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Kinetics of polarization switching in relaxor-ferroelectric Sr0.5Ba0.5Nb2O6 crystaldoped with chromiumR. Z. Rogowski a; K. Matyjasek a; K. Wolska a; S. M. Kaczmarek a

a Institute of Physics, Szczecin University of Technology, Szczecin, Poland

Online Publication Date: 01 November 2008

To cite this Article Rogowski, R. Z., Matyjasek, K., Wolska, K. and Kaczmarek, S. M.(2008)'Kinetics of polarization switching in relaxor-ferroelectric Sr0.5Ba0.5Nb2O6 crystal doped with chromium',Phase Transitions,81:11,1039 — 1047

To link to this Article: DOI: 10.1080/01411590802457946

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Phase TransitionsVol. 81, Nos. 11–12, November–December 2008, 1039–1047

Kinetics of polarization switching in relaxor-ferroelectric

Sr0.5Ba0.5Nb2O6 crystal doped with chromium

R.Z. Rogowski*, K. Matyjasek, K. Wolska and S.M. Kaczmarek

Institute of Physics, Szczecin University of Technology, Szczecin, Poland

(Received 18 May 2008; final version received 5 June 2008)

The kinetics of polarization reversal process in relaxor-ferroelectricSr0.5Ba0.5Nb2O6 (SBN : 50) crystal is studied by switching current registration.The temporal behavior of the polarization is analyzed in terms of the domaindynamics. It has been found that the observed stretched-exponential behavior ofthe polarization relaxation can be the result of a wide distribution of relaxationtimes. It is suggested that the distribution of relaxation times may be attributed toa nonuniform distribution of the local coercive fields within the crystal structure.

Keywords: polarization switching; relaxors; domain dynamics; coercive field

1. Introduction

Relaxors include many compounds, among which the best known are solid solutions oflead magnesium niobate (PMN), first synthesized by Smolenskii and co-workers [1], andsolid solutions of barium–strontium niobate (SBN) [2]. The SBN solid solutions offer anexcellent opportunity to study the mechanism of polarization reversal in relaxor-typeferroelectrics. They are also of great importance in various technical applications due torelatively large values of their characteristic parameters such as pyro- and piezo-electriccoefficients [3], spontaneous polarization [4], and high electro-optic constant [5]. It wasfound that ferroelectric parameters of SBN crystals doped with rare-earth or alkali ionsare more stable and reproducible in comparison with the pure ones [6]. However, in allpractical applications an influence of domain structure and its dynamics is decisive. Thus,investigation of the polarization reversal process in relaxor ferroelectrics (RF), that occursby nucleation and growth of new domains, is very important in this respect. It would allowdetermining the mechanism that controls the switching process in RF and improve itsparameters, meaningful in ferroelectric-based devices (e.g. ferroelectric random accessmemories FeRAM [7]).

Relaxors are disordered systems whose phase transition and temperature anomalies ofall physical properties are significantly broadened over a wide temperature range near theCurie temperature [8]. The ferroelectric-order parameter, the spontaneous polarization like

*Corresponding author. Email: rrogowoski@ps.pl

ISSN 0141–1594 print/ISSN 1029–0338 online

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DOI: 10.1080/01411590802457946

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all other physical parameters characteristic for crystals with no inversion center, does not

vanish spontaneously at the transition temperature. A random-field Ising model was

introduced to account for the observed anomalies that result from structural or

compositional nonuniformities [9]. In the framework of this model, it is assumed that in

RF exist disordered charges that give rise to random fluctuations of the crystalline internal

electric field. The internal bias field strongly influences the kinetics of nucleation andsidewise domain wall motions in ordinary ferroelectrics [10,11]. In such ferroelectric

crystals, the internal bias field manifests itself as a shift of ferroelectric hysteresis loop (HL)

on the electric field axis. However, in the case of the relaxor-ferroelectric SBN crystal

sample under investigation, the asymmetry of P versus E has not been observed. This result

supports the concept of charge disorder that has been widely accepted and evidenced. For

example, Granzow et al. [12] have found that the aging process of SBN doped with Ce ions

was suppressed when the sample was illuminated. They concluded that external

illumination releases the mobile charge carriers, which compensate the sources ofrandomly distributed internal fields, which now cease to block the domain wall motion.

