu sub-lattice,which is 20 K. Furthermore, the effect is not hysteretic, suchthat the twin structure reappears when the field is swept back tozero and the Eu ions resume their antiferromagmetic structure.Nevertheless, this fortuitous effect presents an opportunity tostudy the in-plane electronic anisotropy of EuFe2As2 at lowtemperatures via magnetotransport measurements, though todate we are unaware of any such experiments.
3. In-plane resistivity anisotropy
As described above, the relative population of twin domains ofBa(Fe1−xCox)2As2 can be influenced by an in-plane magneticfield. The resulting magnetoresistance is not insignificant,even for relatively small changes in the twin population, fromwhich it is possible to infer a rather large in-plane resistivityanisotropy with ρb > ρa (Chu et al 2010a). However, themagnetoresistance is rapidly suppressed above TN (figure 7),and mechanically detwinned crystals provide a much bettermethod to explore the intrinsic in-plane anisotropy. At thetime of writing, the in-plane resistivity anisotropy has beeninvestigated for mechanically detwinned crystals of the parent‘122’ compounds AFe2As2 (A = Ca, Sr, Ba) (Blomberget al 2011, Tanatar et al 2010); for the electron-dopedsystems Ba(Fe1−xCox)2As2 (Chu et al 2010b, Liang et al2011), Ba(Fe1−xNix)2As2, Ba(Fe1−xCux)2As2, (Kuo et al2011) and Eu(Fe1−xCox)2As2 (Ying et al 2011); and for thehole-doped system Ba1−xKxFe2As2 (Ying et al 2011). These
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70 75 80 85 90
dρ/d
T
85 90 95 100
dρ/d
T
70 75 80 85 900
90
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270
T(K)
Ang
le (
º)
x = 3.6%
85 90 95 1000
90
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x = 2.5%
–1.5
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TN
Figure 7. In-plane magnetoresistance of Ba(Fe1−xCox)2As2 associated with twin boundary motion for temperatures close to TN. Data wereobtained by rotating a fixed magnetic field of 14 T in the ab plane. The crystals were cut into rectilinear bars and the electrical contactspositioned such that the current was oriented along the a/b direction. Angles are measured with respect to the current direction. Verticallines indicate Ts and TN, as determined for these samples by the derivative of the resistivity in zero field (upper panels), and by heat capacityand neutron scattering measurements for other samples. Reprinted with permission from Chu et al (2010a). Copyright 2010 by theAmerican Physical Society.
Figure 8. Hysteresis of the in-plane magnetoresistance associated with twin boundary motion for a single crystal of Ba(Fe1−xCox)2As2
with x = 0.035 well below TN. As for figure 7, the current is oriented along the a/b direction, and angles are measured with respect to thecurrent direction. Data were obtained by rotating a fixed field of 14 T in the ab plane, first in one direction (solid symbols), and then backagain (open symbols). The data are plotted as a function of B2
x − B2y in the right-hand panel, revealing the hysteresis loops associated with
twin boundary motion, analogous to the motion of FM domains in a ferromagnet. (Figure courtesy of J-H Chu.)
measurements reveal several intriguing and unanticipatedresults which we discuss in greater detail below.
For all of the parent ‘122’ compounds AFe2As2 (A = Ca,Sr, Ba, Eu) it is found that ρb > ρa , as anticipated by the
magnetoresistance measurements of Ba(Fe1−xCox)2As2. Thereader is reminded that the b-axis is the shorter of the twoin-plane lattice parameters, as well as being the direction inwhich the moments align ferromagnetically, so at first glance
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Figure 9. Comparison of the in-plane anisotropy of CaFe2As2,SrFe2As2 and BaFe2As2 . Note the larger induced anisotropy aboveTs for BaFe2As2 relative to the cases of SrFe2As2 and CaFe2As2.Although it is not known whether the same stress is applied for eachmeasurement, nevertheless the larger induced anisotropy isconsistent with the second order nature of the structural phasetransition in BaFe2As2, relative to the more strongly first ordertransition observed for SrFe2As2 and CaFe2As2. Reprinted withpermission from Blomberg et al (2011). Copyright 2011 by theAmerican Physical Society.
this observation seems somewhat counterintuitive. However,the magnitude of the anisotropy for BaFe2As2 is only modest,with maximal values of ρb/ρa ∼ 1.2 for temperatures closeto TN (Chu et al 2010b). The anisotropy is smaller stillfor SrFe2As2 and CaFe2As2 (Blomberg et al 2011). Thetemperature dependence of the anisotropy through TN forthe strained crystals is somewhat different for the four cases(figure 9, Blomberg et al 2011), depending on the degreeto which the coupled structural/magnetic transition is firstor second order, to which we return shortly. Furthermore,absolute values of the anisotropy can vary depending onannealing conditions, implying a sensitivity to disorder(Liang et al 2011).
The in-plane resistivity anisotropy was also measuredfor Ba(Fe1−xCox)2As2 for underdoped, optimally doped andoverdoped compositions (figure 10, Chu et al 2010b). Asfound for the undoped parent compounds, ρb > ρa for allunderdoped compositions. The temperature dependence ofρa remains metallic to the lowest temperatures, whereas ρb
rapidly develops a steep upturn with decreasing temperatureas the dopant concentration is increased from zero. Partialsuppression of the superconductivity by an applied magneticfield oriented along the c-axis reveals that ρb continuesto rise with decreasing temperature for these underdopedcompositions (figure 11). Consideration of the derivative ofthe resistivity reveals that the in-plane anisotropy developsmost rapidly for temperatures close to Ts (see figure 4(b)of Chu et al (2010b)), implying that it is closely associatedwith the nematic transition. The most striking aspects of thedata are both the large magnitude of the anisotropy, and thenon-monotonic doping dependence, both of which are bestappreciated by plotting the resistivity anisotropy ρb/ρa as a
function of temperature and composition (figure 12). Bothresults are in stark contrast to the structural orthorhombicity,characterized by (a − b)/(a + b), which is small (0.4% forx = 0 at 7 K) and monotonically decreases with increasing Coconcentration (Prozorov et al 2009). In contrast, the in-planeresistivity anisotropy rises to a maximum value ρb/ρa ∼ 2for x ∼ 3.5% (Chu et al 2010b). Perhaps coincidentally, thelarge resistivity anisotropy appears to develop for compositionsclose to the onset of the superconducting dome. This isalso close to the composition at which ARPES measurementsindicate the vanishing of a hole-like pocket of reconstructedFermi surface (FS) (Liu et al 2010). We return to the possiblesignificance of this Lifshitz transition in section 6.
