APPLIED PHYSICS LETTERS 95, 092904 共2009兲

Mapping bias-induced phase stability and random fields in relaxor ferroelectrics B. J. Rodriguez,1,a兲 S. Jesse,2 A. A. Bokov,3 Z.-G. Ye,3 and S. V. Kalinin2,b兲 1

University College Dublin, Belfield, Dublin 4, Ireland Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA 3 Department of Chemistry and 4D LABS, Simon Fraser University, Burnaby, British Columbia V5A 1A6, Canada 2

共Received 15 May 2009; accepted 15 August 2009; published online 4 September 2009兲 The spatial variability of polarization reversal behavior in the relaxor 0.9Pb共Mg1/3Nb2/3O3兲 – 0.1PbTiO3 crystal, is revealed on the ⬃100 nm scale using switching spectroscopy piezoresponse force microscopy. Quenched fields conjugate to polarization are found, which show mesoscopic 共⬃100– 200 nm兲 spatial fluctuations around near-zero bias values. The mapping of the stability gap of the bias-induced phase and conjugate random fields is demonstrated. The origin of the observed nanoscale domains and the field-induced part of the polarization are discussed. © 2009 American Institute of Physics. 关DOI: 10.1063/1.3222868兴 Ferroelectric relaxors have attracted much attention as prospective materials for acoustic and medical imaging applications.1 The unique properties of relaxors are traditionally associated with the presence of polar nanoregions 共PNRs兲, the formation and transformations of which result in a broad spectrum of dynamic temperature- and field-induced behaviors. Despite recent progress in understanding relaxor behavior,2,3 a number of aspects remain unresolved, including the polarization switching mechanisms 共rotation versus wall motion兲 and observations of Barkhausen noise during polarization reversal, among others.4 The development of piezoresponse force microscopy 共PFM兲 in the past decade has precipitated several studies of mesoscopic domain polarization distributions in relaxor ferroelectrics, including observations of fractal domain walls in the nonergodic phase of relaxors,5–7 ferroelectric domains in uniaxial relaxors,8,9 and persistent labyrinthine domains of spontaneous polarization in the macroscopically nonpolar “ergodic” relaxor phase.6,10,11 Complementary to imaging static domain patterns, piezoresponse force spectroscopy12 was used to study local polarization dynamics in relaxors.6 These experiments are analogous to macroscopic bias-induced experiments, allowing the phase-field diagram of relaxor ferroelectrics to be sampled locally. Observations of complex static mesoscopic polarization patterns in relaxor materials suggest the corresponding dynamic behavior and bias-induced phase transitions can also be position dependent. Quenched electric random fields are believed to be responsible10 for the alignment of PNRs which lead to the appearance of polar domains, as suggested by the earlier work of Imry and Ma13 on magnetic systems. Westphal et al.14 further showed that the stability of the domain state is tied to the local fluctuations of the random fields. Recently, Shvartsman et al.15 suggested that these polar domains are the quasistatic PNRs themselves 共precursors of ferroelectric domains兲, which are frozen due to their comparatively large size, and that small dynamic PNRs are loa兲

Electronic mail: [email protected]. Author to whom correspondence should be addressed. Electronic mail: [email protected].

