過渡金屬氧化物所構成異質結構之界面電子結構探討

Interfacial Electronic Properties of Transition-Metal-Oxide Heterostructures

10.6843/NTHU.2012.00075

朱晏誼

界面物理 ； 超晶格薄膜 ； 硬X光光電子能譜 ； 軟X光共振散射 ； 過渡金屬氧化物 ； 楊泰勒晶格形變 ； Interface physics ； Superlattices ； X-ray photoelectron spectra ； Resonant soft X-ray scattering ； Transition metal oxides ； Jahn-Teller effect

清華大學材料科學工程學系學位論文

2012年

博士

黃金花;黃迪靖

英文

過渡金屬氧化物已成為新一代電子元件的關鍵材料，這類氧化物所擁有的多樣化物理特性，取決於各自的電子結構。由於近幾年科技的快速進展，更多引人注意、新穎的物理特性，在超薄膜與氧化物異質界面中陸續被發現。因此，本論文主要利用彈性軟X光共振散射與硬X光光電子能譜實驗，來探討這些多層膜與超薄膜氧化物系統的前瞻物理現象。 近幾年的研究發現，氧化物異質結構的界面會產生意想不到的電子結構與磁特性，且不同於其塊材的性質，因而使界面物理成為相當熱門的研究題目。本論文的第一個主題，我們使用硬X光光電子能譜技術，並應用掠角入射的方式，探討移轉至界面的電荷分佈範圍。LaAlO3與SrTiO3所組成的異質結構一直是界面物理研究最具代表性的題目，然而形成於界面的二維電子氣(two-dimensional electron gas)，其電荷的移轉範圍與移轉總量一直是尚待解決的問題。由於硬X光光電子能譜的實驗結果可以提供界面電子結構重組的直接資訊，像是直接量測到三價鈦 (Ti3+) 的訊號，且有限的電子平均自由行徑也可提供我們電荷移轉的空間分佈資訊。當X光入射角度跨越臨界角度時，X光會被大幅吸收，藉由計算模擬，此一實驗結果顯示在界面處約有2% 四價鈦轉變成為三價鈦，且二維電子氣分佈範圍從界面開始往SrTiO3基板內部延伸約 48Å，因此移轉的電荷總量大約為 0.24電子/二維單位晶胞。 異質結構的界面軌域極化方向同樣是重要的研究課題。因此，本論文的第二個研究主軸，我們首次證明了可以利用軟X光共振散射，直接量測到 LaMnO3/SrMnO3 超晶格薄膜界面的軌域極化方向。配合理論分析，此與散射角度相關的量測結果，顯示界面電子結構重組造成軌域極化方向為垂直於膜面法線方向。 最後，我們進一步利用氧化物超晶格結構，搭配軟X光共振散射，探討磁性相轉變對於楊泰勒晶格形變(Jahn-Teller distortion)的影響。一般來說，軌域有序與磁有序結構經常會共存於錳氧化物中，且磁特性與電荷傳導特性皆與軌域有序結構有極大的關聯性。然而到目前為止，錳氧化物軌域有序結構的起因依舊為一尚未解決的問題。因此我們利用特別設計的LaMnO3/SrMnO3超晶格薄膜，搭配軟X光共振散射的實驗技術，我們觀察到實驗上的證據，顯示整體性的楊泰勒晶格形變(Global Jahn-Teller distortion) 與多體性的超交換相互作用(many-body superexchange interaction) 之間密切的相關連性。此一關聯性期望可為解決軌域有序結構的起源帶來另一個方案，也同時展現出整體性的楊泰勒晶格形變源自於錳氧化物系統中多體的本質。

