臺灣博碩士論文加值系統

由於電荷載子的自旋極化特性，半金屬(half metal)鐵磁材料被預期將在自旋相關的電子元件扮演重要的角色。而在這些材料中，由兩種元素所組成的CrO2是最簡單的半金屬材料同時其自旋極化的程度也最高(90%~98%)；而電洞摻雜(hole-doped)的LaMnO3 的自旋極化程度居次(85%~90%)，且因為超巨磁阻(colossal magnetoresistance, CMR)效應而受到矚目。在本論文中我們以這兩種材料為研究對象。
首先，我們發展了利用將TiN 氧化成TiO2 作為緩衝層，在Si 基板上成長高品質CrO2 與La2/3Sr1/3MnO3 薄膜的特殊技術，同時也量測這些薄膜的磁性與傳輸性質，並探討其半金屬特性與磁阻效應的機制。
其次，在電洞摻雜的LaMnO3 中，氧離子在磁性與傳輸性質所扮演的角
色還未完全了解。我們在SrTiO3 單晶基板上製備不同氧含量的La2/3Ca1/3MnO3-y(LCMO)薄膜，並量測其磁性與電阻行為，研究氧空缺對LCMO 薄膜傳輸性質與磁性相變的影響，並進一步探討絕緣-金屬相變與磁性相變之間的關係。
最後，X 光近邊吸收結構(x-ray absorption near-edge structure, XANES)光譜是研究鈣鈦礦(perovskite)結構氧化物之電子結構與未填滿軌域的有利工具。然而所謂的自我吸收效應(self-absorption effect)會引起螢光產率(fluorescence yield)光譜的變形，我們以(110)軸向的YBa2Cu3O7-y 薄膜為例，詳細說明自我吸收效應的修正程序，並探討自我吸收效應對CrO2 與La2/3(Sr, Ca)1/3MnO3 薄膜的螢光產率光譜的影響，並比較修正前後的光譜。

The half-metallic ferromagnets are expected to play a signicant role in the spin-based electronic devices by virtue of the spin-polarized characteristics of the charge carriers. In particular, among these materials, CrO2 with the highest polarization (90%~98%) is the simplest half-metallic ferromagnet, consisting of only two elements. Hole-doped LaMnO3
with the second highest polarization (85%~90%) has attracted much attention recently as a result of the colossal magnetoresistance (CMR) features. Therefore, CrO2 and hole doped LaMnO3 were regarded as the study objects in this dissertation.
Firstly, we developed a novel technique to fabricate high-quality CrO2 and La2/3Sr1/3MnO3 films on silicon substrates by means of oxidizing TiN into TiO2 as buffer layer. Simultaneously, the magnetic and transport properties of the as-grownfilms were also measured. Similarly, the half-metallicity and mechanism of the magnetoresistance were
intensively investigated.
Secondly, the role played by the oxygen ions in the hole-doped LaMnO3 is still not completely understood. We prepared La2/3Ca1/3MnO3-y films with various oxygen contents
on SrTiO3 single-crystalline substrates and measured the resistivity and magnetic properties. The influence of oxygen vacancies on the transport and magnetic phase tranisitions was investigated. Furthermore, the relationship between the insulator-metal and magnetic transitions was also studied.
Finally, x-ray near-edge structure (XANES) is one of the powerful tools to probe the electronic structure and unoccupied states of the perovskite oxides. However, the
so-called self-absorption eects will distort the
uorescence-yield XANES. We took a (110)-oriented YBa2Cu3O7-y film as an example to illustrate the correcting technique
of self-absorption eects in detail. The influence of the self-absorption effects on the fluorescence-yield XANES of CrO2 and La2/3(Sr, Ca)1/3MnO3 films was investigated. The
comparison between the spectra before and after correction was also presented.

