Domain reversal and nonstoichiometry in lithium tantalate...Domain reversal and nonstoichiometry in...

JOURNAL OF APPLIED PHYSICS VOLUME 90, NUMBER 6 15 SEPTEMBER 2001

Domain reversal and nonstoichiometry in lithium tantalateSungwon Kim and Venkatraman Gopalana)

Materials Research Laboratory and Department of Materials Science and Engineering, Pennsylvania StateUniversity, University Park, Pennsylvania 16802

K. Kitamura and Y. Furukawab)

Nano-Materials Laboratory, National Institute for Materials Science, 1-1, Namiki, Tsukuba 305, Japan

~Received 15 January 2001; accepted for publication 24 May 2001!

Recent studies have shown that lithium nonstoichiometry has a tremendous influence on domainreversal characteristics in ferroelectric lithium tantalate. This work presents a systematic study of thedomain reversal characteristics such as threshold coercive fields for domain reversal, domainstabilization times, ‘‘backswitching’’ phenomena, domain switching and wall pinning times, andsideways wall mobility in near-stoichiometric LiTaO3 with Li/ ~Li1Ta!;0.498. These properties arecontrasted with those of congruent LiTaO3 @Li/ ~Li1Ta!;0.485#. A qualitative model is proposedbased on nonstoichiometric dipolar defects to explain the dependence of threshold coercive field ondefect density, and on repeated field cycling, the origin of domain backswitching, and domainstabilization times. ©2001 American Institute of Physics.@DOI: 10.1063/1.1389525#

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I. INTRODUCTION

Ferroelectric lithium tantalate (LiTaO3) and lithium nio-bate (LiNbO3) have emerged as key optical materials in nolinear frequency conversion,1 electro-optics,2 andholography.3 Manipulation of ferroelectric domains into dverse shapes such as gratings, lenses, prisms, andshapes are key to many of these applications. This is pririly achieved by application of an external electric field. Rcent discoveries4,5 show that the threshold coercive fieldrequired for domain reversal change dramatically in thcrystals with changes in lithium stoichiometry. Lithium nostoichiometry also strongly affects the optical, electrical, aelastic properties of crystal lattice near domain walls, anddynamics of domain nucleation and growth as recentlyviewed in detail in a handbook chapter.6 While the domainreversal properties of the lithium-deficient ‘‘congruent’’ composition (C5Li/ @Li1~Ta,Nb)];0.485) have been widely reported~see Ref. 6 and references therein!, limited informa-tion is available so far regarding domain reversal properof stoichiometric (C50.5) or near-stoichiometric crystals.4,5

Any systematic understanding of the role of point defectsdomain reversal characteristics is also lacking at presen

This article attempts to address these two issues aslows. A systematic study of domain reversal characterisof near-stoichiometric (C;0.498) crystals of LiTaO3 is pre-sented. Real-time experiments are presented which tracdividual domain walls and their motion in real time on timscales as small as 0.5 ms. The phenomena of domain slization time, domain ‘‘backswitching,’’ the changesthreshold coercive field with repeated cycling of externelectric field at different frequencies, the switching timewall mobilities, and pinning times are investigated. The

a!Electronic mail: [email protected]!Present address: OXIDE Corp., 9633 Kobuchisawa, Kitakoma, Yaman

408-0044, Japan.

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results are then contrasted with those of congruent comption crystals of LiTaO3. Finally, we propose a qualitativedefect model to interpret some of the observed phenomsuch as internal fields, domain backswitching and stabilition times, and dependence of threshold coercive fieldspolarization cycling.

The article is organized as follows. Sections II–IV, rspectively, present experimental data on crystal growth, rtime domain studies, and polarization reversal characterisof near-stoichiometric composition crystals of LiTaO3. Sec-tion V compares and contrasts the domain reversal charaistics of near-stoichiometric and congruent composition crtals. Section VI presents the defect model followedconclusions in Section VII.

II. NEAR-STOICHIOMETRIC CRYSTAL GROWTHAND PROPERTIES

Stoichiometric crystals of LiTaO3 were grown by thedouble crucible Czochralski~DCCZ! technique as describein detail elsewhere.5,7 Here we briefly describe the salienfacts. In order to grow stoichiometric crystals, a lithium ricmelt ~;60 mol % Li2O! is required. The double crucible geometry consists of an inner and an outer iridium crucibconnected by holes in the wall of the inner crucible. Thallows the growth melt to be replenished with material~inthe outer crucible! in exact proportion to the weight of thcrystal grown from the inner melt using an automatic weiging and powder supply system. The crystals grown alongcrystallographicy axis @lying in the (112̄0) mirror plane#were transparent and crack-free. The Curie temperaturemeasured as 68561 °C, which is very close to the Curietemperature of 69061 °C for sintered stoichiometric LiTaO3powder. Assuming a linear relationship between Curie teperature and crystal composition,8 the crystal compositionLi/ ~Li1Ta! is estimated to be 0.4977–0.4992, which is quclose to the stoichiometric composition of 0.5. We will, however, show that this deviation from stoichiometry is nonethless significant enough to introduce defect fields and in

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2950 J. Appl. Phys., Vol. 90, No. 6, 15 September 2001 Kim et al.

ence the physical properties of these crystals. An impuconcentration of 0.9 wt ppm Fe was measured. Copperchromium were less than 0.1 and 0.2 wt ppm, respectivThe as-grown crystals were observed to be multidomain.crystal was cut into az-cut block, which was annealed in aat 750 °C, and subsequently cooled down at a rate of 2min to room temperature under a dc electric field along thzdirection. These blocks were cut intoz-cut plates of 1031030.25 mm, and optically polished, resulting in plates whiwere single crystal and single domain, though some micdomains of 50mm or less size were also observed. Thstarting state of the crystal will be referred to in the restthis article as the ‘‘virgin state’’ with a ferroelectric polarization of 2Ps .

III. REAL-TIME OBSERVATION OF DOMAIN WALLMOTION IN NEAR-STOICHIOMETRIC COMPOSITION

Starting from the virgin state of a 0.25 mm thickz-cutcrystal, electric field is applied across thez faces to reversethe ferroelectric polarization at room temperature. Tap wais used as electrodes, with no dissolved salts, since disstion of KNO3 salt, for example, to any saturation level dnot appear to change the observed results. The applicatioan electric fieldE3 parallel to thez axis also gives rise to anindex difference 2Dn235no

3r 23E3 across a 180° domain wawherer 23 is the electro-optic coefficient andno the ordinaryindex. This index difference gives rise to scattering of lightthe wall which is optically imaged.9 For example, the domainwall is not visible in Fig. 1~a!, but becomes visible in Fig1~b!, when an electric field of 10 kV/cm~which is less thanthe field required for wall motion! is applied along thez axisof the crystal.

Since the electric field employed for domain reversal calso aid in optically imaging the domain wall, we can stuthe real-time motion of domain walls under electric fieldThe real-time movie was recorded using either a standvideo recorder with 30 frames/s or a high-speed cam~Kodak Ektapro! with 2000 frames/s. The frames were thdigitally extracted from the recorded movie using compusoftware.

Figure 2~a! shows a series of selected optical imagshowing the progression of domain wall creation and motunder an electric field. Also shown in Fig. 2~a! is the corre-

FIG. 1. Optical microscope image, in unpolarized transmitted light, o180° domain wall inz-cut near-stoichiometric LiTaO3 . ~a! No electric fieldapplied. The wall is not visible.~b! An electric field of 10 kV/cm applied tothe crystal along thez axis, rendering the wall visible through the electroptic effect. The polarization is normal to the image plane.


