掺杂及磁电耦合对量子顺电体的影响
|
摘要
量子顺电体是一类特殊的电介质，和通常的铁电体有所不同。量子顺电体的介电常数在低温时呈现类似于居里-外斯定律的行为，即显示出将要发生铁电相变的征兆，但直至最低温度都不发生铁电相变。这一现象可被解释为量子涨落使顺电相稳定而铁电相完全被抑制。量子顺电体的结构和铁电体很相似，大部分属于ABO_3的钙钛矿结构，所以应力或掺杂等易使之成为铁电体。易于有外界条件诱发铁电性是量子顺电体的本质特征之一。SrTiO_3和KTaO_3是典型的量子顺电体，实验表明当两者分别掺杂Ba~(2+)和Li~+且杂质浓度超过各自的临界浓度时，顺电相不再稳定，出现由杂质导致的铁电相变。EuTiO_3是另一种特殊的量子顺电体，该材料同时也是尼尔反铁磁体，我们称它为量子顺电-反铁磁体。实验表明在该材料中，磁和介电性质之间存在耦合，其介电常数在尼尔温度附近出现异常。
对磁和介电性质之间的耦合作用的研究由来已久，在铁电磁材料中便存在这样的耦合。铁电磁系统是指在某一温度范围内，同时具有铁电有序和铁磁有序的体系。自上世纪60-70年代以来，由于这类材料的不断发现以及两种有序共存耦合导致某些特有的物理性质，而使之备受人们的关注。通过磁电耦合，铁电有序或外电场可导致自旋的再分布而改变系统的磁性性质，同样由于自旋有序的涨落通过磁致伸缩或可能的电-声子作用可导致铁电弛豫或介电异常。磁电效应主要存在于两类物质中，一类是自旋-轨道有序的物质所表现出的外场(磁场或电场)诱导的线性磁电效应(ME)_(H，E)，又被称为磁场感生的电矩效应或电场感生的磁矩效应。通常将这类具有线性磁电效应的物质称为磁电体。而另一类是铁电磁体，它除了具有一般磁电体的性质外，还由于固有的本征磁有序和铁电有序的耦合使之存在自发的磁电效应。实验上已经发现了由于自发的磁电耦合导致的介电异常和损失正切。但就这两种有序的耦合机制及其作用形式和本质还缺乏深入的研究。尽管Eu TiO_3在整个温度范围内不出现铁电有序态，可视为其电序参量平均值为零，但电系统和磁系统序参量某种形式的耦合导致了该材料在尼尔温度附近的介电反常。
本文从最典型的量子顺电体SrTiO_3出发，基于横场伊辛模型研究了Ba~(2+)的掺杂
掺杂及磁电祸合对量子顺电体的影响
摘要
对其介电性质及相变性质的影响，发现Baxsrl一xTIO3的性质由纯的BaTIO3和SrTIO3
的性质综合决定。进而发展Jassen一维畴壁运动理论至三维用电序参量和自旋关联的
相互作用来计入EuTIO3中磁和介电性质之间可能的祸合，运用平均场近似下的软模
理论、谐振动的二次量子化表示及海森堡模型讨论了该藕合对软模频率的影响。我们
发现磁和电序参量的藕合导致软模频率在尼尔温度附近的异常，从而导致其特殊的介
电性质。在此基础上，在横场伊辛模型的框架下进一步讨论了Ba2+掺杂的EuTi03的
磁电性质及热力学性质。我们发现BaxEul_xTIO3(O‘x‘0.2)的介电常数和由内察的
偏置场导致的电极化除了随杂质浓度产生相应的变化，同时在磁和介电性质的藕合作
用影响下在低温下偏离通常的量子顺电体行为，在尼尔温度附近出现异常，且磁场通
过对最近邻自旋关联的作用来影响介电常数和电极化。同时，拙合作用对磁系统也有
影响，随着杂质浓度的增加，藕合作用对磁系统的影响增强。
Quantum paraelectrics are quite different from the normal ferroelectrics as far as the dielectric susceptibility is concerned. The susceptibility increases with decreasing temperature, following the Curie-Weiss law, which indicates the appearance of the ferroelectric ordering. But at low temperatures it deviates from the Curie-Weiss behavior and saturates at even lower temperatures, which can be attributed to the effect of quantum fluctuation that stabilizes the paraelectric phase and suppresses the ferroelectric phase transition entirely. The crystal structure of the quantum paraelectrics is mainly perovskite type, similar to most of the ferroelectrics, and external factors, e.g. impurity doping, may induce ferroelectric phase. Some cubic perovskites are good cases in point such as SrTiO3 and KTaO3. Experimental results show that when Ba2+ and Li+ are doped into the above materials respectively and at the same time the impurity content is higher than their critical concentration, the impurity induced ferroe
lectric phase transition occurs. EuTiO3 is another special quantum paraelectric. It is at the same time a type-G antiferromagnet. So we call it quantum paraelectric-antiferromagnet. Experimental data shows that there exists coupling between the magnetism and dielectric properties, which leads to the dielectric anomaly near its Neel temperature. A great deal of studies have been proceeded on coupling between the magnetism and dielectric properties, which actually exists in the ferroelectromagnets. The ferroelectromagnets, in which ferroelectric ordering and magnetic spin ordering coexist spontaneously at low temperature, have been the object of intensive theoretical and experimental studies from the 60-70's last century for its connection with the finding out this kind of material and theirs some special properties of physics own to magnetoelectric coupling. By magnetoelectric coupling, the application of an electric field or ferroelectric polarization can change one or more of the parameters governing the ma
gnetic behavior of the system. Correspondingly, being possible magnetostrictive effect or electron-phonon interaction, the fluctuation of spin ordering may
lead to a dielectric anomaly and ferroelectric relaxation.