1 Introduction
2 Transition metal oxides
2.1 Introduction
2.1.1 Mott-Hubbard insulators
2.1.2 Charge transfer insulators
2.2 Origin of magnetism
2.2.1 Direct exchange
2.2.2 Superexchange
2.2.3 Double exchange
2.2.4 Crystal field splitting and Jahn-Teller effect
2.3 CrO2
2.4 Hole-doped LaMnO3
3 The magnetic and transport properties of CrO2 films grown on TiO2-buffered Si and LaAlO3 substrates
3.1 Introduction
3.2 The CrO2 (110) films grown on the TiO2-buered Si (100) substrates
3.2.1 The growth of epitaxial TiO2 layers on Si
3.2.2 The growth of CrO2 films
3.2.3 Structure characterization
3.2.4 Temperature dependence of the resistivity
3.2.5 Magnetoresistance
3.2.6 Further analysis of the transport properties
3.2.7 The magnetic properties and half metalliticy
3.3 Grain-boundary magnetoresistance of CrO2 films grown on TiO2-buffered LaAlO3 substrates
3.3.1 The growth of TiO2 layers
3.3.2 The growth of CrO2
3.3.3 Structure characterization and surface morphology
3.3.4 Magnetic properties
3.3.5 Transport properties
3.3.6 The magneto-transport properties
4 The magnetic and transport properties of La2/3Sr1/3MnO3 films grown on TiO2-buffered Si substrates
4.1 Introduction
4.2 The preparation of the target for pulsed-laser deposition 4.3 The growth of TiO2 buffer layers and La2/3Sr1/3MO3 films
4.4 Structure characterization
4.5 Transport and magnetic properties
4.6 The grain-boundary magnetoresistance
4.7 Resistivity and half-metallicity at low temperatures
4.8 Summary
5 The magnetic and transport properties of oxygen-deffcient La2/3Ca1/3MnO3-y films
5.1 Introduction
5.2 The preparation of oxygen-deficient La2/3Ca1/3MnO3-y films grown on SrTiO3
5.3 Structure characterization
5.4 The magnetic properties
5.5 The transport properties
5.5.1 The adiabatic small polaron and Mott's variable range hopping at temperatures above TIM
5.5.2 The unconventional one-magnon scattering and small polaron metallic conduction at low temperatures
5.6 The magnetotransport properties of oxygen-deficient LCMO films
5.7 The non-linear current-voltage characteristics
5.8 Summary
6 Description of x-ray absorption near-edge structure measurements: YBa2Cu3O7-y, CrO2 and La2/3(Sr, Ca)1/3MnO3 films
6.1 Introduction
6.2 Some notions in the measurement
6.3 A illustrating example of self-absorption effect correction
6.3.1 If(E)/I0(E)
6.3.2 mu_other(E)
6.3.3 mu_t(Ef)
6.3.4 G
6.3.5 f
6.4 O K-edge XANES of (110)-oriented YBa2Cu3O7-y films
6.5 XANES of (110)-oriented CrO2 lms grown on TiO2-buffered SrTiO3
6.6 XANES of La2/3(Sr, Ca)1/3MnO3 films
6.7 Summary
7 Summary
A Appendix
A.1 Exchange interaction for non-degenerate orbitals
A.2 Magnon and Bloch T^3/2 law [121]
A.3 Polarons[121,122]
A.4 Spin glasses [122,125]

[1] R. A. de Groot, F. M. Muller, P. G. van Engen, and K. H. J. Buschow. Phys. Rev. Lett., 50:1983, 2024.
[2] J. M. D. Coey, M.Venkatesan, and M. A. Bari. Half-metallic ferromagnets. 2001.
[3] M. A. Korotin, V. I. Anisimov, D. I. Khomski, and G. A. Sawataky. Phys. Rev. Lett., 80:4305, 1998.
[4] S. P. Lewis, P. B. Allen, and T. Sasaki. Phys. Rev. B, 55:1997, 10253.
[5] B. Nadgorny, I. I. Mazin, M. Osofsky, R. J. Soulen, P. Broussard, R. M. Stroud, D. J. Singh, V. G. Harris, A. Arsenov, and Y. Mukovskii. Phy. Rev. B, 63:184433, 2001.
[6] M. Penicaud, B. Silberchiot, C. B. Sommers, and J. Kubler. J. Magn. Magn. Mater., 103:212, 1992.
[7] D. J. Singh. Phys. Rev. B, 55:313, 1997.
[8] K. I. Kobayashi, T. Kimura, H. Sawada, K. T. Terakura, and Y. Kokura. Nature, 395:677, 1998.
[9] I. I. Mazin. Appl. Phys. Lett., 77:3000, 2000.
[10] R. Weht and W. E. Pickett. Phys. Rev. B, 60:13006, 1999.
[11] S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. Daughton, S. von Molnar, M. L. Roukes, A. Y. Chtchelkanova, and D. M. Treger. 294:1488, 2001.
[12] ed. by D. C. Koningsberger and R. Prins. X-Ray Absorption: Principles, Applications, Techniques of EXAFS, SEXFAS and XANES. John Wiley & Sons, New York, 1988.
[13] B. K. Agarwal. X-Ray spectroscopy: an introduction. Springer-Verlag, Berlin Heidelberg, 1991.
[14] L. Troger, D. Arvanitis, K. Baberschke, H. Michaelis, U. Grimm, and E. Zschech. Phys. Rev. B, 46:1992, 3283.
[15] S. Eisebitt, T. Boske, J.-E. Roubensson, and W. Eberhardt. Phys. Rev. B, 47:1993, 14103.