b兲

0003-6951/2009/95共9兲/092904/3/$25.00

cated between them. The polar, labyrinthine domain shape, roughness, and size are likely dictated by the interplay between strain accommodation as discussed in detail in Ref. 15 and ordering forces including but not limited to the quenched electric random fields. A different model suggested16 that each polar domain consists of a large number of static and dynamic PNRs embedded into a nonpolar matrix. The dipole moments of the static PNRs are fixed in orientation, while the dynamic PNRs are unstable against thermal agitation. Recently, an approach for nanoscale mapping of randomfield and random-bond disorder potential components has been demonstrated for normal ferroelectrics.17 Here, we study the spatial uniformity of polarization reversal at the surface of a relaxor crystal using switching spectroscopy PFM 共SS-PFM兲.18 The 共1 − x兲Pb共Mg1/3Nb2/3兲O3 – x PbTiO3 crystal with x = 0.1 共PMN-10%PT兲 is grown from high temperature solution and has a dielectric maximum at Tmax = 310 K 共at 1 kHz兲.19 The crystal undergoes a phase transition to a rhombohedral ferroelectric state on cooling at Tc ⬵ 280 K,20 thus the measurements are performed in the macroscopically cubic “ergodic” relaxor state 共note that a surface phase can exist in the frozen state due to, e.g., strain effects兲.21 The PFM and SS-PFM measurements are performed on the mirror-polished 共001兲 crystal surface using a commercial atomic force microscope system 共Veeco MultiMode NSIIIA兲, which was modified as described elsewhere.18 During SS-PFM, hysteresis loops are measured at every point in a mesh grid 共a 40⫻ 40 array with a 12.5 nm step size兲 and analyzed to yield two-dimensional maps of switching properties including imprint, switching bias, and the area within the loop 共i.e., the work of switching兲. In SS-PFM, the writing and reading state durations were 39.06 ms, while the 15 ms measurement window immediately followed a 15 ms delay from the end of the writing state. PFM and SS-PFM data were acquired with a 615 kHz, 2 V bias to the tip 共Mikromasch Au-Cr coated Si tip, with spring constant k ⬃ 0.6 N / m兲. The surface topography and the corresponding domain structure 共PFM phase兲 images are shown in Figs. 1共a兲 and 1共b兲. The PFM phase image demonstrates the labyrinthine structure typical of relaxors in the “ergodic” bulk phase.

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Appl. Phys. Lett. 95, 092904 共2009兲

FIG. 1. 共Color online兲 共a兲 Surface topography 共5 nm z-scale兲 and 共b兲 PFM phase signal of the PMN-10PT crystal surface. 共c兲 Positive and 共d兲 negative coercive bias SS-PFM maps. 共e兲 Map of switchable polarization. 共f兲 Work of switching SS-PFM map. The pixel size in panels 关共c兲–共f兲兴 is 12.5 nm. The black lines in 共c兲 are a contour map overlay of 共b兲.

Dark and bright areas in this image correspond to polar domains of static polarization directed upwards and downwards, respectively. To explore the polarization dynamics on relaxor surfaces, we performed SS-PFM mapping within the same region. The hysteresis loops from selected locations are shown in Fig. 2. They are shifted to negative bias values and loops from adjacent locations show close similarity, suggesting the measurements are performed in the dense regime 关note that the pixel size is smaller than the tip radius 共nominally 50 nm兲兴. At the same time, significant variability between wellseparated points 共⬃100– 200 nm兲 is observed. Positive and negative coercive bias SS-PFM maps are shown in Figs. 1共c兲 and 1共d兲, while SS-PFM maps of the reversible polarization and the work of switching are shown in Figs. 1共e兲 and 1共f兲. Note the lack of one to one correspondence between topography, PFM, and SS-PFM maps 共within the limitations imposed by the thermal drift of the microscope兲, illustrating the complementary nature of the data. The hysteresis loop shape in PFM describes the convolution between the bias-induced change in material proper-

FIG. 2. 共Color online兲 共a兲 Piezoresponse SS-PFM map and 关共b兲–共d兲兴 hysteresis loops from selected locations. The lower right corner in 共a兲 is a region exhibiting an experimental artifact. PNB and NNB are indicated in 关共b兲–共d兲兴. Note that the PNB and NNB in 共b兲 are close to zero. Panel a has a 12.5 nm pixel size and was acquired simultaneously with Figs. 1共c兲–1共f兲.