Inspection of figures 10 and 12 reveals that the differencein ρb and ρa begins at a temperature well above Ts. Dependingon composition, and on the magnitude of the applied stress,anisotropy in the resistivity can be observed up to ∼2Ts. Asmentioned previously, in this temperature regime, the valueof the anisotropy, and also the temperature to which theanisotropy persists, depends sensitively on the magnitude ofthe applied stress (figures 5 and 24) (Chu et al 2010b, Lianget al 2011). There is no indication in either the resistivityor its derivatives of an additional phase transition markingthe onset of this behavior in either stressed or unstressedcrystals. Furthermore, diffraction measurements reveal that forunstressed conditions the material is fundamentally tetragonalwithin the available resolution (Goldman et al 2008, Huanget al 2008, Zhao et al 2008, Kim et al 2011). Hence,the simplest explanation of the observed anisotropy aboveTs for the stressed crystals is that this effect is inducedby the uniaxial stress, rather than this being related to thepresence of static nematic order. Within linear responsetheory, such an effect can be described in terms of alarge nematic susceptibility that couples to uniaxial latticestrain. Courtesy of the fluctuation–dissipation theorem, thisimplies a wide temperature range above Ts where nematicfluctuations are appreciable, with possible implications forthe superconducting pairing mechanism. Resonant ultrasoundmeasurements of the elastic moduli of Ba(Fe1−xCox)2As2
also reveal a softening of the sheer modulus, consistentwith the presence of a substantial nematic susceptibility(Fernandes et al 2010).
It is instructive to compare the strain-induced anisotropyfor temperatures above Ts of Ba(Fe1−xCox)2As2, for whichthe structural transition is argued to be second order (Wilsonet al 2009, 2010, Kim et al 2011), with the case of CaFe2As2,for which the coupled magnetic/structural transition is stronglyfirst order (Ni et al 2008b). Specifically, uniaxial stress doesnot seem to cause an appreciable change in the resistivityabove Ts for CaFe2As2 (Tanatar et al 2010), consistent with thereduced effect of fluctuations anticipated for a first order phasetransition. Comparison with SrFe2As2, for which the first ordertransition is somewhat weaker (Yan et al 2008) reveals thatthe induced resistivity anisotropy above Ts is proportionatelylarger (figure 9, Blomberg et al 2011).
It is of course important to ask to what extentthe compositional dependence of the in-plane resistivityanisotropy observed for Ba(Fe1−xCox)2As2 (figure 12) is
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Figure 10. In-plane resistivity anisotropy of Ba(Fe1−xCox)2As2. Red lines show data for current parallel to applied uniaxial stress (ρb
configuration) and green lines show data for current perpendicular to stress (ρa configuration). For each composition, measurements weremade for the same crystal with the same set of contacts. Vertical lines show TN and Ts, determined in the absence of any stress. From Chuet al (2010b). Reprinted with permission from AAAS.
Figure 11. Temperature dependence of the in-plane resistivity anisotropy of Ba(Fe1−xCox)2As2 in the presence of a large magnetic fieldoriented along the c-axis to partially suppress the superconductivity . Red (green) lines show data for current parallel (perpendicular) toapplied uniaxial stress corresponding to the ρb (ρa) configuration in zero field. Dark red (dark green) data points show ρb (ρa) in a field of35 T. For all three compositions, ρb continues to rise to the lowest temperatures, until cut off by the superconducting transition. (Figurecourtesy of J-H Chu.)
generic. Measurements by Ying et al (2011) reveal a similarlylarge in-plane resistivity anisotropy for Eu(Fe1−xCox)2As2.And our own more recent measurements of Ba(Fe1−xNix)2As2
(figure 13) and Ba(Fe1−xCux)2As2 reveal a similar non-
monotonic doping dependence to the anisotropy (Kuo et al2011). Thus, for electron-doped ‘122’ systems which involvesubstitution on the Fe site, the appearance of a large resistivityanisotropy for some intermediate range of compositions seems
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Rep. Prog. Phys. 74 (2011) 124506 I R Fisher et al
Doping x
Tem
pera
ture
(K
)
0 0.02 0.04 0.06 0.08 0.1
20
40
60
80
100
120
140
160
180
200
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
ρb/ρ
a
Figure 12. Temperature and composition dependence of thein-plane resistivity anisotropy ρb/ρa of Ba(Fe1−xCox)2As2 .Structural, magnetic and superconducting critical temperatures,determined in the absence of uniaxial stress, are shown as circles,squares and triangles, respectively. From Chu et al (2010b).Reprinted with permission from AAAS.
Doping x
Tem
pera
ture
(K
)
0 0.01 0.02 0.03 0.04 0.05 0.06
20
40
60
80
100
120
140
160
180
200
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2ρ
b/ρ
a
Figure 13. Temperature and composition dependence of thein-plane resistivity anisotropy ρb/ρa of Ba(Fe1−xNix)2As2
Structural, magnetic and superconducting critical temperatures,determined in the absence of uniaxial stress, are shown as circles,squares and triangles, respectively. Reprinted with permission fromKuo et al (2011). Copyright 2011 by the American Physical Society.
to be generic, at least for the variants studied thus far. Instark contrast, measurements of detwinned single crystals ofthe hole-doped system Ba1−xKxFe2As2 (figure 14, Ying et al2011) indicate a vanishingly small in-plane anisotropy forx = 0.1 and 0.18. It is not yet clear how the anisotropy ofthe parent compound BaFe2As2 evolves to give this essentially
isotropic response for the K-doped samples, but taken at facevalue the result provides evidence that the effects of hole-doping and/or substitution off the FeAs plane might be ratherdifferent to electron-doping and/or substitution on the FeAsplane. We return to this point later.
In addition to the zero-field resistivity measurementsdescribed above, improvements in crystal quality have enabledthe observation of Shubnikov–de Hass oscillations in themagnetoresistance of the parent compound BaFe2As2 overa wider field range than was previously possible (Analytiset al 2009), enabling a clearer identification of the distinctfrequencies and their various harmonics. In a beautiful set ofmeasurements using detwinned single crystals of BaFe2As2,Terashima et al (2011) have been able to map the reconstructedFS, revealing the presence of small isotropic pockets, as wellas somewhat larger, more anisotropic pockets. We return to thesignificance of these observations in relation to the resistivityanisotropy in section 6.
4. Anisotropic charge dynamics
The observation of a large in-plane resistivity anisotropy, atleast for the electron-doped ‘122’ Fe arsenides, bears witnessto the orthorhombicity of the material, but does not distinguishbetween anisotropy in the electronic structure and anisotropyin the scattering rate. To this end, reflectivity measurementsof detwinned single crystals using polarized light can provideimportant insight to the effects of the magnetic and structuraltransitions on the anisotropic charge dynamics and theelectronic band structure. Both the overall spectral weight(SW) distribution and also the scattering rate of itinerantcharge carriers may be extracted from analysis of the metalliccontribution to the excitation spectrum. Such measurementsfor detwinned single crystals of Ba(Fe1−xCox)2As2 haveestablished a direct link between the rather counterintuitivetemperature dependence of the anisotropic dc transportproperties described above and the related charge dynamicsin the underdoped regime (Dusza et al 2011a). Theseobservations also enable a clearer understanding of the averageoptical response previously obtained for twinned crystals of thesame material (Lucarelli et al 2010).