There exists magnetoelectric effects in two type of material, one of them is spin-order material called magnetoelectrics that may exhibits an induced linear magnetoelectric effect by external field. This effect is named as the electrically induced magnetoelectric effect (ME) E or magnetically induced magnetoelectric effect (ME) H A ferroelectromagnet, however, differs from the magnetoelectrics in that it shows spontaneous magnetoelectric effects in addition to the (ME) E, H effects induced by external fields. They are caused by the coexistence in the crystal of spontaneous ferroelectric and magnetic moments. An anomalies in the dielectric constants and loss tangent have been observed experimentally in the ferroelectromagnet near the antiferromagnetic transition temperature, indicative of a coupling between the ferroelectric and magnetic ordering, but the nature of the mechanism of magnetoelectric coupling and the form of interaction is still an important and debated issue. Although ferroelectric ordering doe
s not appear within the whole temperature range in EuTiO3, coupling of a certain form between the ordering parameters in electrical and magnetic subsystems causes the dielectric anomaly near its Neel temperature.
In this paper, we first investigate the impurity effect (Ba2+) on the dielectric and phase transition properties in SrTiO3 within the framework of the transverse-field Ising model (TIM). Then a possible coupling mechanism between the magnetism and dielectric properties in EuTiO3 is discussed and the magnetic influence on the frequency of the soft-phonon mode is investigated via the Heisenberg model, soft-mode theory under the mean field approximation, the second quantization theory and the perturbation theory. And we proceed further investigation on Eu1-xBaxTiO3 of
对磁和介电性质之间的耦合作用的研究由来已久，在铁电磁材料中便存在这样的耦合。铁电磁系统是指在某一温度范围内，同时具有铁电有序和铁磁有序的体系。自上世纪60-70年代以来，由于这类材料的不断发现以及两种有序共存耦合导致某些特有的物理性质，而使之备受人们的关注。通过磁电耦合，铁电有序或外电场可导致自旋的再分布而改变系统的磁性性质，同样由于自旋有序的涨落通过磁致伸缩或可能的电-声子作用可导致铁电弛豫或介电异常。磁电效应主要存在于两类物质中，一类是自旋-轨道有序的物质所表现出的外场(磁场或电场)诱导的线性磁电效应(ME)_(H，E)，又被称为磁场感生的电矩效应或电场感生的磁矩效应。通常将这类具有线性磁电效应的物质称为磁电体。而另一类是铁电磁体，它除了具有一般磁电体的性质外，还由于固有的本征磁有序和铁电有序的耦合使之存在自发的磁电效应。实验上已经发现了由于自发的磁电耦合导致的介电异常和损失正切。但就这两种有序的耦合机制及其作用形式和本质还缺乏深入的研究。尽管Eu TiO_3在整个温度范围内不出现铁电有序态，可视为其电序参量平均值为零，但电系统和磁系统序参量某种形式的耦合导致了该材料在尼尔温度附近的介电反常。
本文从最典型的量子顺电体SrTiO_3出发，基于横场伊辛模型研究了Ba~(2+)的掺杂
掺杂及磁电祸合对量子顺电体的影响
摘要
对其介电性质及相变性质的影响，发现Baxsrl一xTIO3的性质由纯的BaTIO3和SrTIO3
的性质综合决定。进而发展Jassen一维畴壁运动理论至三维用电序参量和自旋关联的
相互作用来计入EuTIO3中磁和介电性质之间可能的祸合，运用平均场近似下的软模
理论、谐振动的二次量子化表示及海森堡模型讨论了该藕合对软模频率的影响。我们
发现磁和电序参量的藕合导致软模频率在尼尔温度附近的异常，从而导致其特殊的介
电性质。在此基础上，在横场伊辛模型的框架下进一步讨论了Ba2+掺杂的EuTi03的
磁电性质及热力学性质。我们发现BaxEul_xTIO3(O‘x‘0.2)的介电常数和由内察的
偏置场导致的电极化除了随杂质浓度产生相应的变化，同时在磁和介电性质的藕合作
用影响下在低温下偏离通常的量子顺电体行为，在尼尔温度附近出现异常，且磁场通
过对最近邻自旋关联的作用来影响介电常数和电极化。同时，拙合作用对磁系统也有
影响，随着杂质浓度的增加，藕合作用对磁系统的影响增强。