Complex transition metal oxides have become key materials for new generations of electronic devices. Physical properties of such oxides are strongly correlated with their electronic structures. Based on the progress of recent technologies, much more fanscinating physical phenomena and novel functionalities, arising from the ultrathin oxide films and oxide interfaces, have been revealed. In this thesis, we mainly performed resonant soft x-ray scattering (RSXS) and hard x-ray photoemission spectroscopy (HAXPES) to study some forefront physical topics in LaAlO3/SrTiO3 heterostructure and manganite LaMnO3/SrMnO3 superlattice. Unexpected electronic and magnetic properties at interfaces between distinct transition-metal oxides have received much attention. The electronic phase at the interface of a heterostructure often diers from those of the sandwiching bulks. In the rst part of this thesis, we present a HAXPES method under grazing incidence to probe the distribution of charge transfer at the interface of LaAlO3/SrTiO3 heterostructure. The heterostructure between LaAlO3 and SrTiO3 is one of representative systems with fascinating interfacial properties. However, dimensionality and quantitative information about the charge distribution of this system near the interface also remains unclear. The HAXPES results, which provide direct information about the prole of electronic reconstruction, not only show the existence of Ti3+ but also reveal its finite distribution depth. By exploiting the collapse of evanescent x-ray waves and the abrupt increase of x-ray absorption at the critical incidence angle, our HAXPES study reveals a 2% electronic reconstruction from Ti4+ to Ti3+ occurring near the interface. Such an electronic reconstruction also extends from the interface into SrTiO3 with a depth of about 48 A (12 unit cells) and an estimated total charge transfer of 0.24 electrons per two-dimensional unit cell. Among the interface physics, particularly, orbital polarization is one of the most interesting topics. The second subject in this thesis, we measured directly the orbital polarization of interfacial electronic states in a system of LaMnO3/SrMnO3 superlattice. A theoretical analysis of the angular dependence of scattering yields measurements on the electronic reconstruction across the interface exhibits an in-plane orbital polarization. We for the rst time demonstrated that resonant soft x-ray scattering is a unique means to measure directly the interfacial orbital polarization of a superlattice, in contrast to the measurement of linear dichroism in x-ray absorption. At the last part of this thesis, by applying advantages of thin film synthesis on this specially designed LaMnO3/SrMnO3 superlattice, we further examine experimentally the change in Jahn-Teller distortions across a magnetic transition. Since spin and orbital orderings coexist in manganites, and the magnetic and transport properties are closely related to the orbital ordering. Yet a fundamental unresolved issue is to explain the formation of orbital ordering in manganites. As a consequence, we provide experimental evidence that the global Jahn-Teller distortion is tied up with the many-body superexchange interaction. The measured Jahn-Teller distortion is markedly enhanced upon the emergence of magnetization and strongly correlated with the spin ordering in manganites. Such a close connection sheds light on the mystery of the mechanism of orbital ordering and reveals the many-body origin of the global Jahn-Teller distortions in manganites.