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sponding transient current,i, observed during domain revesal wherei 5dq/dt5d/dt(2PsA). HereA is the area of re-versed domain regions,Ps is the spontaneous polarization,qthe charge, andt the time. The transient currents are in thform of spikes, suggesting a very fast domain wall motiwithin a few milliseconds followed by no domain motioand so on. The video frames shown here, with only a relution of 33 ms per frame, nonetheless show the net dommotion corresponding to the transient current spikesserved in the interval between two frames. F1 shows nomain walls. After one frame interval~33 ms! correspondingto F2, three small domains have nucleated, corresponmost likely to the first three main current spikes seen in F2~b!. The domain merging process is observed betwframes F2 and F3, and therefore frame F3 shows twomerged domains. Finally these two remaining domamerge between frames F3 and F4. It is interesting to noteeven though domain reversal is complete in frame F4, a ftrace of the original domain wall position in F3 is still retained in F4. After;33 ms this contrast disappears resultiin frame F5. This is the faint residual optical contrast alocation of a domain wall after the wall has moved away.arises from residual strains at the domain wall which in tuarise from a small amount of lithium nonstoichiometry in tcrystal and induce optical contrast through elasto-optic efas well as through coupled piezoelectric and electro-oeffects.6 Though faint, and difficult to observe under brigillumination conditions@such as in Fig. 1~a!#, under carefulobservation, this contrast is visible at a wall in neastoichiometric crystals. The total time to reverse a domaina given area is called the switching time,ts , which in Fig.2~a! is 80 ms as determined from the transient current da

IV. THRESHOLD COERCIVE FIELDS, SWITCHINGAND STABILIZATION TIMES, AND WALL MOBILITYIN NEAR-STOICHIOMETRIC CRYSTALS

Under an electric field, the first polarization reversal~orpoling! of a virgin crystal from the ‘‘virgin state’’ to a ‘‘do-main reversed state’’ is termed forward poling~denoted bysymbol f1!, and the second reversal back to virgin statecalled reverse poling~denoted by symbol r1!. Subsequentforward and reverse poling operations are then successilabeled f2, f3, f4,...,etc. and r1, r2, r3,...,etc., respectiveThe polarization hysteresis loop is measured by linearamping the electric field and tracking the transient currecreated during domain reversal. When the spontaneouslarization reverses from1Ps to 2Ps ~or vice versa!, thetotal chargeq, observed under the transient currenti, is q5* idt52PsA, whereA is the electrode area andt the time.The threshold coercive field is arbitrarily chosen as the etric field value at which the integrated charge under the trsient current peak is 1% of the total integrated chargeq un-der the peak. The domain switching times are typicagreater than 30 min at these measured threshold coerfields. This definition was chosen over the conventional dnition of coercive field at 50% domain reversed area, sinwe wanted to measure the lowest threshold coercive fieldwhich reversal begins. In order to study the effect of repeacycling of ferroelectric polarization between1Ps and

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2951J. Appl. Phys., Vol. 90, No. 6, 15 September 2001 Kim et al.

FIG. 2. Tracking domain wall motion under external field in az-cut near-stoichiometric LiTaO3 crystal. Electrode area was 1.2 mm2. ~a! The applied step fieldof ;20 kV/cm and the corresponding transient current response, and~b! the corresponding optical images of the moving wall recorded with a video cam~33 frames/s!. The time instants of the five frames shown in~b! are marked by F1–F5 in~a!.

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2Ps , another experimental variable was introduced calthe cycling time gap,tg, j , wherej 5 f ~for forward poling! orj 5r ~for reverse poling!. This time gap is a measure of thtime gap allowed between the beginning of one domainversal sequence~as monitored by the transient current pea!and the beginning of another. For example,tg,r is the timegap between the beginning of f1 and the beginning osuccessive r1, andtg, f is the time gap between the beginninof r1 and the beginning of a successive f2. In other wortg,r is the longest time period that any part of the crysunder the electrode stays in domain state1Ps ~after its cre-ation! before beingreverse poledinto the 2Ps state. Simi-larly, tg, f is the longest time period that a domain stays in2Ps state~after its creation! before being forward poled intothe 1Ps state.

A. Threshold coercive fields

Figure 3 shows the hysteresis loops of polarization vsus electric field fortg, j5300 and 60 s. The observed thresold coercive fields fortg, j5300 s areEc, f;16.7 kV/cm andEc,r;14.5 kV/cm. For tg, j560 s, the threshold coercivfields decrease toEc, f;13.6 kV/cm and Ec,r;12.3 kV/cm.The internal field,Eint5(Ec, f2Ec,r)/2;1.1 kV/cm for


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tg, j5300 s and 0.7 kV/cm fortg, j560 s. In both cases, thoffset of the hysteresis loop is along the positive~forwardpoling! field axis.

FIG. 3. The polarization hysteresis loops of near-stoichiometricz-cutLiTaO3 crystals. The outer and inner loops are measured for time gapstg, j

spent in any domain state before successive polarization reversal of 30060 s, respectively. Lower time gaps reduce the coercive fields as well asaturation polarizations6Ps .


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For tg, j,300 s the threshold coercive field shows a shdecrease. Figures 4~a! and 4~b!, respectively, show the forward (Ec, f) and reverse (Ec,r) threshold coercive fields asfunction of total cycling timetg, j . The data corresponding tthe shortest time gap,tg, j , was obtained by measuring thstabilization time,tstab,j , for forward and reverse poling. Bthe definition of stabilization time~as explained in the fol-lowing section!, whentg,r5tstab,f , Ec,r50; and similarly, attg, f5tstab,r , Ec, f50. The solid line fits to the measuremen~for tg, j.tstab,j 8! are based on a double exponential functiof the form

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wherei 51,2 and (j , j 8)5( f ,r ) or (r , f ), referring to forward~f! or reverse~r! poling directions. Table I lists the time con

FIG. 4. The dependence of coercive fieldEc, j on the cycling time gaptg, j

for ~a! forward poling (j 5 f ) and ~b! reverse poling (j 5r ) for z-cut near-stoichiometric LiTaO3 . The time axis crossings atEc, j50 are equal to themeasured stabilization times oftstab,j 8 , where (j , j 8)5( f ,r ) or (r , f ). Theseare shown more clearly in the insets. The solid lines are double exponefits as described by Eq.~1!. The fitting parameters are given in Table I.single data point in the negative coercive field range as shown was meafor both forward and reverse poling.


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stantst i , j , tstab,j 8 and the preexponentsEi , j . Note that bydefinition, attg, j5tstab,j 8 , Ec, j50. The relaxation timest i , j

are very similar for forward and reverse poling suggestsimilar relaxation mechanisms. An important aspect of tfigure is the presence of negative threshold coercive fiewhen tg, j,tstab,j 8 .

The presence of negative threshold coercive fieldsFigs. 4~a! and 4~b! appear counterintuitive, but are physicalreal. In this regime the negative threshold coercive fieldfers to the minimum baseline voltage that should be appfollowing the end of the original pulse of widthtg, j in orderto prevent domain backswitching after the pulse. Such baline voltages are often used to stabilize domains createdshort pulses while fabricating domain microengineerdevices.1 The behavior of threshold coercive fields with timgap,tg, j , appears in general to follow a different exponenttime constant for time gaps shorter and longer than thebilization time,tstab,j 8 . The functional form for this behaviofor tg, j,tstab,j 8 is the same as Eq.~1!. In near-stoichiometriccrystals, only one data point could be obtained for the netive threshold coercive field regime due to the short timscales over which they occur. However, for congruent crtals, negative threshold coercive fields~reported in Sec. V!show a clear trend with at least one exponential (j 51) witha corresponding time contant,t i j ~see Table I!. Negativethreshold coercive fields are discussed further in the folloing section and in Sec. V.