Quantum paraelectrics are quite different from the normal ferroelectrics as far as the dielectric susceptibility is concerned. The susceptibility increases with decreasing temperature, following the Curie-Weiss law, which indicates the appearance of the ferroelectric ordering. But at low temperatures it deviates from the Curie-Weiss behavior and saturates at even lower temperatures, which can be attributed to the effect of quantum fluctuation that stabilizes the paraelectric phase and suppresses the ferroelectric phase transition entirely. The crystal structure of the quantum paraelectrics is mainly perovskite type, similar to most of the ferroelectrics, and external factors, e.g. impurity doping, may induce ferroelectric phase. Some cubic perovskites are good cases in point such as SrTiO3 and KTaO3. Experimental results show that when Ba2+ and Li+ are doped into the above materials respectively and at the same time the impurity content is higher than their critical concentration, the impurity induced ferroe
lectric phase transition occurs. EuTiO3 is another special quantum paraelectric. It is at the same time a type-G antiferromagnet. So we call it quantum paraelectric-antiferromagnet. Experimental data shows that there exists coupling between the magnetism and dielectric properties, which leads to the dielectric anomaly near its Neel temperature. A great deal of studies have been proceeded on coupling between the magnetism and dielectric properties, which actually exists in the ferroelectromagnets. The ferroelectromagnets, in which ferroelectric ordering and magnetic spin ordering coexist spontaneously at low temperature, have been the object of intensive theoretical and experimental studies from the 60-70's last century for its connection with the finding out this kind of material and theirs some special properties of physics own to magnetoelectric coupling. By magnetoelectric coupling, the application of an electric field or ferroelectric polarization can change one or more of the parameters governing the ma
gnetic behavior of the system. Correspondingly, being possible magnetostrictive effect or electron-phonon interaction, the fluctuation of spin ordering may
lead to a dielectric anomaly and ferroelectric relaxation.
There exists magnetoelectric effects in two type of material, one of them is spin-order material called magnetoelectrics that may exhibits an induced linear magnetoelectric effect by external field. This effect is named as the electrically induced magnetoelectric effect (ME) E or magnetically induced magnetoelectric effect (ME) H A ferroelectromagnet, however, differs from the magnetoelectrics in that it shows spontaneous magnetoelectric effects in addition to the (ME) E, H effects induced by external fields. They are caused by the coexistence in the crystal of spontaneous ferroelectric and magnetic moments. An anomalies in the dielectric constants and loss tangent have been observed experimentally in the ferroelectromagnet near the antiferromagnetic transition temperature, indicative of a coupling between the ferroelectric and magnetic ordering, but the nature of the mechanism of magnetoelectric coupling and the form of interaction is still an important and debated issue. Although ferroelectric ordering doe
s not appear within the whole temperature range in EuTiO3, coupling of a certain form between the ordering parameters in electrical and magnetic subsystems causes the dielectric anomaly near its Neel temperature.