Exploiting a similar concept as described in section 2.1(figure 2(a)), a detwinning device (figure 2(c)) that allowsoptical measurements under constant uniaxial pressure wasdeveloped (Dusza et al 2011a). The device consists of amechanical clamp and an optical mask attached on top and intight contact. The pressure-device was designed according tothe following specific criteria: (i) it leaves the (0 0 1) facet of thesingle domain samples exposed, enabling optical reflectivity(R(ω)) measurements; (ii) the optical mask guarantees datacollection on surfaces of the same dimension for the sample(S) and the reference mirror (M) and therefore on equivalentflat spots; (iii) the uniaxial stress is applied by tightening ascrew and drawing the clamp against the side of the crystal,cut such that in the orthorhombic phase the a/b axes of thetwinned samples would lie parallel to the stress direction; (iv)the major axis of the tightening screw lies nearby and parallel
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Rep. Prog. Phys. 74 (2011) 124506 I R Fisher et al
Figure 14. Temperature dependence of the in-plane resistivity ρa and ρb for strained crystals of the hole-doped system Ba1−xKxFe2As2 for(a) x = 0.1 and (b) x = 0.18. Insets to panel (a) show polarized light images which reveal the presence (absence) of twin domains for theunstressed (stressed) conditions. In stark contrast to the cases of Ba(Fe1−xCox)2As2 and Ba(Fe1−xNix)2As2, no appreciable in-planeresistivity anisotropy is observed for Ba1−xKxFe2As2. Reprinted with permission from Ying et al (2011). Copyright 2011 by the AmericanPhysical Society.
to the surface of the sample so that the shear- and thermal-stress effects are minimized. The thermal expansion L ofthe tightening screw, exerting the uniaxial pressure, can beestimated to be of the order of L = αLT = 20 µm (forscrew-length L = 5 mm, typical metallic thermal expansioncoefficient α = 2 × 10−5 K−1, and thermal excursion T =200 K). This corresponds to a relative variation of about 0.4%.By reasonably assuming L/L = p/p, the influence of thethermal expansion is then negligible.
Prior to inserting the sample holder into the cryostatthe alignment conditions between M and S were verifiedby imaging on both spots a red laser point source. Withinthe cryostat a micrometer allows a very accurate positioningof S and M with respect to the light beam. R(ω) datawere thus collected as a function of temperature on thesedetwinned, single domain samples in the far- and mid-infrared(FIR and MIR) spectral range between 30 and 6000 cm−1
(Dressel and Gruner 2002). Data were complemented withroom temperature measurements from the near-infrared (NIR)up to the visible and ultra-violet spectral range (3200–4.8 ×104 cm−1). Light in all spectrometers was polarized alongthe a- and b-axes of the detwinned samples. The polarizerschosen for each measured frequency range have an extinctionratio greater than 200, thus reducing leakages below our 1%error limit. The real part σ1(ω) of the optical conductivity wasobtained via the Kramers–Kronig transformation of R(ω) byapplying suitable extrapolations at low and high frequencies.For the ω → 0 extrapolation, the Hagen–Rubens (HR) formula(R(ω) = 1 − 2
√(ω/σdc)) was used, inserting σdc values in
fair agreement with Chu et al (2010b), while above the upperfrequency limit R(ω) ∼ ω−s(2 < s < 4) (Dressel and Gruner2002). Prior to performing optical experiments as a functionof the polarization of light, the electrodynamic response ofthe twinned (i.e. unstressed) samples was first checked withunpolarized light, consistently recovering the same spectrapreviously presented by Lucarelli et al (2010). Although thedetwinning device does not permit a precise control of theapplied pressure, the uniaxial stress was carefully increasedenough to observe optical anisotropy, which was verified todisappear when the pressure was subsequently released. Asa control measurement, optical reflectivity data were also
collected for a Cu sample of the same size (surface area andthickness) as that of the pnictide crystals and in the samesetup with the uniaxial pressure. As expected, there is a totalabsence of dichroism for the stressed Cu sample, implyinga vanishingly small sensitivity of the electronic structure tothe modest uniaxial stresses employed in this measurement.The two compositions of Ba(Fe1−xCox)2As2 with x = 0and 0.025 displayed overall similar features in their opticalresponse (Dusza et al 2011a). To avoid repetition, raw dataare shown only for x = 0. Nevertheless, the discussion ofthe resulting optical anisotropy with respect to the dc findingsis provided here for both compositions. Furthermore, a fullaccount of our results and analysis is available in Dusza et al(2011b).
The real part σ1(ω) of the optical conductivity of the parentcompound at 10 and 150 K along both polarization directionsis shown in figure 15. Consistent with previous data ontwinned samples (Lucarelli et al 2010), σ1(ω) is dominated by astrong absorption peaked at about 4300 cm−1 and a pronouncedshoulder at 1500 cm−1 on its MIR frequency tail. Inspectionof figure 15 reveals a distinct optical anisotropy that extendsup to energies that far exceed the energy scales set by thetransition temperatures. A similar optical anisotropy was alsodetected for the parent compound at 5 K by an independentinvestigation (Nakajima et al 2011a). In addition, the opticalanisotropy of the stressed crystals is found to persist wellabove Ts, similar to the observation of an induced dc resistivityanisotropy for stressed crystals (section 3). The anisotropy inthe optical response for the magnetic state can be anticipatedby ab initio calculations based on density-functional-theory(DFT) as well as dynamical mean-field theory (DMFT) (Sannaet al 2011, Sugimoto et al 2011, Yin et al 2011). It was firstshown that the optical anisotropy of the magnetic state, notpresent within the local spin density approximation, may resultfrom DMFT-correlation (Yin et al 2011). Alternatively, DFT-calculations of the optical conductivity within the full-potentiallinear augmented plane-wave method reproduce most of theobserved experimental features, in particular an anisotropicmagnetic peak located at about 0.2 eV, which was ascribed toantiferromagnetically ordered stripes (Sanna et al 2011).
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Rep. Prog. Phys. 74 (2011) 124506 I R Fisher et al
0 2000 4000 6000
0.0 0.2 0.4 0.6 0.8
0
1000
2000
3000
Frequency (cm–1)
σ 1(ω
) (Ω
cm)–1
10 K (E||b)150 K (E||b)10 K (E||a)150 K (E||a)
BaFe2As2
0 100 200 300 400 500
0.00 0.02 0.04 0.06
0
500
1000
ω1
ω2
Energy (eV)
Figure 15. Real part σ1(ω) of the optical conductivity of BaFe2As2
at 10 and 150 K in the MIR–NIR range for both polarizationdirections. The vertical dashed lines mark the frequencies ω1 and ω2
(see text). Inset: infrared part of σ1(ω) at 10 and 150 K for bothaxes. Reprinted with permission from Dusza et al (2011a).