1. Chapter 1
   連結：
2. [1] J. G. Bednorz and K. A. Muller, Z. Phys. B: Condens. Matter 64, 189(1986).
   連結：
3. [2] L. Gao et al., Phys. Rev. B 50, 4260 (1994).
   連結：
4. [3] J. Orenstein and A. J. Millis, Science 288, 468 (2000).
   連結：
5. [5] F.-C. Hsu et al., Proc. Natl. Acad. Sci. USA. 105, 14262 (2008).
   連結：
6. [6] D. Khomskii, Physics 2, 20 (2009).
   連結：
7. [7] T. Kimura, Annu. Rev. Mater. Res. 37, 387 (2007).
   連結：
8. [9] M. Fiebig, J. Phys. D: Appl. Phys. 38, R123 (2005).
   連結：
9. [10] A. J. Milli, Nature 392, 147 (1998).
   連結：
10. [11] Y. Tokura, Colossal Magnetoresistive Oxides, Gordon & Breach, 2000.
    連結：
11. [12] E. Dagotto, Nanoscale phase separation and colossal magnetoresistance: the physics of manganites and related compounds, New York: Springer, 2003.
    連結：
12. [13] S. Jin et al., Science 264, 413 (1994).
    連結：
13. [14] M. Imada, A. Fujimori, and Y. Tokura, Rev. Mod. Phys. 70, 1039 (1998).
    連結：
14. [15] C. N. Berglund and H. J. Guggenheim, Phys. Rev. 185, 1022 (1969).
    連結：
15. [18] A. I. Abramovich and A. V. Michurin, Low Temp. Phys. 27, 278 (2001).
    連結：
16. [20] J. Zaanen, G. A. Sawatzky, and J. W. Allen, Phys. Rev. Lett. 55, 418(1985).
    連結：
17. [24] C. Zener, Phys. Rev. 81, 440 (1951).
    連結：
18. [25] C. Zener, Phys. Rev. 82, 403 (1951).
    連結：
19. [26] P. W. Anderson and H. Hasegawa, Phys. Rev. 100, 675 (1955).
    連結：
20. [27] P. G. de Gennes, Phys. Rev. 118, 141 (1960).
    連結：
21. [34] J. van den Brink, New J. Phys. 6, 201 (2004).
    連結：
22. [35] M. Coey, Nature 430, 155 (2004).
    連結：
23. [36] J. Hemberger et al., Phys. Rev. B 66, 094410 (2002).
    連結：
24. [38] Y. Lu et al., Phys. Rev. B 54, R8357 (1996).
    連結：
25. [40] S. Ikeda et al., Appl. Phys. Lett. 93, 082508 (2008).
    連結：
26. [41] A. V. Ramos et al., Appl. Phys. Lett. 91, 122107 (2007).
    連結：
27. [42] P. Maksymovych et al., Science 12, 1421 (2009).
    連結：
28. [43] V. Garcia et al., Nature 460, 81 (2009).
    連結：
29. [44] G. C. Xiong et al., Appl. Phys. Lett. 67, 3031 (1995).
    連結：
30. [45] A. Urushibara et al., Phys. Rev. B 51, 14103 (1995).
    連結：
31. Matter. 20, 273201 (2008).
    連結：
32. [49] T. Kimura et al., Nature 426, 55 (2003).
    連結：
33. [50] J. Wang et al., Science 299, 1719 (2003).
    連結：
34. [52] S. Valencia et al., Nat. Mater. 10, 753 (2011).
    連結：
35. [54] A. Ohtomo and H. Y. Hwang, Nature 427, 423 (2006).
    連結：
36. [55] N. Reyren et al., Science 317, 1196 (2007).
    連結：
37. [56] K. S. Takahashi, M. Kawasaki, and Y. Tokura, Appl. Phys. Lett. 79, 1324(2001).
    連結：
38. [57] T. Koida et al., Phys. Rev. B 66, 144418 (2002).
    連結：
39. [58] J. Chakhalian et al., Nat. Phys. 2, 244 (2006).
    連結：
40. [61] P. Perna et al., Appl. Phys. Lett. 97, 152111 (2010).
    連結：
41. [62] Y. Hotta, T. Susaki, and H. Y. Hwang, Phys. Rev. Lett. 99, 236805(2007).
    連結：
42. [64] J. Chakhalian et al., Science 318, 1114 (2007).
    連結：
43. [65] J. Hoppler et al., Nat. Mat. 8, 315 (2009).
    連結：
44. [66] O. Yuli et al., Phys. Rev. Lett. 101, 057005 (2008).
    連結：
45. [67] A. Gozar et al., Nature 455, 782 (2008).
    連結：
46. [68] A. D. Caviglia et al., Phys. Rev. Lett. 104, 126803 (2010).
    連結：
47. [70] Ariando et al., Nat. Commun. 2, 188 (2011).
    連結：
48. [72] J. A. Bert et al., Nat. Phys. 7, 767 (2011).
    連結：
49. [73] C. Aruta et al., Phys. Rev. B 80, 140405 (2009).
    連結：