In homogeneous ferroelectrics, the switching process has often been analyzed on the

basis of Kolmogorov–Avrami–Ishibashi (KAI) statistical theory [13]. This model assumes

that the great number of domain nuclei is randomly distributed over the volume of the

crystal and that the domains overlap each other (domain coalescence) as the polarization

reversal proceeds. It has been found that over a very wide range of electric fields, the KAI

model is not a good description of switching processes in RF as it can give physically

unclear values of fitting parameters [14–16].The purpose of the present article is to study the kinetics of slow polarization

relaxation process at constant electric fields in relaxor-ferroelectric SBN crystal doped

with chromium.

2. Experimental details

The single SBN crystal samples were grown by the Czochralski method in an induction

furnace. As starting materials, high-purity powders of SrCO3, BaCO3 and Nb2O5 were

used and the all compounds were mixed in a ratio corresponding to composition of

Sr0.5Ba0.5Nb2O6. Doping was performed by adding Cr2O3 (0.02wt%) in the melt. SBN

crystals are a typical representative of tetragonal unfilled tungsten–bronze-type

compounds in which only five of six available positions of Sr2þ and Ba2þ cations are

occupied. These unfilled sites, randomly distributed in each unit cell, create local lattice

distortion. The SBN crystal undergoes a phase transition from the ferroelectric low-temperature phase (point group 4mm) into the paraelectric high-temperature phase

(4/mmm) so they exhibit 180� domains, and thus, only two possible directions of the

spontaneous polarization can be chosen [17,18]. The phase-transition temperature defined

as the temperature at which the low-frequency dielectric permittivity reaches its maximum,

was found to be 389K [19].Measurements were performed on a c-cut SBN sample (normal to the polar direction)

having an electrode area of 0.3 cm2 and thickness of 1mm. HLs were obtained by means of

a modified Sawyer–Tower bridge using an ac electric field of 50Hz. The switching currents

were measured by applying square-wave electric pulses (two positive pulses followed bytwo negative ones) amplified with a Kepco bipolar amplifier, model BOP500. The voltage

across the 50� resistor, connected in series with the crystal sample, was measured using

a digital oscilloscope. Air-drying silver paste was used as the electrodes.

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3. Results and discussion

3.1. Hysteresis loop

The main characteristic of a ferroelectric material is its HL, obtained when the material isswitched from one saturated state of polarization to another with an external electric field.Figure 1 shows the shape of HL for the examined SBN crystal sample. With the increase ofthe electric field the part of the crystal, which has undergone switching, increases. Theremnant polarization and the coercive field are 17 mCcm�2 and 3.5 kV cm�1 respectively,at an applied field amplitude of 6.8 kV cm�1 (about 2EC). It is seen that the HL is nearlysymmetrical with respect to the electric field axis that indicates the lack of a built-ininternal bias field that would stabilize domain structure in a preferential direction. Thecoercive field, EC, defined as the field at which half of the polarization is reversed, is nearlyindependent of the ac field amplitude. This means that there exists a certain value of athreshold field below which the realignment of domains cannot occur or is least probable.