FIG. 3. 共Color online兲 共a兲 Stability gap and 共b兲 built-in field maps and 关共c兲 and 共d兲兴 corresponding histograms. Panels 共a兲 and 共b兲 were constructed from the same SS-PFM data set shown partially in Figs. 1 and 2 and have a 12.5 nm pixel size. The black lines in 共a兲 and 共b兲 represent domain walls.

ties and the signal generation volume in a PFM experiment. In classical ferroelectrics, the material evolution can be well described as the sequential intrinsic domain nucleation and subsequent domain growth by wall motion.22 A number of observations suggest that the polarization reorientation mechanism in relaxors is drastically different, and proceeds through a gradual evolution and decay of bias-induced states16,23 similarly to the macroscopic case.24 Comparison with relaxation studies suggests that the loops in PMN10%PT are related to a large bias-induced polarization with a relaxation time of ⬃10 s,16 i.e., much longer than the dc bias cycling in the SS-PFM experiments. Note that some hysteresis loops have nearly overlapping or in some cases, overlapping values of positive and negative nucleation biases 共PNB and NNB, respectively兲 suggesting that the bias-induced state is unstable. We propose that the value of the stability gap 共SG兲, SG= 共PNB− NNB兲 provides a measure of the absolute stability of the bias-induced phase, with SG⬎ 0 corresponding to thermodynamically or kinetically stable bias-induced state, and SG⬍ 0 corresponding to an unstable state. Furthermore, independent of the microscopic origin of the loops in PMN-10%PT, the influence of the built-in field is expected to be similar, namely, the loop is shifted in a horizontal direction 共the effect known as imprint in ferroelectric materials兲. Hence, PNB+ NNB allows mapping of built-in fields as proposed earlier.17 The stability gap and built-in field maps for a PMN10%PT crystal surface are shown in Figs. 3共a兲 and 3共b兲. The two maps are generally uncorrelated, indicative of the veracity of the measurements. The corresponding histograms of PNB− NNB and PNB+ NNB are shown in Fig. 3共c兲 and 3共d兲. The images show large scale features, characteristic of the presence of disorder in the material on the mesoscopic scale. In the built-in field map 关Fig. 3共b兲兴, regions of positive 共yellow and red兲 and negative 共blue兲 fields separated by the regions 共green兲 where the field is close to zero can be observed. This picture corresponds to the frozen fluctuations of the local field with a period of ⬃100– 200 nm and differs drastically from that found in the normal ferroelectric phase of lead zirconate titanate 共PZT兲.17 In PZT, a rather abrupt

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alternation of the field sign can be observed and a number of pointlike defects associated with a single pixel are found. The field distribution 关Fig. 3共d兲兴 is centered near zero, which means that on the macroscopic scale, the near-surface field is absent or much smaller than the amplitude of the local field fluctuations. In the framework of the picture of static and dynamic PNRs 共Ref. 16兲 our current results suggest that the polarization of static PNRs 共labyrinthine domains兲 are not switched by external electric field and that their configuration after the application of dc bias remains unchanged. The observed comparatively large bias-induced polarization can be due to the reorientation of the dynamic PNRs, variation of the size of the dynamic PNRs, and, in stronger fields, due to the transition into a metastable ferroelectric phase. Though the spatial inhomogeneities of characteristics of bias-induced polarization, including stability gap 关Fig. 3共a兲兴, switchable polarization 关Fig. 1共e兲兴, and work of switching 关Fig. 1共f兲兴 are correlated, they reveal no direct correlation with the labyrinthine domain structure 关Fig. 1共b兲兴, which confirms a different origin and the relative independence of the labyrinthine domains 共created by static PNRs兲 and the bias-induced polarization 共coming from reorientations of dynamic PNRs, and, possibly, the growth of their size兲. To summarize, the spatial variability of polarization switching on a PMN-10%PT crystal relaxor ferroelectric surface is studied by SS-PFM. The SS-PFM maps reveal a significant variability of switching behavior associated with mesoscopic disorder. The static labyrinthine domain pattern does not correlate directly with the distribution of quenched local fields at the surface of the relaxor crystal, indicating that the fields are not the sole cause of the domain formation. The mapping of the stability gap for the bias-induced phase and the built-in field distributions is demonstrated, illustrating the presence of quenched random fields with mesoscopic 共⬃100– 200 nm兲 inhomogeneities. This research is supported 共B.J.R., S.J., and S.V.K.兲 by the Division of Scientific User Facilities, Office of Basic Energy Sciences, U.S. Department of Energy and was part of a CNMS User Program 共Grant No. CNMS2007-085兲. The