In this paper, we first investigate the impurity effect (Ba2+) on the dielectric and phase transition properties in SrTiO3 within the framework of the transverse-field Ising model (TIM). Then a possible coupling mechanism between the magnetism and dielectric properties in EuTiO3 is discussed and the magnetic influence on the frequency of the soft-phonon mode is investigated via the Heisenberg model, soft-mode theory under the mean field approximation, the second quantization theory and the perturbation theory. And we proceed further investigation on Eu1-xBaxTiO3 of
引文
1、Müller K A, Burkard H, Phys. Rev. B, 1979, 19, 3593
2、Hchli U T, Boatner LA, Phys. Rev. B, 1979, 20, 266
3、Rytz D, Hchli U T, Bilz H, Phys. Rev. B, 1980, 22, 359
4、Bednorz J G, Müller K A, Phys. Rev. lett., 1984, 52, 2289
5、Hchli U T, Baeriswyl, J. Phys. C: Solid State Phys., 1984, 17, 311
6、Hchli U T, Weibel H, Boatner L A, J. Phys. C: Solid State Phys., 1979, 12, L563
7、Vugmeister B, Glinchuk M, Pechenyi A, Sov. Phys.-Solid State, 1984, 26, 2036
8、Vugmeister B E, Glinchuk M D, Rev. Mod. Phys., 1990, 62, 993
9、Miura S, Marutake M, Unoki H, Uwe H, Sakudo T, J. Phys. Soc. Jpn., 1975, 38, 1056
10、Roth P, Hegenbarth E, Müller M, Escher U, Ferroelectrics, 1987, 74, 331
11、Bednorz J G, Phy. D thesis, Swiss Federal Institute of Technology, Zürich, 1982
12、Lemanov V V, Smirnova E P, Syrnikov P P, Tarakanov E A, Phys. Rev. B, 1996, 54, 3151
13、Wang Ruiping, Inaguma Yoshiyuki, Itoh Mitsuru, Material Research Bulletin, 2001, 36, 1693
14、Astrov D N, J. Expt. Theoret. Phys. (U. S. S. R), 1960, 38, 984
15、Rado G T, Folen V J, Phys. Rev. Letter, 1961, 7, 310
16、Smolenskii G A, Chupis I E, Sov. Phys. Usp. 1982, 25, 475
17、Tomuta D G, Ramakrishnan. dag S, Nieuwenhugs G J, Mydosh J A, cond-mat/0103609
18、Mcguire T R, Shafer M W, Joenk R J, Alperin H A, Pickart S J, J. Appl. Phys., 1966, 31, 981
19、Shafer M W, J. Appl. Phys., 1965, 36, 1145
20、Ravel B, Stern E A, Physica B, 1995, 208 & 209, 316
21、Katsufuji T, Takagi H, Phys. Rev. B, 2001, 64, 054415
22、Srinivasan G, Rasmussen E T, Gallegos J, Srinivasan R, Phys. Rev. B, 2001, 64, 214408
23、Bichurin M I, Kornev I A, Retrov V M, Tatarenko A S, Kililo Yu V, Srinivasan G, Phys. Rev. B, 2001, 64, 094409
24、Slater J C, Phys. Rev., 1950, 78, 748
25、Barret J H, Phys. Rev., 1952, 86, 118
26、Hemberg J, Lunkenheimer P, Viana R, Bhmer R, Loidl A, Phys. Rev. B, 1995, 52, 13159
27、Morf R, Schneider T, Stoll E, Phys. Rev. B, 1977, 16, 462
28、Stachiotti M G, Migoni R L, J. Phys: Condens. Matter, 1990, 2, 4341
29、Girshberg Y, Yacoby Yizhak J, Phys. Condens. Matter, 1999, 11, 9807
30、Bursian E V, Girshberg Y G, Starov E N, Phys. Status Solidi b, 1971, 46, 529
31、Mahgereften D, Kirilow D, Cudney R S, Bacher G D, Pierce R M, Feinberg J, Phys. Rev. B, 1996, 53, 7094
32、Blinc R, Zeks B, Soft mode in Ferroelectrics and Antiferroelectrics (North-Holland, Amsterdam, 1974)
33、Wang Y G, Kleemann W, Zhong W L, Zhang L, Phys. Rev. B, 1998, 57, 13343