3.2. Kinetics of polarization relaxation

The measured current transients in static electric fields enable a more detailed discussion ofpolarization switching than the conventional P–E loop method. To measure the switchingcurrents, four square-wave voltage pulses were applied (of 10ms duration). The firstpositive and/or negative pulse will be a switching pulse. The subsequent pulses of the samepolarity (nonswitching pulses) caused the appearance of DC current only, without domainswitching. A true switching current transient was then obtained by subtracting thenonswitching current from the switching one, for a given value of an electric field. Thenthe switching current data were integrated in order to obtain the temporal dependence ofthe switched polarization. It should be pointed out that no backswitching response hasbeen recorded, that corresponds to the symmetry of the HLs and the lack of directionalinternal bias field. Figure 2 shows the field dependence of the polarization recorded forboth positive and negative electric field pulses. It is seen that the switched polarizationincreases with the electric field strength but does not saturate. The electric field of4 kV cm�1 (the upper limit set in this experiment) is not sufficient to obtain a completereversal of polarization in the 10ms pulse duration. Figure 3 presents the time dependence

Figure 1. HL of the examined SBN crystal sample obtained at the external field amplitude of6.8 kV cm�1 (nearly twice EC). The horizontal and vertical large divisions are equal to 2 kV cm�1 and7mCcm�2, respectively.

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of switched polarization obtained after integration of the switching current curves forseveral amplitudes of the external electric field. The observed partial ‘‘freezing’’ ofpolarization may confirm the fact that there are slow switching regions in SBN crystal,that do not contribute to the switching current signals, even in E4EC. This should berelated to the pinning effect of the domain walls in SBN single crystals. As can be seen inFigure 3, two stages of the polarization relaxation can be distinguished. The first one

6

4

2

0

−2

−4

−6

0 1 2 3 4

E. kV/cm

P. µ

C/c

m2

Figure 2. Field dependence of the polarization recorded for positive and negative electric fieldpulses. The negative branch of the polarization was fitted with P(E)� exp(�E/E0)

n formula in orderto calculate the coercive field distribution function.

7

6

5

4

3

2

1

00 2 4 6 8 10

Time ,ms

P, µ

C/c

m2

Figure 3. Temporal dependence of the polarization, obtained by integration of the switching currentcurves for several amplitudes of the external electric field. The polarization data were fitted withKWW functions.

1042 R.Z. Rogowski et al.

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occurs very quickly while the later one represents a remarkable slowing down. In suchcases, the relaxation of the polarization during the switching process can be described bya Kohlrausch–Williams–Watts (KWW)-stretched exponential function P(t)¼P0[1�exp(�t/�)n] with 05n51, that has been widely used in describing many slow relaxationprocesses [20,21]. The fits to the KWW function are represented with dashed curves inFigure 3. The values of the fitting parameters for various electric fields are presented inFigure 3. This type of relaxation was found to apply not only to ferroelectrics, but also toother forms of relaxation, including mechanical, magnetic relaxation, light scattering, andluminescence decay [20]. A stretched exponential behavior with 05n51 has beenaddressed as a dispersive transport or random walk process [22]. It is interesting to notethat the same relaxation law described the relaxing domains on a nanoscale, with PFMimaging of domains configuration in SBN : 61 doped with cerium [23], as well as thepolarization decay during the aging process in this crystal [12].

The stretched-exponential relaxation of the polarization is directly related to thesidewise domain wall motions that move through the pinning and depinning mechanism.Matyjasek et al. [24] have found that the sidewise domain wall velocity is not constantduring the domain wall propagation in SBN crystal doped with Cr and Yb ions. Thefluctuations of the domain wall velocity by nearly two orders of magnitude indicate thatthe doped SBN crystals have a broad distribution of the domain wall mobility. It meansthat they contain pinning centers which stabilize certain regions of the crystal sample whileswitching the rest of the sample in an external electric field. The pinning centers stronglyaffect the properties of polarization reversal and may be responsible for a broaddistribution of domain sizes, as was observed in SBN :Ce crystal at room temperature [25].The presence of pinning centers may be attributed to the charge disorder inherent to dopedSBN crystals. The crystal in its ferroelectric phase contains only needlelike 180� domainsparallel to the crystallographic c axis, so the spontaneous polarization vector can assumeonly two equivalent directions. During the switching, the moving domain walls mayexperience local perturbations of symmetry acting as sources of local internal field. Theperturbations in the domain wall propagation are responsible for the stretched relaxationof polarization especially at the last stage of the switching process. This can be explainedby assuming a broad distribution of relaxation times of regions that independentlyundergo the switching.