The inset in figure 15 shows an expanded view of the FIRσ1(ω) well above and below TN for both a- and b-axes. Withdecreasing temperature, an overall enhancement of σ1(ω) isobserved in the FIR along the a-axis and its depletion alongthe b-axis. This reinforces the scenario for the opening ofa pseudogap in the excitation spectrum for E ‖ b at TN,reminiscent of what has been observed in twinned samples(Lucarelli et al 2010). As will be discussed in greater detailbelow, such a depletion removes SW, which principally piles upin the MIR feature at 1500 cm−1. These findings demonstratethat the magnetic transition at TN seems to partially gap theportion of the FS pertinent to the b-axis response, whileenhancing the metallic nature of the charge dynamics for thea-axis response.
A detailed analysis of the excitation spectrum wasperformed within the same Drude–Lorentz approach,previously introduced for the twinned samples (Lucarelli et al2010) and adapted to both polarization directions. Figure 16emphasizes the most relevant fit components, pertinent forthe spectral range characterized by a temperature dependentanisotropic optical response. The metallic part of σ1(ω)
consists of a narrow (N) and broad (B) Drude term; theformer is obviously tied to the zero frequency extrapolation ofR(ω), while the latter largely dominates the optical response.The two Drude terms imply the existence of two electronicsubsystems (Wu et al 2010) and phenomenologically mimicthe multiband scenario in the iron pnictides. A broad Lorentzharmonic oscillator (HO) is used to describe the MIR energyinterval (figure 16) (Lucarelli et al 2010), which accounts forthe so-called magnetic peak in σ1(ω). Three high frequencyHOs finally shape the interband transitions with onset at
Figure 16. Phenomenological modeling of the optical conductivitywithin the Drude–Lorentz approach: the narrow and broad Drudeterms, the MIR HO as well as the first and low-frequency tail of thesecond HO shaping σ1(ω) above 2000 cm−1 and reproducing thehigh frequency interband transitions. A third HO (not shown) finallyallows the reproduction of the high frequency tail of the strongabsorption in σ1(ω) centered at about 4300 cm−1. The coloredshaded areas emphasize the SWs of both Drude terms (proportionalto the squared plasma frequency) and MIR-band (proportional to theoscillator strength) (Dressel and Gruner 2002). The total fitreproduces in great detail the measured spectrum (here as anexample the parent compound BaFe2As2 at 120 K). This fittingapproach applies to all temperatures and doping levels (Lucarelliet al 2010) and can be easily adapted to both polarization directionsin detwinned materials (Dusza et al 2011a).
ω ∼2000 cm−1. Such an analysis allows the SW distributionto be disentangled with respect to the various energy intervalsamong all fit components, adding up in order to reproduce thecomplete excitation spectrum. The SW is here defined in unitsof cm−2 as SW = (120/π)
∫σ i
1(ω) dω, where∫
σ i1(ω) dω
corresponds to the area of the ith component (Drude termor Lorentz HO) shaping σ1(ω) (figure 16). Physically, thequantity SW corresponds to the square of the plasma frequencyfor the Drude terms or to the oscillator strength for the Lorentzcomponents.
Figure 17 displays for both directions the total SW,obtained from the sum of all oscillator strengths contributingto σ1(ω) (figure 16), and its redistribution in terms of SWfor the Drude terms, the MIR-band as well as the highfrequency electronic interband transitions. The total SW isconstant along both polarization directions, thus satisfyingthe well-known f -sum rule (Dressel and Gruner 2002). ForE ‖ a (figure 17, upper panel), the SW moves from energiesaround the peak at 4300 cm−1 into the broad MIR shoulderat 1500 cm−1 (figure 15) and also down to low energiesinto the metallic contribution upon cooling below TN. ForE ‖ b (figure 17, lower panel) on the other hand, there isa reshuffling of weight, which is lost by the Drude termsand piles up into the MIR band. A similar trend in the
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Rep. Prog. Phys. 74 (2011) 124506 I R Fisher et al
Temperature (K)
Spe
ctra
l Wei
ght (
cm–2
)
2.4×109
2.5×109
2.6×109
0
1×108
2×108
TotalDrudeMIR-bandInterband
E||aBaFe2As2
0 100 200 3002.4×109
2.5×109
2.6×109
0
1× 108
2×108
TotalDrudeMIR-bandInterband
E||bBaFe2As2
Spe
ctra
l Wei
ght (
cm–2
)
Figure 17. Temperature dependence of the SW redistribution alongthe a- and b-axis for x = 0, extracted from the Drude–Lorentz fit(figure 16) of the optical response (Lucarelli et al 2010, Dusza et al2011a). Both panels display SW encountered in both Drude terms,in the MIR-band and in the HOs reproducing the high frequencyinterband transitions, as well as the resulting total SW. The verticaldashed line in both panels marks the phase transition at Ts (TN).Reprinted with permission from Dusza et al (2011a).
SW reshuffling is also observed for x = 0.025, althoughsomewhat less pronounced than for the parent compound. Inorder to emphasize the temperature dependence of the totalDrude weight, we display the comparison between the twopolarization directions in figure 18 for both compositions.Across the structural/magnetic phase transitions there is animportant enhancement/depletion of the Drude weight withdecreasing temperature along the a- and b-axis, respectively,indicative of a reconstruction of the FS in the orthorhombicAFM phase. The behavior of the Drude weight above Ts
is also interesting. It saturates to a constant value and getslarger along the b-axis than along the a-axis for x = 0, whilefor x = 0.025 it just merges into a constant and equal valuefor both directions. Figure 19 shows the scattering rates (i.e.the width at half maximum of the Drude terms (Dressel andGruner 2002), figure 16) of the itinerant charge carriers forboth narrow (N) and broad (B) Drude terms. Data areonly displayed here for x = 0, but these are representativefor all compositions in the underdoped regime. N and B
Temperature (K)
Dru
de S
pect
ral W
eigh
t (10
7 c
m–2
)
0
1
2
3
0 100 2000
2
4
6
8E||aE||b
Ba(Co0.025 Fe0.975)2As2
E||aE||b
BaFe2As2
Dru
de S
pect
ral W
eigh
t (10
6 cm
–2)
Figure 18. Comparison of the total Drude SW (sum of narrow andbroad terms) of Ba(Fe1−xCox)2As2 for E||a and E||b as a functionof temperature for (a) x = 0 and (b) x = 0.025. Vertical lines markTN and Ts.
increase along the AFM a-axis, while they decrease along theferromagnetic (FM) b-axis for T < TN, as expected. Indeed,the large scattering rate along the a-axis may arise because ofscattering from spin fluctuations with large momentum transfer(i.e. by incoherent spin waves) (Turner et al 2009, Chen et al2010). The temperature dependence of the scattering ratespaired with the non-negligible changes at energy scales close tothe Fermi level shapes the dc transport properties (see below).