B. Domain backswitching and stabilization time

Domain backswitching and stabilization processescongruent LiTaO3 crystals have been previously reported.6 Adomain created by the application of an electric field needcertain minimum amount of time for which the electric fiethat created it should remain and stabilize it. This timecalled the stabilization time, ortstab,j , for the domain andsubscriptj 5( f ,r ) refers, respectively, to forward or reverspoling. If the electric field is removed in a timetg, j

,tstab,j 8 , where (j , j 8)5( f ,r ) or (r , f ), then the newly cre-ated domain shrinks and reverts back to the original domconfiguration that existed before the application of the fieThis reversible domain wall motion is called domain bacswitching. In reality, a range of stabilization times is founsuch that when, for example,tg, f,(tstab,r)start, complete do-main backswitching is observed. Whentg, f.(tstab,r)end, nodomain backswitching is observed. In the intermediate puwidths, partial domain backswitching is observed. The stalization time was measured by applying square electric fipulses with varying pulse widths and electric field magtudes and observing the transient currents.

Figure 5~a! shows the negative transient current respoduring domain backswitching on application of a voltapulse of 60 kV/cm and 10 ms duration. Figure 5~b! showsthe corresponding optical images of the domain walls durthe backswitching process. These images were taken whigh-speed camera capable of 2000 frames/s. The time rlution was therefore 0.5 ms between frames, and the tinstant starting from the beginning of the voltage pulse at50 is indicated on each frame. Domain reversal takes pl

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TABLE I. The fitting parameters in Eq.~1! describing the experimental dependence of coercive fieldsEc, j on the time gaptg, j spent in the previous domainstate as given in Figs. 4 and 10.

LiTaO3 compositionPoling direction E1,j (kV/cm) t1,j (s)

E2 j

~kV/cm! t2,j (s) tstab,j 8 (s)

near-stoichiometric forward 14.5061.50 26.466 2.2161.49 177.56104 0.05860.043poling ~f! 4 3tg, j.tstab,j 8 ; ( j , j 8)5( f ,r )

near-stoichiometric 14.3860.55 32.462.6 0.3360.14 310.36200 0.5560.43reverse poling~r! 0tg, j.tstab,j 8 ; ( j , j 8)5(r , f )

congruent 175.6663.80 20.360.9 31.2963.23 399.6668 0.0560.03forward poling~f! 3tg, j.tstab,j 8 ; ( j , j 8)5( f ,r )

congruent 237.7861.06 0.002760.006 0.0560.03forward poling~f! 6tg, j,tstab,j 8 ; ( j , j 8)5( f ,r )

congruent 100.3768.25 26.563.9 19.8067.82 3166179 0.760.2reverse poling~r! 2tg, j.tstab,j 8 ; ( j , j 8)5(r , f )

congruentreverse poling~r! 2104.0664.19

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until the first 10 ms, when the voltage pulse is on, followby backswitching after the pulse disappears. In this casebackswitching time was.60 ms. When the external pulseshorter, back switching time is;1–10 ms. If the externapulse time is close to stabilization time, back switching timincreases to several hundred milliseconds. Figure 6~a! showsstabilization times (tstab,j )start and (tstab,j )end as a function ofelectric field. Many interesting aspects can be observed.stabilization time decreases rapidly as the electric fieldceeds the threshold coercive field for domain reversal. Ifexternal field exceeds 20 kV/cm in the forward poling andkV/cm in reverse poling, the stabilization times are relativeinsensitive to the electric field magnitude and are appromately (tstab,f)start;300 ms, and (tstab,r)start;30 ms. The sta-bilization time in forward poling is;10 times higher than inreverse poling at the same electric field. Figure 6~b! shows alogarithmic plot of the dependence of stabilization timethe electric field. An exponential dependence is found(tstab,j )start as a function of electric field for most of the fielrange except for fields very close to the threshold coercfield in forward poling geometry. Dropping the subscri‘‘start’’ we can write this dependence as

tstab,j5tstab,jo expS dstab,j

E2Ec, jD , ~2!

where j 5 f or r, the activation values aredstab,f51.7260.32 kV/cm anddstab,r511.661.67 kV/cm. The preexponents values are ln@tstab,f o(ms)#55.660.05 andln@(tstab,ro(ms))#52.0860.53.

Referring back to the discussion of Fig. 4 in Sec. IVwe now briefly discuss the negative threshold coercive fiewhen the cycling timetg, j is below the pulse stabilizationtime tstab,j 8 where (j , j 8)5( f ,r ) or (r , f ). As an example, leta square electric field pulse withE.Ec, f and a pulse width


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of approximately equal to, but slightly smaller tha(tstab,f)start be applied to the crystal in forward poling. Domain reversal~forward poling! takes place during the pulsduration, and domain backswitching~reverse poling! takesplace immediately after the pulse has ended and the elefield E is zero. In this situation, the external electric fierequired for reverse poling is zero, i.e.,Ec,r;0 and tg,r

;(tstab,f)start. This defines the zero crossing of the threshocoercive field curve in Fig. 4~b!. When the pulse width of theexternal pulse is much less than (tstab,f)start, Ec,r,0 in Fig.4~b!, implying that a short electric field pulse of magnitud>Ec,r in the forward poling direction would be neededprevent domain reversal in the reverse poling direction frtaking place during backswitching. A similar case can alsomade for negativeEc, f in Fig. 4~a! by interchanging thephrase ‘‘forward poling’’~and subscriptsf! and the phrase‘‘reverse poling’’ ~and subscriptsr! in the above arguments

C. Switching times

Figure 7 shows electric fieldE versus switching time,ts, f ~during forward poling! and ts,r ~during reverse poling!,respectively. Switching time here is interpreted as the totime required to switch the entire electrode area~20 mm2 inthis case!. Two sets of data are shown, one fortg, j5300 sand tg, j540 s. Fortg, j5300 s two distinct activation fieldsappear to be present for each of the forward and revedomain reversal processes that follow the exponenswitching time relationships given by

ts, j5ts, jo expS d j

E2Ec, jD , ~3!

where j 5 f or r. By this definition, when the electric fieldE5Ec, f or Ec,r , the switching timests, f and ts,r tend to


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infinity. For practical purposes, the extrapolated switchtimes at the measured threshold coercive fields are grethan 30 min in our case. A logarithmic plot of electric fieldEversus switching timets, f in Fig. 7~b! shows the differentactivation field regimes more clearly. Table II lists the acvation fieldsd f , d r and the preexponentst f o and t ro .

Some key observations are as follows.~1! Switchingtime decreases with decreasingtg, j following a similar trendas the threshold coercive fields in Fig. 4. As already sho~see Fig. 4!, decreasing time gaptg, j results in a decreasinthreshold coercive fieldEc, j . For a fixed external electricfield, a decrease in threshold coercive field will result ingreater mobility of the domain wall and therefore a decrein the switching time, which qualitatively explains this oservation.~2! For tg, j5300 s, the switching times in the for

FIG. 5. Tracking domain ‘‘backswitching’’ phenomenon inz-cut near-stoichiometric LiTaO3 following the application of a forward poling electrifield pulse of 60 kV/cm and 10 ms width at timet50 ms. Electrode areawas 20 mm2. ~a! Voltage~broken line! and transient current~solid line!. ~b!The corresponding selected video frames using a 2000 frames/s camerfirst six frames of optical microscope images show forward switchingmain motion. A large domain wall sweeps away smaller domain nucleatstarting from the top right corner to bottom left corner. After a 10 ms framdomain backswitching is captured starting from the bottom left corner.time elapsed from the start of the voltage pulse for each frame is mark


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ward and reverse poling regimes show two distinct slo~activation fields! for low and high external field regimes, thslope being considerably higher in the high field regime.~3!For tg, j540 s, the distinction between high and low fieregimes disappears, resulting in only one field regime. Insingle regime, the switching times as well as the activatfields are equal for the forward and reverse poling as listeTable II. For shorter time gaps,tg, j approaching the stabili-zation timetstab,j 8 , the difference between threshold coercifields Ec, f and Ec,r become similar as seen from Fig. 4,both of these quantities rapidly tend to zero. The switchtimes therefore become similar as will be seen here. Tdifferences in forward and reverse threshold coercive fieand switching times are accentuated only for long time gatg, j .