34、Prosandeev S A, Kleemann W, Dec J, J. Phys: Condens. Matter, 2001, 13, 5957
35、Zhang L, Kleemann W, Zhong W L, Phys. Rev. B, 2002, 66, 104105
36、Landau L D, Lifshit E M, "Electrodynamics of continuous Media" (Addison-Wesley Reading MA 1960)
37、Alcantara O F, Gehring G A, Advances in Physics, 1980, 29, 731
38、Yatom H, Englman R, Phys. Rev., 1969, 88, 793
39、Baturov L N, AI'shin B I, Yarmukhamedov Yu N, Fiz. Tverd, Sov. Phys. Solid State, 1978, 20, 1300
40、Ascher E, Rieder H, Schmid H, Stossel H, J. Appl. Phys., 1966, 37, 1404
41、Brown W E, Hornreich R M, Strikman S, Phys. Rev., 1968, 168, 574
42、Janssen T, Ferroelectrics, 1994, 162, 265
43、Gao X S, Liu J M, Chen X Y, Liu Z G, J. Appl. Phys., 2000, 88, 4250
44、Gao X S, Liu J M, Li Q C, Liu Z G, Ferroelectric, 2001, 252, 69
45、Zhong W, Vanderbilt D, Phys. Rev. B, 1996, 53, 5047
46、Lemanov V V, Sotnikov A V, Smirnova E P, Solid State Commu., 1999, 110, 611
47、钟维烈，铁电体物理学，2000，156
48、李正中，固体理论，1985，36
49、Comes R, Lambert M, Guinier, Solid State Commu., 1968, 6, 715
50、Ehses H, Bock H, Fischer K, Ferroelectrics, 1981, 37, 507
51、Itoh K, Zeng L Z, Nakamura E, Mishima N, Ferroelectrics, 1985, 63, 29
52、Wang Y G, Kleemann W, Dec J, Zhong W, Europhys. Lett., 1998, 42, 173
53、Hemberger J, Nicklas M, Viana R, Lunkengeimer P, Loidl A, Bhmer R, J. Phys: Condens. Matter, 1996, 8, 4673
54、Kleemann W, Dec J, Lehnen P, Wang Y G, Prosandeev S A, J. Phys. Chem. Solids., 2000, 61, 167
55、Kleemann W, Wang YG, Lehnen P, Dec J, Ferroelectrics, 1999, 229, 39
56、Zhang L, Zhong WL, Kleemann W, Europhys. Lett., 2001, 53, 401
57、Zhang L, Zhong WL, Kleemann W, Phys. Lett. A, 2000, 276, 162
58、Hchli U T, Weibel H E, Boatner L A, Phys. Rev. lett., 1978, 41, 1410
59、Van der Klink J J, Rytz D, Borsa F, Hchli U T, Phys. Rev. B., 1983, 27, 89
60、Janssen T, Tjon J A, Phys. Rev. B., 1981, 24, 2245
2、Hchli U T, Boatner LA, Phys. Rev. B, 1979, 20, 266
3、Rytz D, Hchli U T, Bilz H, Phys. Rev. B, 1980, 22, 359
4、Bednorz J G, Müller K A, Phys. Rev. lett., 1984, 52, 2289
5、Hchli U T, Baeriswyl, J. Phys. C: Solid State Phys., 1984, 17, 311
6、Hchli U T, Weibel H, Boatner L A, J. Phys. C: Solid State Phys., 1979, 12, L563
7、Vugmeister B, Glinchuk M, Pechenyi A, Sov. Phys.-Solid State, 1984, 26, 2036
8、Vugmeister B E, Glinchuk M D, Rev. Mod. Phys., 1990, 62, 993
9、Miura S, Marutake M, Unoki H, Uwe H, Sakudo T, J. Phys. Soc. Jpn., 1975, 38, 1056
10、Roth P, Hegenbarth E, Müller M, Escher U, Ferroelectrics, 1987, 74, 331
11、Bednorz J G, Phy. D thesis, Swiss Federal Institute of Technology, Zürich, 1982
12、Lemanov V V, Smirnova E P, Syrnikov P P, Tarakanov E A, Phys. Rev. B, 1996, 54, 3151
13、Wang Ruiping, Inaguma Yoshiyuki, Itoh Mitsuru, Material Research Bulletin, 2001, 36, 1693
14、Astrov D N, J. Expt. Theoret. Phys. (U. S. S. R), 1960, 38, 984
15、Rado G T, Folen V J, Phys. Rev. Letter, 1961, 7, 310
16、Smolenskii G A, Chupis I E, Sov. Phys. Usp. 1982, 25, 475
17、Tomuta D G, Ramakrishnan. dag S, Nieuwenhugs G J, Mydosh J A, cond-mat/0103609