In some disordered ferroelectric crystals, the empirical power-law function was used todescribe the polarization dynamics [26]. It is seen in Figure 4, that the power-law functionP(t)¼P0[1�(1þ t/tr)

�k], where P0 is the saturated value of polarization, tr is acharacteristic relaxation time and k is a fitting parameter, can also be used to describethe experimental P(t) data. The fits to the power-law function are represented with brokencurves in Figure 4. As was reported by Gladkii et al. [26], the dimensionless polarizationfunction p(t)¼ [P0�P(t)]/P0 can be related to the distribution function of relaxation times,as a mathematical identity of the power law function is written as

pðtÞ ¼ ð1þ t=trÞ�k¼

Z 10

fð�Þ exp�t

�

� �d�, ð1Þ

where fð�Þ is the distribution of characteristic relaxation times satisfying the commonnormalization condition. By applying the Laplace transformation to the above equality, itis possible to obtain an analytical formula for fð�Þ, which reads

fð�Þ ¼ ½tr�ðkÞ��1 tr

�

� �kþ1exp�tr�

� �, ð2Þ

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where �ðkÞ is the gamma function and k is a fitting parameter that can take values between0 and 1.

Approximating the polarization relaxation curves with the power-law function(as presented in Figure 4), one can obtain the distribution of relaxation times with thehelp of the above formula. Figure 5 shows the distribution functions of relaxation timesfor several amplitudes of the external electric field. One can see that the width of the

Figure 5. Distribution functions of relaxation times for several amplitudes of the external electricfield, calculated with Equation (2).

Figure 4. Time dependence of the polarization for several amplitudes of the external electric fieldfitted with the power-law function.

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distribution function grows as the amplitude of the external field increases. It means thathigher fields are able to overcome the local potential barriers for nucleation in a greaternumber of regions of the crystal. The local barriers for nucleation are related to the localcoercive fields. The probable distribution of EC can be estimated, assuming that thepolarization P is proportional to the volume fraction of the polarized region witha spontaneous polarization PS, as was presented by Gladkii et al. [26]. As is shown inFigure 2, in the case of examined SBN crystal sample, the switched polarizationas a function of electric field P(E) can be well fitted by the following functionP(E)� exp(�E/E0)

n (given by a solid curve in Figure 2), with the parameters n¼ 12.8 andE0¼ 4.2 kV cm�1. Then, the EC distribution function D(EC)¼ dP(E)/dE/PS is a normal-ized distribution of characteristic coercive fields EC, satisfying the normalization conditionR10 DðECÞdEC ¼ 1. Figure 6 presents the probable distribution of the coercive field for theexamined SBN crystal sample obtained on the basis of P(E) data approximation inFigure 2 for the negative electric field pulses. From this figure it can be seen that the mostprobable value of EC (the maximum in the D(EC) curve) is equal to about 2.85 kV cm�1,which almost coincides with the HL half-width (Figure 1).

4. Conclusions

Our results confirm that the slow regime of polarization relaxation can be explained interms of the coercive field distribution D(EC) being a result of charge disorder. Variationof local EC values creates a random distribution of barriers for nucleation which act aspinning centers for the domain walls. The polarization reversal process proceeds in twodistinct time regimes in the examined field range E (E�EC), as can be seen in Figure 3.The fast one is accompanied by domain nucleation and growth in the polar direction andlasts within the time range of tenths of milliseconds, while the slow one is dominated bysidewise domain wall motion and lasts a few milliseconds.

Figure 6. Probable distribution of the coercive fields in the examined SBN crystal sample obtainedon the basis of the P(E) data approximation in Figure 2 for negative electric field pulses.

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It should be emphasized, that the switching current data do not contain information

about the real switching time, needed to complete switching in the whole crystal sample.

This is because it does not include the slow component of sidewise domain wall motion,

which may last over seconds even in electric fields higher than the coercive field.

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