D. Wall mobility

As seen in Fig. 2, the transient current shows a serievery sharp spikes on the order of milliseconds even aconstant driving field. Real-time video confirms this to co

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FIG. 6. ~a! The forward and reverse stabilization timeststab,j wherej 5 f forforward poling and j 5r for reverse poling in near-stoichiometricz-cutLiTaO3 crystals. The subscript ‘‘start’’ refers to the time gaptg, j5tstab,j 8 ,( j , j 8)5( f ,r ) or (r , f ) below which complete domain backswitching is observed, and ‘‘end’’ refers to the time gap above which no backswitchoccurs. ~b! A log plot of the same information as in~a!, linear fits areaccording to Eq.~3!. The coercive fieldsEc, f518.7 kV/cm and Ec,r

514.4 kV/cm.


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FIG. 7. ~a! The domain switching time forz-cut near-stoichiometric LiTaO3crystals in forward~f! and reverse~r! poling for various time gaps,tg, j , j5( f ,r ). The electrode area was 20 mm2. ~b! A log plot of the same infor-mation as in~a! the solid lines are fits according to Eq.~3!. The coercivefields Ec, f518.7 kV/cm andEc,r514.4 kV/cm for tg, j5300 s andEc, f

51.36 kV/cm andEc,r51.23 kV/cm fortg, j540 s. The activation field andpreexponents from the fit are listed in Table II.


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tion occurs over a few milliseconds or less during the occrence of transient current spikes. These spikes are sporand are often separated by seconds or minutes, in wtime, no domain motion is seen on the macroscopic lenscales~.10 mm!. Since the regular VCRs with 30 framesdo not have the dynamic time range of milliseconds-minutes, real-time measurement of domain mobility is nfeasible. At higher electric fields of.22 kV/cm, which liewell within the high field regime discussed in Sec. IV C, tswitching times are in the millisecond range, and the trsient current shows peaks which are merged into each oas shown in Fig. 8~a!. The fast domain wall velocities wermeasured with a high speed charge coupled device cam~Kodak Ektapro! capable of 2000 frames per s in real timFigure 8~b! shows a series of images from real-time domamotion with a time resolution of 0.5 ms between frames. Inoted that domain walls still show pinning and sporadic mtion at these high fields. At all the studied fields, a singdomain wall front was observed to sweep across the viscreen in this particular sample area. Two parameters wmeasured from these real-time images: the maximum domwall velocity of this wall, vs, f and the pinned time,tp, f ,spent by this domain wall in a pinned state, when it is nmoving.

Analyzing video frames in Fig. 8~b! and other similarones at different electric fields shows that the measumaximum sideways wall velocitiesvs, f increase with electricfield. The maximum pinning timetp, f and switching timets, f

decrease with electric field. These are plotted in Fig. 9~a!.Figure 9~b! shows the relative time fractiontp, f /ts, f that thedomain front spends not moving, as a function of electfield. It is clear that the domain wall pinning dominates ttotal switching timets, f at lower electric fields. Based oMiller–Weinreich analysis,10 we assume an exponential velocity dependence on electric field as

vs, j5vs, jo expS 2as, j

E2Ec, jD , ~4!

wherej 5 f or r. The velocity data is replotted as a log plotFig. 9~c!. Our experimental measurements of the velochave very low scatter in the high field regime as compared

e-
TABLE II. The fitting parameters for switching timests, j in Eq. ~4! obtained from transient current measurments in near-stoichiometric~Fig. 7! and congruent~Ref. 13! compositions of LiTaO3 .
Crystal;~coercive fields!

Poling direction;tg, f Field regimes

d j (kV/cm);j 5( f ,r )

ln@ts,jo(ms)#;j 5( f ,r )

Near-stoichiometricLiTaO3

forward ~f!tg, f5300 s

E2Ec, f.13.9 kV/cm 26.4862.1 2.1 60.10

E2Ec, f,13.9 kV/cm 5.3460.2 3.1860.10

~Ec, f518.7 kV/cmEc,r514.4 kV/cm!

reverse~r!tg,r5300 s

E2Ec,r.16.1 kV/cm 33.4 62.1 1.9860.08E2Ec,r,16.1 kV/cm 19.8561.4 2.2 60.34


E.Ec, f 64.7361.3 1.5760.05

reverse~r!tg,r540 s

E.Ec,r 70.0562.3 1.3960.10

CongruentLiTaO3


E2Ec, f.3.8 kV/cm 51.4 65.9 20.4 61.04E2Ec, f,3.8 kV/cm 1.4960.5 11.3560.35

(Ec, f5211 kV/cm) reverse~r!tg,r5300 s

E2Ec,r.2.1 kV/cm 36.9365.0 21.8 61.03E2Ec,r,2.1 kV/cm 0.9560.5 10.4460.76


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the larger scatter in the low field measurements wheredom pinning events dominate. A linear fit in the high fieregime alone (E2Ec, f.19 kV/cm) gives ln@l/vfo(s/mm)#526.5960.06 andas, f522.0962.17 kV/cm, which doesnot extrapolate well into low field regime data. Thereforeconclude that the data really represents two field regimFor E2Ec, f,19 kV/cm, the scatter in the measured velocdata is large, and therefore a range of activation fields exwith a mean value ofas, f;6.8 kV/cm. The fitting param-

FIG. 8. High speed, real-time tracking of domain motion inz-cut near-stoichiometric LiTaO3 under a forward poling external field of 30 kV/cmThe transient current~a! and the corresponding optical images~b! using ahigh speed camera~Kodak Ektapro! capable of real-time 2000 frames/s. Thtime instant,t elapsed after the application of field att50, is also marked ineach frame.


n-

s.

ts,

eters are summarized in Table III. We assume an exponebehavior of the pinned timetp, f as a function of electric fieldE as

tp, f5tp, f o expS dp, f

E2Ec, fD , ~5!

FIG. 9. ~a! Analysis of the switching timets, f , the maximum pinning timetp, f , and the sideways wall velocityvs, f , analyzed from the video frameshowing domain motion in Fig. 8~b!. ~b! The ratio of the pinning time to theswitching time,tp, f /ts, f , indicating that at lower electric fields the pinnintime dominates the switching time.~c! The log plots ofts, f , vs, f , and tp, f

plotted according to Eqs.~3!–~5!, respectively. The coercive fieldsEc, f

518.7 kV/cm. The fitting parameters to the linear solid line fits are givenTable III.


g.


TABLE III. The fitting parameters for switching timets, f , pinning timetp, f , and sideways wall velocityvs, f measured from the real-time video data in Fi8~b! during forward poling in near-stoichiometric LiTaO3 . The results for congruent crystals~Refs. 9 and 13! are also given for comparison.