It is interesting to compare the anisotropic optical responsewith the anisotropy ratio of the dc transport properties,defined here as ρ/ρ = 2(ρb − ρa)/(ρb + ρa). Fromthe Drude terms the dc limit of the conductivity (σ opt
0 =(ωpN)2/(4πN) + (ωpB)2/(4πB)) for both axes) can beestimated more precisely than simply extrapolating σ1(ω) tozero frequency. The anisotropy ratio ρopt/ρ, reconstructedfrom the optical data (i.e. σ opt
0 ), is compared with the equivalentquantity from the transport investigation in figure 20. Theagreement in terms of ρ/ρ between the optical and dcinvestigation is outstanding for x = 0.025 at all temperatures
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Rep. Prog. Phys. 74 (2011) 124506 I R Fisher et al
200
400
600
800
Γ Dru
de (c
m–1
)
E||a E||b baxis (narrow)aaxis (narrow)
0 100 200 3000
20
40
Temperature (K)
Narrow Drude
Broad Drude
BaFe2As2
Figure 19. Scattering rates N and B (figure 16) along the a- andb-axis for x = 0, extracted from the Drude–Lorentz fit of the opticalresponse (Lucarelli et al 2010, Dusza et al 2011a). The verticaldashed line marks the phase transition at Ts (TN). Reprinted withpermission from Dusza et al (2011a).
(figure 20, lower panel). In comparison, ρopt/ρ forx = 0 is slightly larger than the dc transport anisotropy forT < Ts (figure 20, upper panel). This difference mightoriginate from a difference in the applied stress in the opticaland dc transport measurements, or from differences in thescattering rate of samples used for the two measurements (seediscussion in section 6). Significantly, analysis of the opticalreflectivity for all compositions indicates that anisotropy inthe FS parameters, such as the enhancement (depletion) ofthe total Drude SW occurring along the a(b)-axis (figure 18),outweighs the anisotropy in the scattering rates (figure 19) thatdevelops below TN in terms of the effect on the dc transportproperties. This is an important result from the opticalinvestigation, which indeed enables both pieces of informationgoverning the behavior of the dc transport properties to beextracted.
In order to emphasize the significant polarization depen-dence in σ1(ω) at high frequencies, it is instructive to considerthe difference σ1(ω) = σ1(ω, E ‖ a) − σ1(ω, E ‖ b) at allmeasured temperatures. σ1(ω) represents an estimation ofthe dichroism and turns out to be very prominent in the MIRand NIR ranges (figure 15, as well as figure 3(d) in Duszaet al (2011a)). It is especially interesting to compare the tem-perature dependence of the dc (ρ/ρ) and optical (σ1(ω))
anisotropy in the temperature range T > Ts for which a largeinduced anisotropy is observed in the resistivity for stressedcrystals (section 3). Two characteristic frequencies are se-lected to follow the temperature dependence, identifying theposition of the peaks in σ1(ω) (figure 15); namely, ω1 = 1500(1320) cm−1 and ω2 = 4300 (5740) cm−1 for x = 0 (0.025).It is remarkable that the temperature dependence of σ1(ω)
at ω1 and ω2 follows the temperature dependence of ρ/ρ inboth compounds (figure 20). σ1(ωi) (i = 1,2) saturates at
0.0
0.1
0.2
–150
–100
–50
0
50
1000
20
40
60
80
∆σ1 (ω
1 ) (Ωcm
) –1
∆σ1 (ω
2 ) (Ωcm
) –1
∆ρ(T
)/ρ(
T)
∆ρ/ρ∆σ1(ω1)
∆σ1(ω2)
∆ρopt/ρ (x0.5)
x=0
0 100 200 3000.0
0.2
0.4
0.6
0
50
100
150–30
–20
–10
0
Temperature (K)
∆ρ(T
)/ρ(
T)
∆σ1 (ω
1 ) (Ωcm
) –1
∆σ1 (ω
2 ) (Ωcm
) –1
∆ρ/ρ
∆ρopt/ρ
x=0.025
Ba(Fe1-xCox)2As2
∆σ1(ω2)∆σ1(ω1)
Figure 20. Temperature dependence of the dichroism σ1(ω) forx = 0 and 0.025 at ω1 and ω2 (figure 15) compared with ρ/ρ fromthe dc transport data (Chu et al 2010b), as well as from the Drudeterms in σ1(ω) (ρopt/ρ). The vertical dashed and dashed-dottedlines mark the magnetic and structural phase transitions at TN andTs, respectively, for unstressed conditions Reprinted with permissionfrom Dusza et al (2011a).
constant values well above Ts and then displays a variation forT < 2Ts. The rather pronounced optical anisotropy, extend-ing up to temperature higher than Ts for the stressed crystals,clearly implies an important induced anisotropy in the elec-tronic structure (Sanna et al 2011, Sugimoto et al 2011, Yinet al 2011), which is also revealed by ARPES measurements(section 5). Since the dichroism directly relates to a reshufflingof SW in σ1(ω) in the MIR–NIR range (figure 15), σ1(ω) atω1 is interrelated to that at ω2, so that the behavior of σ1(ω)
is monotonic as a function of temperature and opposite in signbetween ω1 and ω2 (figure 20). As anticipated, σ1(ωi) = 0for T Ts for x = 0.025 (figure 20, lower panel). However,for x = 0, σ1(ωi) is found to be constant but apparently dif-ferent from zero for T Ts (figure 20, upper panel). The ori-gin of the finite (but constant) dichroism at high temperaturesfor this sample is at present unclear, and might reflect a sys-tematic effect due to imperfect experimental conditions (e.g.too strong applied uniaxial pressure). Nevertheless, the over-all temperature dependence seems to behave in a very similar
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Rep. Prog. Phys. 74 (2011) 124506 I R Fisher et al
Figure 21. The FS of (a) twinned and (b), (c) untwinned crystals of BaFe2As2 in the SDW state. For twinned samples measurements reveala superposition of the electronic structure observed for the detwinned crystals. Light polarization as indicated in each panel. Reprinted withpermission from Yi et al (2011). (d) Similar results have also been obtained by Kim et al (2011) for detwinned single crystals, shown herealong the X direction (the axes are rotated by 45 with respect to panel (b)). Reprinted with permission from Kim et al (2011). Copyright2011 by the American Physical Society.
manner for the two compositions. Significantly, the absolutevariation of the dichroism across the transitions at selectedfrequencies is larger for x = 0 than for x = 0.025. Thisdoping dependence needs to be studied in a controlled pres-sure regime in order to exclude effects arising from differentdegrees of detwinning (T < Ts) and different magnitude of in-duced anisotropy (T > Ts). Even so, it is encouraging to findevidence for changes in the electronic structure that, contraryto the dc resistivity (Chu et al 2010b), appear to follow thesame doping dependence as the lattice orthorhombicity (Pro-zorov et al 2009). This behavior is clearly revealed in ARPESmeasurements of stressed crystals of Ba(Fe1−xCox)2As2, de-scribed below.
5. Electronic anisotropy determined via ARPES
Adaptation of mechanical detwinning devices to allowcleaving of strained crystals in situ has recently enabledARPES measurements on detwinned samples of BaFe2As2
(Kim et al 2011) and Ba(Fe1−xCox)2As2 (Yi et al 2011).Hence, the band structure and reconstructed FS canbe determined without the need to consider the effectsassociated with the superposition arising from different twinorientations. Furthermore, measurements performed fordifferent orientations of the incident light polarization provideinformation about the dominant orbital characters of thebands via the photoemission matrix elements. Finally, thesemeasurements also reveal the effect of uniaxial stress on theband structure for temperatures above Ts.