18、Mcguire T R, Shafer M W, Joenk R J, Alperin H A, Pickart S J, J. Appl. Phys., 1966, 31, 981
19、Shafer M W, J. Appl. Phys., 1965, 36, 1145
20、Ravel B, Stern E A, Physica B, 1995, 208 & 209, 316
21、Katsufuji T, Takagi H, Phys. Rev. B, 2001, 64, 054415
22、Srinivasan G, Rasmussen E T, Gallegos J, Srinivasan R, Phys. Rev. B, 2001, 64, 214408
23、Bichurin M I, Kornev I A, Retrov V M, Tatarenko A S, Kililo Yu V, Srinivasan G, Phys. Rev. B, 2001, 64, 094409
24、Slater J C, Phys. Rev., 1950, 78, 748
25、Barret J H, Phys. Rev., 1952, 86, 118
26、Hemberg J, Lunkenheimer P, Viana R, Bhmer R, Loidl A, Phys. Rev. B, 1995, 52, 13159
27、Morf R, Schneider T, Stoll E, Phys. Rev. B, 1977, 16, 462
28、Stachiotti M G, Migoni R L, J. Phys: Condens. Matter, 1990, 2, 4341
29、Girshberg Y, Yacoby Yizhak J, Phys. Condens. Matter, 1999, 11, 9807
30、Bursian E V, Girshberg Y G, Starov E N, Phys. Status Solidi b, 1971, 46, 529
31、Mahgereften D, Kirilow D, Cudney R S, Bacher G D, Pierce R M, Feinberg J, Phys. Rev. B, 1996, 53, 7094
32、Blinc R, Zeks B, Soft mode in Ferroelectrics and Antiferroelectrics (North-Holland, Amsterdam, 1974)
33、Wang Y G, Kleemann W, Zhong W L, Zhang L, Phys. Rev. B, 1998, 57, 13343
34、Prosandeev S A, Kleemann W, Dec J, J. Phys: Condens. Matter, 2001, 13, 5957
35、Zhang L, Kleemann W, Zhong W L, Phys. Rev. B, 2002, 66, 104105
36、Landau L D, Lifshit E M, "Electrodynamics of continuous Media" (Addison-Wesley Reading MA 1960)
37、Alcantara O F, Gehring G A, Advances in Physics, 1980, 29, 731
38、Yatom H, Englman R, Phys. Rev., 1969, 88, 793
39、Baturov L N, AI'shin B I, Yarmukhamedov Yu N, Fiz. Tverd, Sov. Phys. Solid State, 1978, 20, 1300
40、Ascher E, Rieder H, Schmid H, Stossel H, J. Appl. Phys., 1966, 37, 1404
41、Brown W E, Hornreich R M, Strikman S, Phys. Rev., 1968, 168, 574
42、Janssen T, Ferroelectrics, 1994, 162, 265
43、Gao X S, Liu J M, Chen X Y, Liu Z G, J. Appl. Phys., 2000, 88, 4250
44、Gao X S, Liu J M, Li Q C, Liu Z G, Ferroelectric, 2001, 252, 69
45、Zhong W, Vanderbilt D, Phys. Rev. B, 1996, 53, 5047
46、Lemanov V V, Sotnikov A V, Smirnova E P, Solid State Commu., 1999, 110, 611
47、钟维烈，铁电体物理学，2000，156
48、李正中，固体理论，1985，36
49、Comes R, Lambert M, Guinier, Solid State Commu., 1968, 6, 715
50、Ehses H, Bock H, Fischer K, Ferroelectrics, 1981, 37, 507
51、Itoh K, Zeng L Z, Nakamura E, Mishima N, Ferroelectrics, 1985, 63, 29
52、Wang Y G, Kleemann W, Dec J, Zhong W, Europhys. Lett., 1998, 42, 173
53、Hemberger J, Nicklas M, Viana R, Lunkengeimer P, Loidl A, Bhmer R, J. Phys: Condens. Matter, 1996, 8, 4673
54、Kleemann W, Dec J, Lehnen P, Wang Y G, Prosandeev S A, J. Phys. Chem. Solids., 2000, 61, 167
55、Kleemann W, Wang YG, Lehnen P, Dec J, Ferroelectrics, 1999, 229, 39
56、Zhang L, Zhong WL, Kleemann W, Europhys. Lett., 2001, 53, 401
57、Zhang L, Zhong WL, Kleemann W, Phys. Lett. A, 2000, 276, 162
58、Hchli U T, Weibel H E, Boatner L A, Phys. Rev. lett., 1978, 41, 1410
59、Van der Klink J J, Rytz D, Borsa F, Hchli U T, Phys. Rev. B., 1983, 27, 89
60、Janssen T, Tjon J A, Phys. Rev. B., 1981, 24, 2245