50. [1] V. Berestetskii, E. Lifshitz, and L. Pitaevskii, Quantum Electrodynamics (2nd ed.), Reed, Oxford, 1982.
    連結：
51. [2] A. Akhiezer and V. Berestetskii, Quantum Electrodynamics, Wiley, New York, 1965.
    連結：
52. [3] J. Jackson, Classical Electrodynamics (2nd ed.), Wiley, New York, 1975.
    連結：
53. [6] D. S. billeau, X-ray and Electron Spectroscopies: An Introduction, Lect. Notes. Phys. 697, 15-57, 2006.
    連結：
54. [10] S. Hfner, Photoelectron Spectroscopy, Springer-Verlag, Berlin, 1995.
    連結：
55. [11] A. Damascelli, Physica Scripta T 109, 61 (2004).
    連結：
56. [13] K. Kobayashi, Nucl. Instrum. Methods Phys. Res. A 601, 32 (2009).
    連結：
57. [15] E. W. Plummer and W. Eberhardt, Angle-Resolved Photoemission as a Tool for the Study of Surfaces, John Wiley & Sons, Inc., Hoboken, NJ, 2007.
    連結：
58. [16] S. Hanfer, Photoelectron Spectroscopy Principles and Applications (3rd ed.), Springer-Verlag: Berline Heicelberg, 2003.
    連結：
59. [17] C. J. Powell, Surf. Sci. 44, 29 (1974).
    連結：
60. [18] M. P. Seah and W. A. Dench, Surf. Interface Anal. 1, 2 (1974).
    連結：
61. [19] D. R. Penn, Phys. Rev. B 13, 5248 (1976).
    連結：
62. [20] M. P. Seah and W. A. Dench, Surf. Interface Anal. 1, 2 (1979).
    連結：
63. [21] J. J. Yeh and I. Lindau, Atomic Data and Nuclear Data Tables 32, 1(1985).
    連結：
64. [22] K. Kobayashi et al., Appl. Phys. Lett. 83, 1005 (2003).
    連結：
65. [2] H. Takagi and H. Y. Hwang, Science 327, 1601 (2010).
    連結：
66. [3] A. Ohtomo and H. Y. Hwang, Nature 427, 423 (2006).
    連結：
67. [4] N. Reyren et al., Science 317, 1196 (2007).
    連結：
68. [5] A. Brinkman et al., Nat. Mater. 6, 493 (2007).
    連結：
69. [7] M. Huijben et al., Nat. Mater. 5, 556 (2006).
    連結：
70. [8] W. Siemons et al., Phys. Rev. Lett. 98, 196802 (2007).
    連結：
71. [9] G. Herranz et al., Phys. Rev. Lett. 98, 216803 (2007).
    連結：
72. [10] A. Kalabukhov et al., Phys. Rev. B 75, 121404 (2007).
    連結：
73. [11] P. R. Willmott et al., Phys. Rev. Lett. 99, 155502 (2007).
    連結：
74. [13] A. S. Kalabukhov et al., Phys. Rev. Lett. 103, 146101 (2009).
    連結：
75. [15] M. Salluzzo et al., Phys. Rev. Lett. 102, 166804 (2009).
    連結：
76. [16] M. Basletic et al., Nat. Mater. 7, 621 (2008).
    連結：
77. [18] C. Noguera, J. Phys. Condens. Matter 12, R367 (2000).
    連結：
78. [19] H. Y. Hwang, Science 313, 1895 (2006).
    連結：
79. [20] M. Takizawa, S. Tsuda, T. Susaki, H. Y. Hwang, and A. Fujimori, arXiv, 1106.3619v1 (2011).
    連結：
80. [21] M. Sing et al., Phys. Rev. Lett. 102, 176805 (2009).
    連結：
81. [22] G. Berner et al., Phys. Rev. B 82, 241405 (2010).
    連結：
82. [23] K.-J. Zhou et al., Phys. Rev. B 83, 201402 (2011).
    連結：
83. [24] J. Als-Nielsen and D. McMorrow, Elements of Modern X-ray Physics, John Wiley & Sons Inc, Chichester, 2001.
    連結：
84. [25] R. Pentcheva and W. E. Pickett, Phys. Rev. B 78, 205106 (2008).
    連結：
85. [26] P. Delugas, A. Filippetti, and V. Fiorentini, Phys. Rev. Lett. 106, 166807(2011).
    連結：
86. [27] Z. S. Popovic, S. Satpathy, and R. M. Martin, Phys. Rev. Lett. 101, 256801 (2008).
    連結：
87. [1] J. Chakhalian et al., Nat. Phys. 2, 244 (2006).
    連結：
88. [3] S. Okamoto and A. J. Millis, Nature 428, 630 (2004).
    連結：
89. [4] P. A. Salvador and A. M. Haghiri-Gosnet, Appl. Phys. Lett. 75, 2638(1999).
    連結：
90. [6] S. Smadici et al., Phys. Rev. Lett. 99, 196404 (2007).
    連結：