Crystal;~coercive field! ts, f , vs, f , or tp, f

Electric fieldregimes

Activation fieldsds, f

or as, f (kV/cm)Pre-exponential factors

ln(ts,fo), ln(1/vs, f o), ln(tp,fo)

Near-stoichiometricLiTaO3

~Ec, f518.7 kV/cmEc,r514.4 kV/cm!

ts, f E2Ec, f.20 kV/cm ds, f520.8660.75 ln@ts,fo(ms)#53.1560.22

E2Ec, f,20 kV/cm ds, f56.860.54 ln@ts,fo(ms)#53.9060.60vs, f E2Ec, f.19 kV/cm as, f522.0962.17 ln@1/vs, f o(s/mm)#526.5960.06

E2Ec, f,19 kV/cm as, f56.862.39 ln@1/vs, f o(s/mm)#52.2060.34tp, f E2Ec, f.18 kV/cm dp, f570.561.78 ln@tp,fo(ms)#520.5860.32

E2Ec, f,18 kV/cm dp, f54.860.91 ln@tp,fo(ms)#52.7060.10

Congruent LiTaO3 ts, f E2Ec, f.3.8 kV/cm ds, f551.465.88 ln@ts,fo(ms)#520.4061.04(Ec, f5211 kV/cm)

E2Ec, f,3.8 kV/cm ds, f51.4960.52 ln@ts,fo(ms)#511.3560.35vs, f E2Ec, f.4 kV/cm as, f542.56 ln@1/vs, f o(s/mm)#522.95

E2Ec, f,2 kV/cm as, f50.46 ln@1/vs, f o(s/mm)#510.09

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and overlay this plot as well in Fig. 9~c!. In addition, forcomparison we plot the switching timets, f obtained from thevideo data on the same plot. The fitting parametersswitching time@Eq. ~3!#, sideways wall velocity@Eq. ~4!#,and pinning time@Eq. ~5!# are presented together in Table IIAll three physical properties show a discontinuity aroundfield range ofE2Ec, f518– 20 kV/cm. In the higher electricfield regime (E2Ec, f.19 kV/cm) the activation fieldsas, f(;22 kV/cm) for the sideways domain wall velocity anthe activation fieldd f(;21 kV/cm) for the total switchingtime are similar, while that for pinning timedp, f

(;70.5 kV/cm) is significantly higher, indicating that sidways domain wall motion dominates the switching timets, f

in this field regime. In the low electric field regime (E2Ec, f,19 kV/cm), the activation fieldsdp, f , as, f , andd f

are all similar. However, the magnitude of switching timedominated by the pinning time in this regime as seen in F9~b!.

V. COMPARISON OF NEAR-STOICHIOMETRICAND CONGRUENT COMPOSITION CRYSTALS

Many of the polarization reversal properties depestrongly on the lithium nonstoichiometry in LiTaO3 andLiNbO3. This section compares and contrasts the congru@Li/ ~Li1Ta!;0.485# and near-stoichiometric @Li/ ~Li1Ta!;0.4977–0.4992# compositions of LiTaO3.

The most dramatic difference is that the threshold cocive field required for domain reversal in congruent LiTa3

is ;210–220 kV/cm for forward poling and;110–120kV/cm for reverse poling direction at room temperature. Tinternal field is thereforeEint;45–50 kV/cm. This contrastswith threshold coercive fields of 17 kV/cm for forward an15 kV/cm for reverse poling directions, and therefore anternal fieldEint;1 kV/cm in the near-stoichiometric crystastudied here. In lithium niobate similar large changesobserved, and the variation of threshold coercive fields wlithium concentration,C5Li/ ~Li1Nb), is found to be ap-


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proximately linear in this composition range.4 This linearity,though not strictly confirmed in isostructural LiTaO3, is alsoexpected.5

Another clear difference is the domain wall contrast uder optical microscope at room temperature. In congrucrystals, domain walls are easily observed under an optmicroscope without any external field. The region adjacenthese walls has been shown to possess optical birefringen11

of 1025 to 1024, lattice strains,12 and local electric fields.6

On the other hand, in near- stoichiometric crystals, optibirefringence is significantly lower~estimated well below1026!, and strains can hardly be observed even with x-synchrotron imaging. Therefore there is a close relationsbetween lithium nonstoichiometry and domain wall struture. The local relaxation of point defect dipoles arising frononstoichiometry in the region of the domain wall leadsthe observed strains, fields, and optical birefringence.

The variation of threshold coercive fields with repeatpolarization cycling shows similarities and differencescongruent and near-stoichiometric composition crystals. Fure 10 shows the threshold coercive fieldEc, j versus timegap tg, j for congruent LiTaO3. Like near-stoichiometriccrystals, congruent crystals also show large negative throld coercive field when the time gap is shorter than its sbilization times. Again, the data point for the zero crossingthe field axis was obtained from the stabilization timetstab,j 8where (j , j 8)5( f ,r ) or (r , f ). Similar to the measurementon near-stoichiometric crystals shown in Fig. 4~a!, this mea-surement on congruent crystals can be fit to multipexponential curves given by Eq.~1!. However, one clearlynotes that the fit for the negative threshold coercive fielddifferent from that for positive threshold coercive field, wia discontinuity of the derivative at the zero field crossicorresponding to the stabilization time. In Table I the paraeters for this fit are shown, with the caveat that the zero tigap intercept for the fit to negative coercive fields has launcertainty due to the very small time gaps involved. Bostoichiometric and congruent crystals show an abrupt


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crease in threshold coercive field attg, f;5 min. For timegaps longer than stabilization time, near-stoichiometric copositions exhibit time constants oft1,f526 s and t2,f

5177 s, while congruent compositions exhibitt1,f529 s andt2,f5523 s. The time constantst i , j are very similar for bothcompositions even though the magnitudes of threshold ccive fields show an order of magnitude difference. This iplies that even though the defect densities in the two copositions are very different, the relaxation mechanism occby the same underlying physical phenomenon. In Sec. VIpropose such a mechanism based on slow reorientatiodefect dipoles following polarization reversal.

The switching times for congruent and stoichiometcompositions exhibit similarities and differences as well. Tswitching timets, j as a function of external electric fieldE2Ec, j for congruent crystals is shown in Fig. 11. Showoverlapped are the switching times for stoichiometric crtals as well. Note that these measurements for congrcrystals were reported before in literature, but were plotted

FIG. 10. The dependence of coercive fieldEc, j as a function of the cyclingtime gaptg, j for forward and reverse poling forz-cut congruent LiTaO3 ,where~a! j 5 f and ~b! j 5r . The time axis crossings atEc, j50 is equal tothe measured stabilization time oftstab,j 8 , where~a! ( j , j 8)5( f ,r ) and ~b!( j , j 8)5(r , f ). This crossing and the negative coercive fields are shomore clearly in the insets. The solid line is a double exponential fit fortg, j

.tstab,j 8 and a single exponential fit fortg, j,tstab,j 8 as described by Eq.~1!.The fitting parameters are given in Table I. The inset schematic describemeaning of negative coercive field as a minimum baseline voltage followthe main pulse needed to prevent domain backswitching after the end opulse.


