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Based on the theory of random fluctuation of polarization clusters and the model of Wiener random process, the relaxation law of long-range fluctuation of polarization and the possible forms of light intensity autocorrelation function g2(τ) measured from photon correlation spectroscopy (PCS) experiments have been derived. The relationship between relaxation mechanisms of microscopic polarization clusters and macro relaxation laws is expounded. This research supplies a theoretical model for the application of PCS in researching the relaxation process of polarization clusters in ferroelectrics. Based on the improved He-Ne laser PCS experimental set-up, the relaxation process of long-range fluctuation of polarization clusters in BaTiO3 and 0.71Pb (Mg1/3Nb2/3) O3-0.29PbTiO3 single crystals near phase transition temperature is studied. As for BaTiO3, the dual relaxation processes of long-range fluctuation of polarization clusters are observed at temperatures above TC+4 K, which may be related to its order-disorder mechanism of phase transition. For 0.71Pb (Mg1/3Nb2/3) O3-0.29PbTiO3, the dual relaxation processes exist on both sides of the cubic-tetragonal phase transition temperature. The PCS experimental results are fitted well by the derived theoretical model, and the characteristic relaxation times of long-range fluctuation of polarization clusters are extracted. Two relaxation times, τs and τl corresponding to short and long relaxation time, respectively, are initially observed, where τs is several microseconds, and τl is tens of microseconds. The abrupt increase of relaxation times at phase transition temperature and the phenomenon of critical slowing down can be observed in the two samples.
[1] Pike E R, Abbiss J B 1997 Light Scattering and Photon Correlation Spectroscopy (Vol. 40) (Dordrecht: Kluwer Academic Publishers) pp65-67
[2] Lin Y, Yang G C, Wang Y W 2013 Acta Phys. Sin. 62 118702 (in Chinese) [林瑜, 杨光参, 王艳伟 2013 62 118702]
[3] Liu X Y, Shen J, Zhu X J, Sun X M, Liu W 2012 Acta Opt. Sin. 32 0629002 (in Chinese) [刘晓艳, 申晋, 朱新军, 孙贤明, 刘伟 2012 光学学报 32 0629002]
[4] Wang L N, Zhao X Y, Zhang L L, Huang Y N 2012 Chin. Phys. B 21 086403
[5] Kleemann W, Licinio P, Woike T, Pankrath R 2001 Phys. Rev. Lett. 86 6014
[6] Elissalde C, Ravez J 2001 J. Mater. Chem. 11 1957
[7] Zhao J Y, Cui B, Chang Z G, Tang Z X 2008 Mater. Rev. 22 21 (in Chinese) [赵俊英, 崔斌, 畅柱国, 唐宗薰 2008 材料导报 22 21]
[8] Chu R Q, Xu Z J, Li G R, Zeng H R, Yu H F, Shao X, Luo H S, Yin Q R 2005 Acta Phys. Sin. 54 935 (in Chinese) [初瑞清, 徐志军, 李国荣, 曾华荣, 余寒峰, 邵鑫, 罗豪甦, 殷庆瑞 2005 54 935]
[9] Cochran W 1960 Advan. Phys. 9 387
[10] Harada J, Axe J D, Shirane G 1971 Phys. Rev. B 4 155