The FSs of twinned and detwinned BaFe2As2 crystals inthe SDW state at 10 K are compared in figure 21 (Yi et al 2011).
Measurements were made using 25 eV photon energy and theFS was determined using an integration window of 5 meVabout EF. The Brillouin zone (BZ) is labeled corresponding tothe true crystallographic 2-Fe unit cell in which –X is alongthe AFM crystal axis and –Y is along the FM crystal axis.As can be clearly seen, in the twinned case (figure 21(a)), thenearly orthogonal domains mix signals from both –X and–Y directions, masking any intrinsic differences betweenthese directions and leading to a very complex FS topologyand band dispersion. However, once detwinned, one clearlyobserves that the reconstructed FS appears very different in thetwo orientations (figures 21(b) and (c)). Further measurementsperformed for different photon polarizations enable a morecomplete mapping of the reconstructed FS, and show that theFS remains multi-orbital in the SDW state (Yi et al 2011).
The most anisotropic features on the FS are the brightspots along –X and petals along –Y . Corresponding banddispersions (not shown here; see Yi et al (2011)) revealthat these features arise from anti-crossing between hole andelectron bands. Moreover, the bands cross at different energiesin the two directions: close to EF along –X inducing tinyFermi pockets observed as bright spots, and 30 meV below EF
along –Y resulting in bigger electron pockets on the FS. Theareas of these small pockets, corresponding to approximately0.2% and 1.4% of the paramagnetic BZ, are in reasonableagreement with frequencies reported from quantum oscillationmeasurements (Analytis et al 2009). These features have beenobserved in earlier ARPES data on twinned BaFe2As2 (Yiet al 2009, Liu et al 2010, Richard et al 2010) and SrFe2As2
(Hsieh et al 2008). However, measurements of detwinnedcrystals clearly reveal that the bright spots and petals reside
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Rep. Prog. Phys. 74 (2011) 124506 I R Fisher et al
Figure 22. (a) Second derivatives of spectral images taken along the –X and –Y high symmetry directions (upper panels) of detwinnedcrystals of Ba(Fe0.975Co0.025)2As2 taken at 60 K with 62 eV photons reveal a clear splitting of hole-like bands close to the X and Y points,identified from polarization dependence as being principally dyz and dxz character, respectively. Similar measurements of twinned crystals(lower panel) reveal a superposition of the two upper panels. (b) EDCs at the momentum marked by the yellow line of the raw spectralimages corresponding to the spectral images shown in (a). (c) Second derivatives of the EDCs shown in panel (b), revealing that the splittingof the two bands for stressed (detwinned) and unstressed (twinned) crystals is the same within the resolution of the measurement. The curvefor the twinned crystal is offset for clarity. Reprinted with permission from Yi et al (2011).
along two orthogonal directions, manifesting the orthorhombicsymmetry of the electronic structure in the SDW state. Similarresults were obtained by Kim et al (2011).
The most anisotropic feature in the low temperature stateis a pronounced hole-like dispersion near the X and Y points,which evolves from the degenerate hole-like dispersion centredat the same points in the paramagnetic state (figure 22).Consideration of the polarization dependence of the matrixelements (Yi et al 2011) allows an identification of the orbitalcharacter of these bands, which turn out to be principallydyz along –X and dxz along –Y , consistent with orbitalassignments by the non-magnetic local density approximationin the paramagnetic state (Graser et al 2010).
For temperatures well above Ts, cuts along –X and–Y reveal an identical electronic structure, as anticipated forthe tetragonal crystal symmetry (where X and Y refer hereto directions perpendicular and parallel to the compressiveuniaxial stress). As temperature is lowered towards TSDW,the dyz band along –X shifts up and crosses EF whereasthe dxz band along –Y shifts down in energy, resulting in anunequal occupation of the dyz and dxz orbitals. The energysplitting between the originally degenerate dyz and dxz bandsreaches ∼60 meV at 80 K for the parent compound BaFe2As2
(Yi et al 2011).
Since uniaxial stress is used to detwin the single crystals, itis natural to ask whether the applied stress affects the splittingof the dyz and dxz bands. Figure 22(a) shows cuts alongthe –X and –Y directions taken at 60 K for a detwinnedsingle crystal of Ba(Fe1−xCox)2As2 with x = 0.025, forwhich TS = 99 K and TN = 94.5 K, together with similardata for an unstressed sample. Panels (b) and (c) showthe energy distribution curves (EDCs) of the photoemissionintensity and its second derivative for the momentum indicatedby the vertical yellow line in panel (a). As can be seen,within the uncertainty of the measurement, the energy splittingof the two bands is identical in the stressed and unstressedcrystals. It appears that the modest uniaxial stress thatis employed is sufficient to detwin the samples, but doesnot otherwise significantly perturb the band structure forT < Ts. The magnitude of the splitting of the dyz and dxz
bands was measured as a function of cobalt concentration,for both stressed and unstressed crystals at a temperature of10 K (figure 23). These measurements reveal that the bandsplitting is uniformly suppressed together with the latticeorthorhombicity, as anticipated and consistent with the dopingdependence of the dichroism observed in the MIR σ1(ω1) andσ1(ω2) observed in reflectivity measurements for the sameCo concentration (figure 20(b) and section 4).
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Rep. Prog. Phys. 74 (2011) 124506 I R Fisher et al
Figure 23. Doping dependence of the splitting of the dyz and dxz
bands for twinned and detwinned single crystals ofBa(Fe1−xCox)2As2 measured at momentum k = 0.9π/a taken at10 K, with 47.5 eV photons (kz = 0). The energy splitting ismonotonically suppressed with increasing Co substitution, and is thesame for stressed (detwinned) and unstressed (twinned) crystalswithin the resolution of the measurement. Reprinted withpermission from Yi et al (2011).
Finally, we comment on the effect of uniaxial pressure fortemperatures above Ts. For stressed samples a clear splittingof the dyz and dxz bands can be observed for temperatures wellabove Ts (summarized in figure 24—details can be found inYi et al (2011)). This is consistent with the observation of aninduced resistivity anisotropy for stressed samples, and pointsto the presence of a large electronic nematic susceptibilitywhereby a small uniaxial pressure generates a large differencein the band structure in the directions parallel and perpendicularto the applied stress. In contrast, unstressed crystals reveal nosplitting well above Ts, as anticipated for the tetragonal crystalsymmetry. Closer inspection of the data reveals a possiblebroadening or splitting of the bands close to Ts. Unstressedcrystals reveal no features in the resistivity or its derivativein this regime (figures 24 panels (b) and (c)), and hence it isunlikely that there is another phase transition associated withthe onset of static electronic nematic order above Ts. It seemsmore likely that any slight splitting of the bands observed inthe regime close to Ts reflects the effect of nematic fluctuationsclose to the phase transition, or perhaps the presence of a slightrelaxation at the surface which affects Ts relative to the bulk.