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a function ofE2Eint .13,14 However, based on the expone

tial relationship between switching time and electric fie@see Eq.~3!#, at E5Ec, j the switching time goes to infinityThis is physically more realistic than assuming the sathing atE5Eint as was done in Refs. 13 and 14. Both cogruent and stoichiometric crystals exhibit two distinct eletric field regimes ofE2Ec, j , where the activation fieldsd j

are different. These activation fields are listed in TableNote that in the high field regime, the activation fields fboth congruent and near-stoichiometric LiTaO3 are similarindicating again a similar mechanism for domain wall mtion. In the low electric field regime, the domain wall pinning dominates the switching time as shown earlier in F9~b!. This is true for both near-stoichiometric and congruecompositions. However, since the nonstoichiometric defdensity is lower in the near-stoichiometric crystals, the pning process and hence the switching time is quite randand varies drastically from one area of the same samplanother. With higher defect density in congruent LiTaO3 thisvariance from area to area decreases. The difference inswitching time behavior with field in the low field regimbetween the near-stoichiometric and congruent compositis a direct result of this process. Note that implicit in thargument, we are proposing that the pinning sites arecorrelated with nonstoichiometric defects or defect agggates. This proposition is supported by the fact thatthreshold coercive field in congruent crystal appears to bpinning–depinning transition. Small reversible pinning abending of a domain wall locally on micrometer lengscales has been observed11 in congruent crystals at fields oE,20 kV/cm which is an order of magnitude lower than tthreshold coercive field of;210 kV/cm. Since the thresholdcoercive field also changes drastically with point defect ccentration, the process of pinning and the actual pinning sthemselves must be correlated with point defects. We ppose below that the point defect complexes have an electdipole, which prefer to orient parallel to the lattice polariz

n

theghe

FIG. 11. The domain switching times forz-cut congruent LiTaO3 crystals inforward for time gapstg, f5300 s. The linear solid line fits are accordingEq. ~4!. The coercive fieldsEc, f5211 kV/cm for congruent LiTaO3 . Theactivation field and preexponents from the fit are listed in Table II. Aoverlapped for comparison are the switching times forz-cut near-stoichiometric LiTaO3 crystals from Fig. 7~b!. The electrode area was 2mm2 for both cases.


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tion. Simple electrostatic calculations then show that theran energy barrier associated with a domain wall havingcross a defect dipole in its path, which is the precise rolea pinning site.

The concept of stabilization time also is closely relatto the presence of point defect dipoles in the crystal. At rotemperature, the stabilization times for forward and revepoling in congruent LiTaO3 are tstab,f51.4– 2 s andtstab,r

50.1– 0.3 s, respectively. On the other hand, the near-ichiometric composition exhibits stabilization timeststab,f50.25– 0.9 s andtstab,r50.015– 0.1 s. Both compositions show an order of magnitude difference betweentstab,f

and tstab,r . In addition, the stabilization times for congruecompositions are an order of magnitude larger than thatstoichiometric crystals in both forward and reverse poldirections. In the following section we present a modwhere the origin of domain stabilization time is proposedbe directly related to the time taken for the slow reorientatof the electrical dipole moment associated with the moment of TaLi defect ions through close packed oxygen planLonger stabilization times in congruent crystals suggestthis movement of the defect ion is slower in congruent crtals as compared to near-stoichiometric crystals. The difence in forward versus reverse stabilization time in ecomposition arises from the fact that the lithium vacancVLi surrounding a TaLi defect ion do not rearrange around tnew TaLi position after domain reversal at room temperatuthus creating a frustrated defect dipole. These are explain greater detail in the following section.

Figure 12 shows the sideways wall velocityvs, f as afunction of electric fieldE2Ec, f for congruent LiTaO3.10

The wall velocity of independently growing domains isorder of magnitude lower than merged, serrated domfronts as reported earlier due to preferential nucleationthe serrations at the domain walls.10,14 We note that the behavior of switching timets, f and sideways wall velocity1/vs, f , as a function of electric fieldE2Ec, f , show similari-ties in both congruent and stoichiometric compositions. Bswitching timests, f and inverse sideways wall velocity 1/vs, f

FIG. 12. Sideways wall velocityvs, f as a function of electric field forz-cutcongruent LiTaO3 . The measured coercive fieldEc, f5213 kV/cm. Solidline fits are according to Eq.~5!. The fitting parameters are listed in TabIII.


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show two electric field regimes where the activation fieldsd f

and as, f change from one regime to another. These elecfield regimes are similar, as are the activation fieldsd f andas, f for the switching times and the sideways wall velocitierespectively. In congruent composition, the high electric firegime is E2Ec, f.3.8 kV/cm for switching time andE2Ec, f.4 kV/cm for sideways wall velocity. The activatiofields ared f;51 kV/cm andas, f;43 kV/cm in the high fieldregimes andd f;1.5 kV/cm andas, f;0.5 kV/cm in the lowfield regime. In the near-stoichiometric composition, the helectric field regime isE2Ec, f.14 kV/cm for switchingtime andE2Ec, f.17 kV/cm for sideways wall velocity. Theactivation field values are d f;26 kV/cm and as, f

;22 kV/cm in the high field regime and d f

;5.4– 6.8 kV/cm andas, f;6.8 kV/cm in the low field re-gime. @The as, f in the low field regime is very approximatdue to a large scatter in the velocity data in Fig. 9~c!.# Thesecomparisons show that while the actual magnitudes ofthreshold coercive fields and wall velocities are very diffeent in the congruent and the stoichiometric compositiothere are strong similarities. Above the threshold coercfield, the electric field shows at least two distinct rangesboth cases, which we denote as low and high electric firanges. The domain wall pinning is dominant in the low fieregime, and wall velocity is dominant in the high field rgime in both compositions.

VI. DEFECT DIPOLES AND DOMAIN REVERSAL

In this section we present a defect model based on nstoichiometric dipolar defects in LiTaO3. This model isbased on the basic concept of bulk dipolar defect complegiving rise to domain stabilization and internal fields in feroelectrics as has been detailed in the works of Arl15

Lambeck,16 and Warren.17 The model provides a qualitativexplanation of the domain reversal processes such as thependence of threshold coercive field on defect density andrepeated cycling at different frequencies, the phenomendomain stabilization time, and that of domain ‘‘backswitcing’’ in lithium niobate and tantalate.

A. Nonstoichiometric dipolar defects

A comparison of stoichiometric and congruent crystmakes it clear that nonstoichiometry in LiTaO3 is intricatelyrelated to the domain wall structure and kinetics.6 The abovediscussion raises the question as to what the exact natunonstoichiometric point defects or defect complexes is. Blow we will discuss defect models in isostructural congrueLiNbO3 which has been more extensively studied. We wthen draw a parallel between defect models in LiNbO3 andLiTaO3 based on the fact that they have the same latstructure, threshold coercive fields, switching times, interfields, domain wall contrast, and phenomena of domain wpinning and stabilization, differing only in the magnitudesthese effects.6

In congruent composition of LiNbO3, Prokhorov andKuzminov18 concluded that lithium vacancies (VLi)

1 andoxygen vacancies (VO)21 dominate at room temperaturecorresponding to a congruent defect [email protected]#[email protected]# which we refer to as model I


l ofe.


FIG. 13. Schematic of defect dipoles in nonstoichiometric lithium tantalate at room temperature, composed of 4@TaLi41#5@VLi

2#. Schematics~a! and~c! showstable low energy defect configurations in1Ps and2Ps domain states, respectively. Schematic~a! shows a frustrated defect state after domain reversastate~a! by an external electric field at room temperature. State~b! will relax to state~c! after~b! is annealed at.200 °C and cooled back to room temperatur

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However, the density of LiNbO3 increases with increasinlithium deficiency which is incompatible with the oxygevacancy model.19 Schirmeret al.concluded that niobium antisites (NbLi)

41 and niobium vacancies (VNb)52 are the

dominant point defects and that oxygen vacancy is presemost in negligible concentrations, except when brute fotreatments such as high energy electron irradiationapplied.20 The chemical formula for this defect model sugested by Abrahams and Marsh [email protected]#[email protected]#O3, to be referred to as model II. HoweveDonnerberget al.21 showed that the formation of a niobiumvacancy was found to be energetically unfavorable as cpared to the formation of a lithium vacancy. The third prposed defect model~model III! is the presence of niobiumantisites (NbLi)