[11] Vogt H, Sanjurjo J A, Rossbroich G 1982 Phys. Rev. B 26 5904
[12] Presting H, Sanjurjo J A, Vogt H 1983 Phys. Rev. B 28 6097
[13] Sokoloff J P, Chase L L, Rytz D 1988 Phys. Rev. B 38 597
[14] Comes R, Lambert M, Guinier A 1968 Solid State Commun. 6 715
[15] Zalar B, Laguta V V, Blinc R 2003 Phys. Rev. Lett. 90 037601
[16] Zalar B, Levar A, Seliger J, Blinc R, Laguta V V, Itoh M 2005 Phys. Rev. B 71 064107
[17] Ko J H, Kim T H, Roleder K, Rytz D, Kojima S 2011 Phys. Rev. B 84 094123
[18] Yamada Y, Shirane G, Linz A 1969 Phys. Rev. 177 848
[19] Tai R Z, Namikawa K, Sawada A, Kishimoto M, Tanaka M, Lu P, Nagashima K, Maruyama H, Ando M 2004 Phys. Rev. Lett. 93 087601
[20] Namikawa K, Kishimoto M, Nasu K, Matsushita E, Tai R Z, Sukegawa K, Yamatani H, Hasegawa H, Nishikino M, Tanaka M, Nagashima K 2009 Phys. Rev. Lett. 103 197401
[21] Yan R, Guo Z, Tai R, Xu H, Zhao X, Lin D, Li X, Luo H 2008 Appl. Phys. Lett. 93 192908
[22] Zhang M J, Guo Z, Tai R Z, Luo H S, Namikawa K 2015 Jpn. J. Appl. Phys. 54 042401
[23] Li F, Zhang S J, Li Z R, Xu Z 2012 Prog. Phys. 32 178 (in Chinese) [李飞, 张树君, 李振荣, 徐卓 2012 物理学进展 32 178]
[24] Tyunina M, Levoska J 2001 Phys. Rev. B 63 224102
[25] Smolenskii G A, Isupov V A, Agranovskaya A I, Popov S N 1961 Sov. Phys. Solid State 2 2584
[26] Cross L E 1987 Ferroelectrics 76 241
[27] Viehland D, Jang S J, Cross L E 1990 J. Appl. Phys. 68 2916
[28] Pirc R, Blinc R 1999 Phys. Rev. B 60 13470
[29] Ko J H, Kim D H, Tsukada S, Kojima S 2010 Phys. Rev. B 82 104110
[30] Xu G, Wen J, Stock C, Gehring P M 2008 Nat. Mater. 7 562
[31] Bovtun V, Petzelt J, Porokhonskyy V, Kamba S, Yakimenko Y 2001 J. Eur. Ceram. Soc. 21 1307
[32] Tagantsev A K, Glazounov A E 1998 Phys. Rev. B 57 18
[33] Lambert M, Comes R 1969 Solid State Commun. 7 305
[34] Bokov A A, Ye Z G 2006 J. Mater. Sci. 41 31
[35] Shamblin S L, Hancock B C, Dupuis Y, Pikal M J 1999 J. Pharm. Sci. 89 417
[36] Apitz D, Johansen P M 2005 J. Appl. Phys. 97 063507
[37] Maglione M, Böhmer R, Loidl A, Höchli U T 1989 Phys. Rev. B 40 11441
[38] Hlinka J, Ostapchuk T, Nuzhnyy D, Petzelt J, Kuzel P, Kadlec C, Vanek P, Ponomareva I, Bellaiche L 2008 Phys. Rev. Lett. 101 167402
[39] Ji K, Namikawa K, Zheng H, Nasu K 2009 Phys. Rev. B 79 144304
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[1] Pike E R, Abbiss J B 1997 Light Scattering and Photon Correlation Spectroscopy (Vol. 40) (Dordrecht: Kluwer Academic Publishers) pp65-67
[2] Lin Y, Yang G C, Wang Y W 2013 Acta Phys. Sin. 62 118702 (in Chinese) [林瑜, 杨光参, 王艳伟 2013 62 118702]
[3] Liu X Y, Shen J, Zhu X J, Sun X M, Liu W 2012 Acta Opt. Sin. 32 0629002 (in Chinese) [刘晓艳, 申晋, 朱新军, 孙贤明, 刘伟 2012 光学学报 32 0629002]
[4] Wang L N, Zhao X Y, Zhang L L, Huang Y N 2012 Chin. Phys. B 21 086403
[5] Kleemann W, Licinio P, Woike T, Pankrath R 2001 Phys. Rev. Lett. 86 6014