6. Discussion
At this stage it is perhaps helpful to briefly summarizethe key results gleaned thus far from measurements ofdetwinned single crystals. dc transport measurements ofthe parent compounds BaFe2As2, SrFe2As2 and CaFe2As2
reveal a modest in-plane anisotropy for temperatures belowTs (Blomberg et al 2011, Chu et al 2010a, 2010b, Tanataret al 2010, Liang et al 2011). The resistivity is found tobe larger along the shorter of the orthorhombic crystal axes,
Figure 24. Temperature dependence of (a) the energy of the dyz anddxz bands for twinned (black data points) and detwinned (red andgreen data points) crystals, (b) the resistivity and (c) the temperaturederivative of the resistivity, for single crystals ofBa(Fe0.975Co0.025)2As2. The data indicate a remarkable sensitivity touniaxial stress of the electronic structure and the associatedresistivity anisotropy for temperatures above Ts. (Figure modifiedfrom data shown in Yi et al (2011) and Chu et al (2010b).)
corresponding to the direction in which the moments alignferromagnetically. Substitution of Co, Ni or Cu suppresses thelattice orthorhombicity (Prozorov et al 2009), but in contrastthe in-plane resistivity anisotropy is found to initially increasewith the concentration of the substituent, before revertingto an isotropic in-plane conductivity once the structuraltransition is completely suppressed (Chu et al 2010b, Kuoet al 2011). Perhaps coincidentally, the onset of the largein-plane anisotropy for the cases of Co and Ni substitutionoccurs rather abruptly at a composition close to the start ofthe superconducting dome. For temperatures above Ts, thereis a remarkably large sensitivity to uniaxial pressure, leadingto a large induced in-plane resistivity anisotropy that is notobserved for overdoped compositions (Chu et al 2010b). Thereis no evidence in thermodynamic or transport measurementsfor an additional phase transition above Ts for unstressedcrystals, implying that the induced anisotropy is the resultof a large nematic susceptibility, rather than the presence ofstatic nematic order. Despite similarities between Co, Niand Cu substitution, preliminary measurements of the in-plane resistivity of Ba1−xKxFe2As2 indicate that the largeanisotropy observed for the electron-doped cases may not befound for the hole-doped system (Ying et al 2011). Reflectivitymeasurements provide valuable insight to the origin of thetransport anisotropy of Ba(Fe1−xCox)2As2. Measurementsof detwinned single crystals reveal large changes in the low-frequency Drude response on cooling through Ts and TN,with a pronounced dichroism (Dusza et al 2011a). For light
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polarized in the AFM a direction, there is an increase inthe scattering rate, but this is accompanied by a dramaticincrease in the SW that ultimately leads to a reduction in thedc resistivity, consistent with observations. For light polarizedalong the b direction, the dominant effect is a reduction inthe SW, consistent with the increase in the dc resistivity.Thus, it appears that the dominant effect on the dc transportin the regime below TN is associated with changes in theelectronic structure, although the scattering rate is also clearlyaffected. It should also be appreciated that the dichroismextends to very high energies, clearly revealing that changesin the electronic structure are not confined to near the Fermienergy (in keeping with a strong-coupling description of thematerial) and is smaller for higher Co concentrations. Inaddition, ARPES measurements provide clear evidence of theassociated changes in the electronic structure. Measurementsof detwinned single crystals of Ba(Fe1−xCox)2As2 reveal anincrease (decrease) in energy of bands with dominant dyz (dxz)
character on cooling through Ts (Yi et al 2011), leading to adifference in orbital occupancy. The splitting of the dxz anddyz bands is progressively diminished with Co substitutionin Ba(Fe1−xCox)2As2 , reflecting the monotonic decrease inthe lattice orthorhombicity (a − b)/(a + b). For temperaturesabove Ts, the band splitting can be induced up to rather hightemperatures by uniaxial stress, consistent with the dichroismobserved in the MIR by reflectivity experiments. Finally,quantum oscillations in the parent compound reveal that thereconstructed FS comprises several small pockets (Terashimaet al 2011). The smallest of these pockets is essentiallyisotropic in the ab-plane, but the other, larger, pockets are muchmore anisotropic.
For temperatures below TN, the FS is reconstructed dueto the AFM wavevector. In this temperature regime, thereflectivity measurements described above clearly show thatthe surprising dc resistivity anisotropy (ρb > ρa) is principallydetermined by anisotropy in the low-frequency Drude SW(i.e. changes in the electronic structure close to the Fermienergy). The scattering rate is somewhat larger along the AFMa direction, but this effect is outweighed by the substantialincrease in SW for E||a. Of equal or perhaps greater interestis the temperature regime above TN for which the FS is notreconstructed. For strained crystals of Ba(Fe1−xCox)2As2,an induced in-plane resistivity anisotropy is evident to hightemperatures. One would like to understand whether thisalso originates from the FS, perhaps due to the differencein the orbital occupancy revealed by ARPES measurements(Chen et al 2010, Lv and Phillips 2011), or from anisotropicscattering, perhaps associated with incipient spin fluctuations(Fernandes et al 2011). Unfortunately the current reflectivitydata do not permit a conclusive answer to this question.Data for x = 0.025 reveal a progressive suppression of thedifference in the SW for E||b and E||a as the temperatureis increased above TN. Similar to the behavior below TN,the total Drude weight from the narrow and broad terms islarger for E||a, but the two polarizations rapidly merge intoa polarization independent constant value approximately 30 Kabove TN. However, for x = 0 the data appear to exhibita large and nominally temperature-independent anisotropy in
the SW to very high temperatures which is larger for E||bthan for E||a. In both cases, x = 0 and x = 0.025, thescattering rate associated with the broad Drude term appearsto remain anisotropic to temperatures considerably higherthan the dc transport anisotropy. The origin of this effect,and also the different behavior of the total Drude weight forthe two compositions, is currently unclear. These differentbehaviors in the parameters determining the dc propertiesmotivate further experiments in the temperature regime aboveTN in order to definitively address the origin of the anisotropyabove the magnetic phase transition.