41 and lithium vacancies (VLi)2.22 The neu-

tron diffraction studies by Iyiet al.23 and Zotovet al.24 sup-port this defect model with a chemical [email protected]#NbO3. Schirmeret al.20 point out that theniobium vacancy model and the lithium vacancy model cbe reconciled if it is assumed that there are ilmenite tystacking faults in the regular LiNbO3 crystal structure. How-ever, a different suggestion has come from Ivanova andsenkoet al.25,26 who have recently interpreted the nuclemagnetic resonance~NMR! spectra in congruent LiNbO3.They conclude that at room temperature, a combinationmodels I and III in a ratio of 1.1:1.0 would provide a ‘‘rathegood qualitative and quantitative agreement with the NM7Li spectra.’’ However, the authors assert that only the moIII ~with allowance for mobility of Li1 ions in LiO6 octahe-dra! can explain the temperature dependence of the expmental NMR7Li and 93Nb spectra from 77 to 4.2 K. Accordingly, the authors propose the structure of a defect compas comprising of a niobium antisite surrounded by three L1

vacancies in the nearest neighborhood, plus one indepenLi1 vacancy along the polarz direction. Yatsenko27 has alsoreported that the preliminary analysis of the structural distions caused by a NbLi antisite defect reveals a contractionthe nearest three oxygen atoms, and a displacement fromc axis of the nearest three93Nb nuclei. This defect complexcomprising of one NbLi with four VLi certainly possesses a


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electrical dipole moment, arising primarily along thez axisfrom antisite NbLi itself as well as from the relative arrangement of VLi around the antisite. This defect model is alsupported by x-ray and neutron diffuse scattering of congent LiNbO3 reported by Zhdanovet al.,28 Ivanovet al.,29 andmost recently by Zotovet al.30 These studies conclude thathe diffuse lines in scattering arise from a one-dimensio~1D! displacive and substitutional disorder in the thrpseduo-cubic directions along the Li–O–Li–¯ chains.These directions correspond to pseudo-cubic [email protected]#, @22̄.1#, and @42.1# ~in orthohexagonal notation!which are related to each other by the threefold symmeaxis~polarizationc axis! and are inclined at 52° to thec axis.Diffuse maxima around the Bragg positions reflect sothree-dimensional~3D! short-range order of the defect elements and the homogeneous part of the diffuse planes icate random distribution of the defect clusters. Since eniobium antisite requires four lithium vacancies in the neigborhood for overall charge neutrality, Zotovet al.30 suggestchains such as Li–NbLi –h–Li, Li– h–NbLi –h,Li–h–h–NbLi, etc. as possible combinations.

Figure 13 shows a possible schematic of the equilibristates of a defect complex for an up and a down domUpon domain reversal, the niobium antisite defect movesthe neighboring octahedron by movement of NbLi throughthe close-packed oxygen plane. The lithium vacancaround the original defect in Fig. 13~a! need to rearrangearound the new antisite position to reach the stable deequilibrium state of Fig. 13~c!. At room temperature, a lackof lithium mobility can result in the frustrated state of defecomplex as shown in Fig. 13~b!, which can be relieved intostate~c! after a high temperature anneal. However, as poinout by Nassau and Lines,31 the presence of two niobium ionin adjacent oxygen octahedra can be energetically unfaable due to dense positive charge around the cluster. Tpropose extended stacking fault defects in the structure.tov et al.,30 however, restrict the size of such clusters;11.4 Å ~about four cation sites! in order to match the cor-relation lengthLc;13 Å along the chains calculated from thfull width at half maximum of the diffuse streaks in x ra


. 13. Ea

zation


FIG. 14. A schematic describing the process of forward domain reversal and domain backswitching in the presence of dipolar defects shown in Figchof the five schematics~a!–~e! shows the voltage pulseV and the transient currenti ~top!, followed by the corresponding potential energy well~below! for thelattice polarization in the presence of defects at the time instantt denoted by a gray circle in the voltage pulse schematic. The notations are lattice polariPs ~denoted by↑ or ↓!, defect dipole associated with TaLi antisite defect~denoted byD or F!, defect dipole associated with the arrangement ofVLi ~denotedby d or f!, the time gaptg,r that domain spends in the2Ps state before being forward poled to the1Ps state, and stabilization timetstab,r .

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The average spacing between defect clusters along the cis estimated to be;76 Å. The temperature dependencediffuse x-ray streaks30 suggest that at low temperatures, tlateral correlations between defect clusters become qsubstantial. With increasing temperature, these correlatdecrease, resulting in more random 1D disorder. The chain the threshold coercive and internal fields with temperatas reported by Battleet al.32 also point to the breaking up othe 3D clusters with heating followed by reformation of tdefect dipole in an energetically favorable orientation upcooling down to room temperature.

B. Backswitching and internal fields

Following the approach and interpretation of Arlt anNeumann in Ref. 15 we propose a qualitative defect mofor explaining internal fields and stabilization timesLiTaO3 and LiNbO3. Drawing an analogy between LiNbO3

and LiTaO3 we will assume a simple defect model primaribased on a tantalum antisite defect and lithium vacancielithium tantalate as depicted in Fig. 13. With this physicbasis we will now proceed to build a model for domain rversal in LiTaO3.

The process of domain reversal in LiTaO3 involvesmovement of lithium atoms, LiLi, through the adjacent closepacked oxygen planes into the neighboring vacant oxyoctahedra. This is accompanied by a simultaneous motiothe tantalum atom, TaTa, from its acentric location within itsnormal oxygen octahedral site to a centrosymmetricallyposite site within its octahedra. At room temperature,lithium ion has to force its way through the opening in toxygen triangle formed by three adjacent oxygen ions. Tprocess is postulated to be anelastic, in the sense thatmotion requires strain in the close-packed oxygen planethe lattice, creation and relaxation of which is expected totime dependent. At a constant external driving field, sayE,the motion of the lithium ion is a function of time, corresponding to time-dependent changes in the free energytential,G.

Let us now consider the TaLi antisite defect. Upon domain reversal under an electric field we now postulate tthis tantalum atom also has to pass through the adjaclose-packed oxygen layer and into the adjoining vacoxygen octahedron. We start with the premise that this a


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lastic process is driven by the domain reversal causedelectric field, and that this is a key step that needs to ocfor the newly created domain to be stable. Referring backFigs. 13~a! and 13~b!, while the TaLi atoms move upon domain reversal, the lithium vacancies surrounding the antidefects do not move at room temperature. This is suggeby the fact that ionic conduction at room temperature is nligible and becomes substantial only at temperatures ab150 °C, primarily due to lithium-site ionic motion.32 There-fore, at room temperature, the lithium vacancies arountantalum antisite are in a frustrated state@Fig. 13~b!# after thetantalum antisite atom TaLi has moved into the adjoining octahedron under electric field induced domain reversal. Tconfiguration has higher energy, which can be only loweby rearrangement of lithium vacancies in a new configution, achieved by heating and cooling, for example, whyields the final stable configuration of Fig. 13~c!.

The defect complex in Fig. 13 is assumed to comprisea dipole moment, which has two contributions. These are~a!the contribution to the electrical dipole arising only from thTaLi antisite defect, and~b! the contribution to the electricadipole arising from the relative arrangement of the lithiuvacanciesVLi around a tantalum antisite defect TaLi. Upondomain reversal at room temperature, the electric fieldmove the TaLi antisite defect through the neighboring oxygtriangle and therefore reverse the component~a! of the elec-trical dipole moment associated with only TaLi. However, thecomponent~b! of the electrical dipole moment associatewith the arrangement lithium vacancies is not reversed byelectric field. This results in the frustrated domain stashown in Fig. 13~b!. This requires thermal activation a.150 °C for a few minutes followed by cooling to rearranlithium vacancies to achieve the low energy domain stshown in Fig. 13~c!.