work is also supported 共A.A.B. and Z.G.Y.兲 by the Office of Naval Research 共Grant No. N00014–06–1–0166兲. B.J.R. also acknowledges the support of UCD Research. Y. Yamashita, Springer Ser. Mater. Sci. 114, 223 共2008兲. L. E. Cross, Ferroelectrics 76, 241 共1987兲. 3 A. A. Bokov and Z. G. Ye, J. Mater. Sci. 41, 31 共2006兲. 4 E. V. Colla, L. K. Chao, and M. B. Weissman, Phys. Rev. Lett. 88, 017601 共2001兲. 5 F. Bai, J. Li, and D. Viehland, J. Appl. Phys. 97, 054103 共2005兲. 6 V. V. Shvartsman, A. L. Kholkin, A. Orlova, D. Kiselev, A. A. Bogomolov, and A. Sternberg, Appl. Phys. Lett. 86, 202907 共2005兲. 7 V. V. Shvartsman, W. Kleemann, T. Łukasiewicz, and J. Dec, Phys. Rev. B 77, 054105 共2008兲. 8 P. Lehnen, W. Kleemann, T. Woike, and R. Pankrath, Phys. Rev. B 64, 224109 共2001兲. 9 W. Kleemann, G. A. Samara, and J. Dec, in Polar Oxides: Properties, Characterization, and Imaging, edited by R. Waser, U. Böttger, and S. Tiedke 共Wiley, Weinheim, 2005兲. 10 W. Kleemann, J. Dec, V. V. Shvartsman, Z. Kutnjak, and T. Braun, Phys. Rev. Lett. 97, 065702 共2006兲. 11 V. V. Shvartsman and A. L. Kholkin, J. Appl. Phys. 101, 064108 共2007兲. 12 A. N. Morozovska, E. A. Eliseev, S. Jesse, B. J. Rodriguez, and S. V. Kalinin, J. Appl. Phys. 102, 114108 共2007兲. 13 Y. Imry and S.-K. Ma, Phys. Rev. Lett. 35, 1399 共1975兲. 14 V. Westphal, W. Kleemann, and M. D. Glinchuk, Phys. Rev. Lett. 68, 847 共1992兲. 15 V. V. Shvartsman, J. Dec, T. Lukasiewicz, A. L. Kholkin, and W. Kleemann, Ferroelectrics 373, 77 共2008兲. 16 S. V. Kalinin, B. J. Rodriguez, J. D. Budai, S. Jesse, A. N. Morozovska, A. A. Bokov, and Z.-G. Ye, e-print arXiv:0808.3827v1. 17 S. Jesse, B. J. Rodriguez, S. Choudhury, A. P. Baddorf, I. Vrejoiu, D. Hesse, M. Alexe, E. A. Eliseev, A. N. Morozovska, J. Zhang, L. Q. Chen, and S. V. Kalinin, Nature Mater. 7, 209 共2008兲. 18 S. Jesse, H. N. Lee, and S. V. Kalinin, Rev. Sci. Instrum. 77, 073702 共2006兲. 19 M. Dong and Z. G. Ye, J. Cryst. Growth 209, 81 共2000兲. 20 Z. G. Ye, Y. Bing, J. Gao, A. A. Bokov, P. Stephens, B. Noheda, and G. Shirane, Phys. Rev. B 67, 104104 共2003兲. 21 V. V. Shvartsman, J. Dec, T. Łukasiewicz, A. L. Kholkin, and W. Kleemann, Ferroelectrics 373, 77 共2008兲. 22 S. Jesse, A. P. Baddorf, and S. V. Kalinin, Appl. Phys. Lett. 88, 062908 共2006兲. 23 V. V. Shvartsman, A. L. Kholkin, M. Tyunina, and J. Levoska, Appl. Phys. Lett. 86, 222907 共2005兲. 24 B. Dkhil, J. M. Kiat, G. Calvarin, G. Baldinozzi, S. B. Vakhrushev, and E. Suard, Phys. Rev. B 65, 024104 共2001兲. 1 2

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Mapping bias-induced phase stability and random ...

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