91. [7] A. Bhattacharya et al., Phys. Rev. Lett. 100, 257203 (2008).
    連結：
92. [8] A. B. Shah et al., Phys. Rev. B 77, 115103 (2008).
    連結：
93. [9] S. J. May et al., Phys. Rev. B 77, 174409 (2008).
    連結：
94. [11] S. Dong et al., Phys. Rev. B 78, 201102 (2008).
    連結：
95. [12] B. R. K. Nanda and S. Satpathy, Phys. Rev. B 79, 054428 (2009).
    連結：
96. [13] C. Aruta et al., Phys. Rev. B 80, 140405 (2009).
    連結：
97. [14] H. Yamada, P. H. Xiang, and A. Sawa, Phys. Rev. B 81, 014410 (2010).
    連結：
98. [15] B. R. K. Nanda and S. Satpathy, Phys. Rev. B 81, 224408 (2010).
    連結：
99. [16] C. Lin, S. Okamoto, and A. J. Millis, Phys. Rev. B 73, 041104 (2006).
    連結：
100. [17] C. Lin and A. J. Millis, Phys. Rev. B 78, 184405 (2008).
     連結：
101. [18] C. Adamo et al., Appl. Phys. Lett. 92, 112508 (2008).
     連結：
102. [19] T. Koida et al., Phys. Rev. B 66, 144418 (2002).
     連結：
103. [21] P. Abbamonte et al., Science 297, 581 (2002).
     連結：
104. [22] D. J. Huang et al., Phys. Rev. Lett. 96, 096401 (2006).
     連結：
105. Chapter 5
     連結：
106. [1] Y. Tokura and N. Nagaosa, Science 288, 462 (2000).
     連結：
107. [2] J. Kanamori, J. Appl. Phys. 31, S14 (1960).
     連結：
108. [4] J. Rodrguez-Carvajal et al., Phys. Rev. B 57, R3189 (1998).
     連結：
109. [5] Y. Murakami et al., Phys. Rev. Lett. 81, 582 (1998).
     連結：
110. [6] W.-G. Yin, D. Volja, and W. Ku, Phys. Rev. Lett. 96, 116405 (2006).
     連結：
111. [8] A. Sartbaeva, S. A.Wells, M. F. Thorpe, E. S. Bozin, and S. J. L. Billinge, Phys. Rev. Lett. 99, 155503 (2007).
     連結：
112. [9] E. Pavarini and E. Koch, Phys. Rev. Lett. 104, 086402 (2010).
     連結：
113. [10] A. Sadoc et al., Phys. Rev. Lett. 104, 046804 (2010).
     連結：
114. [11] G. Subas et al., Phys. Rev. B 75, 235101 (2007).
     連結：
115. [13] D.-J. Huang, J. Okamoto, S.-W. Huang, and C.-Y. Mou, J. Phys. Soc. Jpn. 79, 011009 (2010).
     連結：
116. [14] J. Okamoto et al., Phys. Rev. Lett. 98, 157202 (2007).
     連結：
117. [16] U. Staub et al., Phys. Rev. B 71, 214421 (2005).
     連結：
118. [17] S. Smadici et al., Phys. Rev. Lett. 99, 196404 (2007).
     連結：
119. [18] A. Bhattacharya et al., Phys. Rev. Lett. 100, 257203 (2008).
     連結：
120. [20] O. Chmaissem et al., Phys. Rev. B 64, 134412 (2001).
     連結：
121. [21] C. W. M. Castleton and M. Altarelli, Phys. Rev. B 62, 1033 (2000).
     連結：
122. [4] Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono, J. Am. Chem. Soc. 130, 3296 (2008).
123. [8] S.-W. Cheong and M. Mostovoy, Nat. Mater. 6, 13 (2007).
124. [16] R. V. Demin, L. I. Koroleva, A. Z. Muminov, and Y. M. Mukovskii, Phys. Solid State 48, 322 (2006).
125. [17] M. R. Ibarra, P. A. Algarabel, C. Marquina, J. Blasco, and J. Garc, Phys. Rev. Lett. 75, 3541 (1995).
126. [19] J. Hubbard, Proc. R. Soc. Lond. 276, 238 (1963).
127. [21] K. I. Kugel' and D. I. Khomskii, Sov. Phys. sp. 25, 231 (1982).
128. [22] A. J. Millis, P. B. Littlewood, and B. I. Shraiman, Phys. Rev. Lett. 74, 5144 (1995).
129. [23] H. Roder, J. Zang, and A. R. Bishop, Phys. Rev. Lett. 76, 1356 (1996).
130. [28] E. Dagottoa, T. Hotta, and A. Moreo, Physics reports 344, 1 (2001).
131. [29] J. B. Goodenough, Magnetism and the chemical bond, New York, : Interscience Publishers, 1963.
132. [30] J. M. Tranquada, B. J. Sternlieb, J. D. Axe, Y. Nakamura, and S. Uchida, Nature 375, 561 (1995).
133. [31] H. Kuwahara, Y. Tomioka, A. Asamitsu, Y. Moritomo, and Y. Tokura, Science 270, 961 (1995).