[6] Elissalde C, Ravez J 2001 J. Mater. Chem. 11 1957
[7] Zhao J Y, Cui B, Chang Z G, Tang Z X 2008 Mater. Rev. 22 21 (in Chinese) [赵俊英, 崔斌, 畅柱国, 唐宗薰 2008 材料导报 22 21]
[8] Chu R Q, Xu Z J, Li G R, Zeng H R, Yu H F, Shao X, Luo H S, Yin Q R 2005 Acta Phys. Sin. 54 935 (in Chinese) [初瑞清, 徐志军, 李国荣, 曾华荣, 余寒峰, 邵鑫, 罗豪甦, 殷庆瑞 2005 54 935]
[9] Cochran W 1960 Advan. Phys. 9 387
[10] Harada J, Axe J D, Shirane G 1971 Phys. Rev. B 4 155
[11] Vogt H, Sanjurjo J A, Rossbroich G 1982 Phys. Rev. B 26 5904
[12] Presting H, Sanjurjo J A, Vogt H 1983 Phys. Rev. B 28 6097
[13] Sokoloff J P, Chase L L, Rytz D 1988 Phys. Rev. B 38 597
[14] Comes R, Lambert M, Guinier A 1968 Solid State Commun. 6 715
[15] Zalar B, Laguta V V, Blinc R 2003 Phys. Rev. Lett. 90 037601
[16] Zalar B, Levar A, Seliger J, Blinc R, Laguta V V, Itoh M 2005 Phys. Rev. B 71 064107
[17] Ko J H, Kim T H, Roleder K, Rytz D, Kojima S 2011 Phys. Rev. B 84 094123
[18] Yamada Y, Shirane G, Linz A 1969 Phys. Rev. 177 848
[19] Tai R Z, Namikawa K, Sawada A, Kishimoto M, Tanaka M, Lu P, Nagashima K, Maruyama H, Ando M 2004 Phys. Rev. Lett. 93 087601
[20] Namikawa K, Kishimoto M, Nasu K, Matsushita E, Tai R Z, Sukegawa K, Yamatani H, Hasegawa H, Nishikino M, Tanaka M, Nagashima K 2009 Phys. Rev. Lett. 103 197401
[21] Yan R, Guo Z, Tai R, Xu H, Zhao X, Lin D, Li X, Luo H 2008 Appl. Phys. Lett. 93 192908
[22] Zhang M J, Guo Z, Tai R Z, Luo H S, Namikawa K 2015 Jpn. J. Appl. Phys. 54 042401
[23] Li F, Zhang S J, Li Z R, Xu Z 2012 Prog. Phys. 32 178 (in Chinese) [李飞, 张树君, 李振荣, 徐卓 2012 物理学进展 32 178]
[24] Tyunina M, Levoska J 2001 Phys. Rev. B 63 224102
[25] Smolenskii G A, Isupov V A, Agranovskaya A I, Popov S N 1961 Sov. Phys. Solid State 2 2584
[26] Cross L E 1987 Ferroelectrics 76 241
[27] Viehland D, Jang S J, Cross L E 1990 J. Appl. Phys. 68 2916
[28] Pirc R, Blinc R 1999 Phys. Rev. B 60 13470
[29] Ko J H, Kim D H, Tsukada S, Kojima S 2010 Phys. Rev. B 82 104110
[30] Xu G, Wen J, Stock C, Gehring P M 2008 Nat. Mater. 7 562
[31] Bovtun V, Petzelt J, Porokhonskyy V, Kamba S, Yakimenko Y 2001 J. Eur. Ceram. Soc. 21 1307
[32] Tagantsev A K, Glazounov A E 1998 Phys. Rev. B 57 18
[33] Lambert M, Comes R 1969 Solid State Commun. 7 305
[34] Bokov A A, Ye Z G 2006 J. Mater. Sci. 41 31
[35] Shamblin S L, Hancock B C, Dupuis Y, Pikal M J 1999 J. Pharm. Sci. 89 417
[36] Apitz D, Johansen P M 2005 J. Appl. Phys. 97 063507
[37] Maglione M, Böhmer R, Loidl A, Höchli U T 1989 Phys. Rev. B 40 11441
[38] Hlinka J, Ostapchuk T, Nuzhnyy D, Petzelt J, Kuzel P, Kadlec C, Vanek P, Ponomareva I, Bellaiche L 2008 Phys. Rev. Lett. 101 167402
[39] Ji K, Namikawa K, Zheng H, Nasu K 2009 Phys. Rev. B 79 144304
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