One of the most striking aspects of the results describedabove, is the non-monotonic doping dependence of the in-planeresistivity anisotropy that is observed for Ba(Fe1−xCox)2As2
and Ba(Fe1−xNix)2As2 (figures 12 and 13). For a multibandsystem, the conductivity tensor is the sum of the contributionsfrom each pocket of the FS. Conversely, if one particularpocket dominates the conductivity tensor, then the transportanisotropy will also be determined by the anisotropy of thatparticular pocket. In the case of BaFe2As2, the reconstructedFS comprises at least three distinct pockets (Terashima et al2011). The angle-dependence of at least one of the frequenciesobserved in quantum oscillation measurements seems to matchthat anticipated for the FS pockets that arise from the protectedband crossing mentioned in section 5 (Harrison and Sebastian2009, Ran et al 2009). Furthermore, the observation of alarge linear magnetoresistance in this compound might alsobe due to the linear dispersion associated with such a Diracpoint (Huynh et al 2010), implying that this pocket is nearthe quantum limit (Abrikosov 1998) and has a relatively highmobility. In a separate ARPES study, Richard et al (2010)found that for BaFe2As2 the Dirac point is very close to theFermi energy, and the associated FS pocket has only a weakin-plane anisotropy, consistent with more recent Shubnikov–de Hass measurements (Terashima et al 2011). It is thereforepossible that the relatively small in-plane anisotropy that isobserved for the parent AFe2As2 compounds (A = Ca, Sr,Ba and Eu) reflects the presence of a high mobility, isotropicpocket of reconstructed FS associated with this Dirac point.Significantly, for Ba(Fe1−xCox)2As2 the onset of the largein-plane resistivity anisotropy occurs for a composition veryclose to that at which earlier ARPES measurements indicatethe disappearance of this small pocket of reconstructed FS(Liu et al 2010). Analysis of the doping dependence of both thelinear coefficient of the magnetoresistance, and also the Hallcoefficient, reveals a progressive erosion of the contributionto the conductivity associated with this pocket over the samerange of compositions (Kuo et al 2011). Taken together,these observations suggest that the onset of the large in-plane resistivity anisotropy is correlated with the progressivesuppression of the contribution to the conductivity arisingfrom the Dirac pocket. That is, the anisotropy associatedwith the other pockets of reconstructed FS can only beappreciated once the contribution from the isotropic pocket isdiminished. Within such a picture, the effect of annealing onthe in-plane resistivity anisotropy in undoped BaFe2As2 (Lianget al 2011) might be understood in terms of changes in therelative contribution to the total conductivity from the different
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pockets of reconstructed FS, though further experiments arenecessary to establish this. In light of this hypothesis, it isinteresting to consider the case of Ba1−xKxFe2As2, for whichpreliminary measurements seem to indicate an essentiallyisotropic resistivity (Ying et al 2011). The difference betweentransition metal substitution and Ba substitution might reflectdifferences in the effect of electron versus hole doping onthe reconstructed FS and/or differences in scattering fromanisotropic spin fluctuations (Fernandes et al 2011). Equally, itis likely that substitution away from the FeAs plane will have aweaker effect on the elastic scattering rate, which in turn wouldmean that the relative contribution to the conductivity arisingfrom the isotropic Dirac pockets would not be diminished asrapidly as for in-plane transition metal substitution, perhapsconsistent with the more isotropic conductivity that is observedfor Ba1−xKxFe2As2 below TN. Further measurements areclearly necessary to provide more detailed information aboutthe evolution of the reconstructed FS for the hole-dopedsystem.
As mentioned in section 1, the origin of the orthorhombictransition has been discussed from the closely relatedperspectives of spin fluctuations (i.e. spin-driven nematicity(Fang et al 2008, Xu et al 2008, Mazin and Johannes 2009,Fernandes et al 2010, Fradkin et al 2010)), and also in termsof a more direct electronic effect involving, for instance,the orbital degree of freedom (Kruger et al 2009, Lee et al2009, Bascones et al 2010, Chen et al 2010, Lv et al 2010,Valenzuela et al 2010, Kontani et al 2011). From theperspective of symmetry, the present measurements cannotdistinguish between these related scenarios, and of course theobservation of in-plane anisotropy is implicit in the symmetryof the orthorhombic phase. Nevertheless, the magnitude ofthe observed effects, including the band splitting observedin ARPES measurements, provides important quantitativetests for more detailed future theoretical descriptions of thenematic phase transition in this material. Similarly, the relativeextent to which uniaxial stress and in-plane magnetic fieldscouple to nematic fluctuations for temperatures above Ts couldpotentially distinguish between pictures that are based on spin-driven nematic order versus orbital order. Such a comparisonrequires quantitative measurements of the pressure dependenceof the induced anisotropy, which at present are unavailable, butnevertheless are entirely feasible.
Arguably the most dramatic effect revealed by all of themeasurements described above is the remarkable sensitivityto uniaxial pressure displayed by the electronic structure fortemperatures above Ts. As mentioned above, quantitativemeasurements of the pressure dependence of the inducedanisotropy (i.e. the nematic susceptibility) as a function ofchemical substitution are not currently available, and wouldclearly be welcome. The current data for Co and Ni substitutedBaFe2As2 appear to indicate that the induced anisotropy islarger (and observed to higher temperatures) as the dopinglevel is increased from the parent compound. The effectpersists up to optimal doping, but is rapidly suppressed on theoverdoped side of the phase diagram. This apparently non-monotonic doping dependence of the nematic susceptibilityis perhaps suggestive of the presence of a quantum critical
point in the phase diagram, but it remains to be seen whethernematic fluctuations play any role in the superconductingpairing mechanism.
Finally, we remind the reader that in this short reviewwe have limited ourselves to a presentation of the currentstate of experimental efforts aimed at revealing the in-planeelectronic anisotropy via measurements of detwinned crystalsof ‘122’ Fe arsenides. It is unclear at this stage which if anyof the results found for this material will be generic for theFe-based superconductors, motivating experiments in otherclosely related families of compounds.
Acknowledgments
This review is inspired by work from several groups, includingthose of the coauthors. We have endeavored to faithfullyreference all of the relevant literature, and apologize in advancefor any inadvertent omissions. From our own collaborationswe are especially indebted to J-H Chu, H-H Kuo, J G Analytis,S C Riggs, M Yi, D-H Lu, C-C Chen, A P Sorini, A F Kemper,B Moritz, R G Moore, M Hashimoto, W-S Lee, T P Devereaux,K De Greve, P L McMahon, and Y Yamamoto (Stanford); S-KMo and Z Hussain (LBNL); Z Islam (ANL); and A Dusza,A Lucarelli, F Pfuner, J Johannsen (ETHZ). We are alsoespecially grateful to S Kivelson, D J Scalapino, P Hirschfeld,S Massidda, J Schmalian, R Fernandez and C Homes for manyhelpful conversations. Work at Stanford is supported by theDOE, Office of Basic Energy Sciences, Division of MaterialsScience and Engineering. Part of the magnetotransportmeasurements were performed at the National High MagneticField Laboratory, which is supported by NSF CooperativeAgreement No DMR-0654118, by the State of Florida, andby the DOE. Work at ETHZ has been supported by the SwissNational Foundation for the Scientific Research within theNCCR MaNEP pool.
Note added in proof. After submission of thisarticle, additional measurements probing the in-plane opticalanisotropy of BaFe2As2 were posted on the arXiv (Nakajimaet al 2011b). These measurements broadly confirm thefindings described above at high frequencies. The temperaturedependence of the optical spectra in the low frequencymetallic part differs among the two investigations, but they areconsistent with respect to the dc properties. The measurementsdescribed in section 4 were performed on as-grown samples,while Nakajima et al used an annealed specimen.
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