Figures 14~a!–14~e! show a schematic of the potentiaenergy diagram at room temperature for the forward switing process at various instants of timet on application of avoltage pulse of widthtg,r . The energy diagram representhe electrostatic energy of the lattice polarization, modifiby the interaction energy resulting from the interaction btween defect polarization and bulk lattice polarization, adue to external field contributions to the total lattice enerFor a first order ferroelectric phase transition, the differen


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between the free energyG per unit volume in a ferroelectricstate and that in the paraelectric stateGo can written as33

G2Gou6Ps52

A

2P21

B

4P42ED~ t !P2EP, ~6!

where P is the lattice polarization,A and B are positivephysical constants,ED(t) is the effective time dependent defect field, andE is the external field applied. Note that thabove equation is applicable near the6Ps states only. HerePs indicates spontaneous lattice polarization at the minimenergy state. Before any external field is applied@E50 at t50; see Fig. 14~a!#, the2Ps lattice polarization state~indi-cated by↓! is stabilized by the defect polarization by aamount ofDw2 per defect dipole, with respect to the1Ps

state. If all the defect dipoles are aligned parallel to the2Ps

direction in Fig. 14~a!, then the magnitude of the defect fieED at time t50 is given by15

ED~0!5NDw2

2Ps, ~7!

whereN is total number of defect dipoles per unit volumAs Arlt and Neumann point out,15 this effective defect field isnot an existing electric field in the material. Rather, it isformal equivalent to the energetic difference between thepoling states.

The defect that stabilizes the2Ps polarization is thoughtof as being comprised of two components: one arising frTaLi ~indicated byF! and the other arising from the relativarrangement of lithium vacancies around the antisite de~indicated byf!. The application of an external electrfield, 1E, decreases the energy of the1Ps state byE•Pand increases the energy of the2Ps state by a correspondinamount. This results in the reversal of the lattice domstate from2Ps(↓) to 1Ps(↑) state as shown in Fig. 14~b!.However, at a time instantt,tstab,f , the defect polarizationsF andf have not reversed from their original state in F14~a!. We now consider three cases.

~i! When the applied voltage pulse widthtg,r is less thanthe stabilization timetstab,f . At the end of the pulse~timeinstant t5tg,r,tstab,f!, domain backswitching occurs ashown in Fig. 14~c!. This is directly due to the fact that thexternal field related energy contributionE•P→0 on re-moval of the voltage pulse, and the system returns to2Ps state, stabilized by defect polarization.

~ii ! When the applied voltage pulse width,tg,r is justequal to or greater thantstab,f @Fig. 14~d!#, no backswitchingoccurs. In this case the defect polarization componentFreverses to theD state, corresponding to a movement of TLi

through close-packed oxygen planes. Referring to Tablthe time constant for the realignment of defect polarizatrelating to TaLi movement is proposed to be of the ordert1,f;20.3 s for congruent and 26.4 s for near-stoichiomeLiTaO3 during forward poling. The stabilization timetstab,r

in this interpretation would approximately correspond totime taken for the TaLi atoms to cross the close-packed oxgen plane. The new defect polarization component stabilthe polarization state1Ps(↑), thus preventing the backswitching. Note, however, that the defect polarization co


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ponentf still does not reverse due to the lack of rearrangment of VLi around the new TaLi position at roomtemperature.

~iii ! When the applied voltage pulse widthtg,r@tstab,f

@Fig. 14~e!#, no backswitching occurs as in case~ii !. In ad-dition, a slow time-dependent relaxation of the lattice polization takes place in the presence of a frustrated defecpole ~a combination ofD andf in Fig. 14!, in reaching afinal equilibrium state as shown in Fig. 14~e!. Referring toTable I, the time constant for this slow relaxation is attriuted to t2,f;399.6 s ~congruent! and 177.5 s ~near-stoichiometric! time constants observed from Eq.~1!. Thefinal effective defect fieldED in Fig. 14~e! is given by

ED~ t@tstab,r !5NDw1

2Ps. ~8!

Note that the effective defect fieldsED in Eqs. ~7! and~8! are not equal, a direct consequence of the frustratedfect dipole componentf related to lithium vacancies in Fig14~e!.

The threshold coercive fieldEc can be written asEc(t)5ED(t)1Eintrinsic(t), whereEintrinsic is the intrinsic thresholdcoercive field of exactly stoichiometric LiTaO3 with no de-fects present. This immediately suggests many qualitafeatures of domain reversal. First, changes in the threshcoercive field with time~see, for example, Figs. 4 and 10! aredirectly related, in part, to the time dependent changes ineffective defect fieldED arising from the reorientation of thedefect dipole denoted byD in Fig. 14. Second, since thmagnitude of the effective defect fieldED is directly propor-tional to the density of defectsN @Eqs. ~7! and ~8!#, thethreshold coercive fieldEc is directly proportional to defecdensityN. This has indeed been confirmed in LiNbO3 wherethe threshold coercive field varies linearly with the raLi/ ~Li1Nb! between congruent and stoichiometrcompositions.6 Third, the internal field,Eint , given by theoffset in the hysteresis loop along the field axis arisesrectly from the difference in the defect fieldsED betweentimes t50 @Eq. ~7!# and t@tstab,j ~Eq. 8!. Assuming thatmagnitude of the intrinsic threshold coercive field,Eintrinsic,does not change between domain state in Figs. 14~a! and14~e!, we can write the internal field4–6 Eint'@ED(t50)2ED(t@tstab,j 8)#/2 for slow polarization cycling (tg, j

@tstab,j 8) as

Eint'N~Dw22Dw1!

4Ps. ~9!

Again, the internal field clearly depends linearly on the desity of defect dipoles as is also experimentally observed.6

As mentioned before, it must be emphasized thatdefect and internal electric fields discussed above are nobe thought of actual electric fields, but as energy equivaleto the differences in the energy levels between differstates. These energy differences can include not only elecstatic energy differences but elastic energy differenceswell due to lattice distortions. The electrical dipoles assoated with defect complexes can therefore also have eladipole components.15


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VII. CONCLUSIONS AND SUMMARY

The central message of this article is that the presencnonstoichiometry in ferroelectric LiTaO3 gives rise to largechanges in the polarization reversal properties of this mrial. In particular we have presented real-time studies ofmain motion in near-stoichiometric composition@C5Li/ ~Li1Ta);0.4977– 0.4992] crystals. We have directimaged and tracked the domain backswitching proceslithium tantalate. We have systematically investigated thelarization hysteresis loops, threshold coercive fields, stazation times, switching times, and wall velocities of thecrystals at room temperature. These results are then cpared and contrasted with those for congruent composit(C50.485).

The threshold coercive field for domain reversal andmain stabilization time increases by an order of magnituwith increasing lithium deficiency from near-stoichiometrto congruent compositions. The presence of lithium nonsichiometry also introduces internal fields, which increawith increasing lithium deficiency. The sideways domawall velocities are two orders of magnitude higher in nestoichiometric crystals as compared to congruent crystThere are similarities between the dependence of switchtimes and wall velocities with electric field in both neastoichiometric and congruent compositions as discusseSec. V. In both compositions the domain wall motiondominated by wall pinning at electric fields close to thresold coercive fields, and by wall velocity in the high fieregime.

We propose a physical defect dipole composedlithium vacancies and tantalum antisites. Based on the ccept of domain stabilization by bulk dipolar defects, thmodel qualitatively predicts many of the observed featuredomain reversal such as the dependence of threshold ccive field on defect density and on time spent in a domstate after its creation, the phenomenon of domain stabiltion time, domain backswitching, and internal fields. The eperiments and modeling results in this article can be appto lithium niobate (LiNbO3) as well, which shows very similar domain reversal properties.6

ACKNOWLEDGMENT

This work was supported by the National Science Fodation CAREER Grant Nos. 9984691 and 9988685.


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