134. [32] Y. Moritomo, H. Kuwahara, Y. Tomioka, and Y. Tokura, Phys. Rev. B 55, 7549 (1997).
135. [33] M. W. Lufaso and P. M. Woodward, Acta. Cryst. B 60, 10 (2004).
136. [37] J. M. D. Coey, M. Viret, and S. von Molnar, Adv. Phys. 48, 167 (1999).
137. [39] S. Yuasa, A. Fukushima, H. Kubota, Y. Suzuki, and K. Ando, Appl. Phys. Lett. 89, 042505 (2006).
138. [46] P. K. Siwach, H. K. Singh, and O. N. Srivastava, J. Phys. Condens.
139. [47] M. Fath et al., Science 285, 1540 (1999).
140. [48] M. Uehara, S. Mori, C. H. Chen, and S.-W. Cheong, Nature 399, 560(1999).
141. [51] C.-G. Duan, S. S. Jaswal, and E. Y. Tsymbal, Phys. Rev. Lett. 97, 047201(2006).
142. [53] A. Ohtomo, D. A. Muller, J. L. Grazul, and H. Y. Hwang, Nature 419, 378 (2002).
143. [59] A. Kalabukhov, R. Gunnarsson, T. Claeson, and D. Winkler, arXiv, 0704.1050v1 (2007).
144. [60] K. Shibuya, T. Ohnishi, M. Lippmaa, and M. Oshim, Appl. Phys. Lett. 91, 232106 (2007).
145. [63] N. Nakagawa, H. Y. Hwang, and D. A. Muller, Nat. Mater. 5, 204 (2006).
146. [69] N. Ogawa, T. Satoh, Y. Ogimoto, and K. Miyano, Phys. Rev. B 78, 212409 (2008).
147. [71] L. Li, C. Richter, J. Mannhart, and R. C. Ashoori, Nat. Phys. 7, 762(2011).
148. [74] R. Yu, S. Yunoki, S. Dong, and E. Dagotto, Phys. Rev. B 80, 125115(2009).
149. Chapter 2
150. [4] J. J. Sakura, Advance Quantum Mechanics, Addison-Wesley, London, UK, 1967.
151. [5] M. Blume, J. Appl. Phys. 57, 3615 (1985).
152. [7] D. Gibbs, D. R. Harshman, E. D. Isaacs, and D. B. Mcwhan, Phys. Rev. Lett. 61, 1241 (1988).
153. [8] J. P. Hannon, G. T. Trammell, M. Blume, and D. Gibbs, Phys. Rev. Lett. 61, 1245 (1988).
154. [9] J. P. Hannon, G. T. Trammell, M. Blume, and D. Gibbs, Phys. Rev. Lett. 62, 2644 (1989).
155. [12] J. F. Watts and J. Wolstenholme, An Introduction to Surface Analysis by XPS and AES (1st ed.), England West Sussex: John Wiley, 2003.
156. [14] H. Luth, Surfaces and Interfaces of Solid Materials (3rd ed.), Springer-Verlag, Berlin Hidelberg, 1995.
157. Chapter 3
158. [1] P. Zubko, S. Gariglio, M. Gabay, P. Ghosez, and J.-M. Triscone, Annu. Rev. Condens. Matter Phys. 2, 141 (2011).
159. [6] S. Thiel, G. Hammerl, A. Schmehl, C. W. Schneider, and J. Mannhart, Science 313, 1942 (2006).
160. [12] N. Nakagawa, H. Y. Hwang, and D. A. Muller, Nat. Mater. 5, 204 (2006).
161. [14] K. Yoshimatsu, R. Yasuhara, H. Kumigashira, and M. Oshima, Phys. Rev. Lett. 101, 026802 (2008).
162. [17] R. Hesper, L. H. Tjeng, A. Heeres, and G. A. Sawatzky, Phys. Rev. B 62, 16046 (2000).
163. Chapter 4
164. [2] A. Ohtomo, D. A. Muller, J. L. Grazul, and H. Y. Hwang, Nature 419, 378 (2002).
165. [5] H. Yamada, M. Kawasaki, T. Lottermoser, T. Arima, and Y. Tokura, Appl. Phys. Lett. 89, 052506 (2006).
166. [10] N. Ogawa, T. Satoh, Y. Ogimoto, and K. Miyano, Phys. Rev. B 78, 212409 (2008).
167. [20] T. S. Santos, S. J. May, J. L. Robertson, and A. Bhattacharya, Phys. Rev. B 80, 155114 (2009).
168. 113
169. [3] K. Kugel and D. Khomskii, Sov. Phys. JETP 37, 725 (1973).
170. [7] X. Qiu, T. Proen, J. F. Mitchell, and S. J. L. Billinge, Phys. Rev. Lett. 94, 177203 (2005).
171. [12] J. P. Hannon, G. T. Trammell, M. Blume, and D. Gibbs, Phys. Rev. Lett. 61, 1245 (1988).
172. [15] N. Stojic, N. Binggeli, and M. Altarelli, Phys. Rev. B 72, 104108 (2005).
173. [19] K. Hirota, N. Kaneko, A. Nishizawa, and Y. Endoh, J. Phys. Soc. Jpn. 65, 3736 (1996).