[16] J. G. Bednorz and K. A. Muller. Z. Phys. B, 64:189, 1986.
[17] K. Schwarz. J. Phys. F, 16:L211, 1986.
[18] S. Jin, T. H. Tiefel, M. McCormack, R. A. Fastnacht, R. Ramesh, and L. H. Chen. Science, 264:413, 1994.
[19] A. S. Alexandrov and N. F. Mott. Polarons and Bipolarons. World Scientific, Singapore, 1996.
[20] H. J. de Boer and E. J. W. Verwey. Proc. Phys. Soc. London A, 49:59, 1937.
[21] N. F. Mott. Proc. Phys. Soc. London A, 62:416, 1949.
[22] N. F. Mott. Metal-insulator transition. Taylor & Francis, London, 1990.
[23] J. Hubbard. Proc. Phys. Soc. London A, 276:238, 1963.
[24] E. H. Lieb and F. Y. Wu. Phys. Rev. Lett., 20:1445, 1968.
[25] S. Hufner. Solid State Comm., 49:1177, 1985.
[26] J. Zaanen, C. Westra, and G. A. Sawatzky. Phys. Rev. B, 33:8060, 1986.
[27] G. van der Laan. Solid State Comm., 42:165, 1982.
[28] J. Zaanen, G. A. Sawatzky, and J. W. Allen. Phys. Rev. Lett., 55:418, 1985.
[29] Z.-X. Shen et al. Phys, Rev. B, 36:8414, 1987.
[30] A. Fujimori and F. Minami. Phys. Rev. B, 30:957, 1984.
[31] G. A. Sawatzky and J. W. Allen. Phys. Rev. B, 53:2339, 1984.
[32] J. B. Goodenough. Magnetism and the Chemical Bond. Interscience Publishers, New York, 1963.
[33] C. Zener. Phys. Rev., 82:403, 1951.
[34] B. J. Thamer, R. M. Douglass, and E. Staritzky. J. Am. Chem. Soc., 79:547, 1957.
[35] J. B. Goodenough. Prog. Solid State Chem., 5:145, 1971.
[36] I. I. Mazin, D. J. Singh, and C. Amobrosch-Draxl. Phys. Rev. B, 59:411, 1999.
[37] K. P. Kamper, W. Schmitt, and G. Guntherodt. Phys. Rev. Lett., 59:2788, 1987.
[38] R. J. Soulen, J. M. Beyers, M. S. Osofsky, B. Nadgorny, T. Ambrose, S. F. Cheng,
P. R. Broussard, C. T. Tanaka, J. Nowak, J. S. Moodera, A. Barry, and J. M. D. Coey. Science, 282:85, 1998.
[39] Y. Ji, G. J. Strijkers, F. Y. Yang, C. L.Chien, J. M.Byers, A. Anguelouch, Gang Xiao, and A. Gupta. Phys. Rev. Lett., 86:5585, 2001.
[40] R. Wiesendanger, H. J. Guntherodt, G. Guntherodt, R. J. Gambino, and R. Ruf. Phys. Rev. Lett., 65:247, 1990.
[41] C. B. Stagarescu, X. Su, D. E. Eastman, K. N. Altmann, F. J. Himpsel, and A. Gupta. Phys. Rev. B, 61:R9233, 2000.
[42] S. Satpathy et al. J. Appl. Phys., 79:4555, 1996.
[43] I. Solovyev et al. Phys. Rev. Lett., 76:1996, 4825.
[44] C. N. R. Rao and B. Raveau. Colossal magnetoresistance, charge ordering and related properties of manganese oxide. World Scientific, Singapore, 1998.
[45] Y. Tokura and Y. Tomioka. J. Magn. Magn. Mater., 200:1, 1999.
[46] W. Prellier, P. Lecoeur, and B. Mercey. J. Phys.: Condens. Matter., 13:R915, 2001.
[47] P. Ramirez. J. Phys.: Condens. Matter., 9:8171, 1997.
[48] E. Dagotto, T. Hotta, and A. Moreo. Physics Reports, 334:1, 2001.
[49] J. M. D. Coey, M. Viret, L. Ranno, and K. Ounadjela. Phys. Rev. Lett., 75:3910, 1995.
[50] A. J. Millis, B. I. Shraiman, and R. Mueller. Phys. Rev. Lett., 77:175, 1995.
[51] H. Roder, J. Zhang, and A. R. Bishop. Phys. Rev. Lett., 76:1356, 1996.
[52] J. H. Park, C. T. Chen, S.-W. Cheong, W. Bao, G. Meigs, V. Chakarian, and Y. U. Idzerda. Phys. Rev. Lett., 76:4215, 1996.
[53] A. S. Alexandrov and A. M. Bratkovsky. Phys. Rev. Lett., 82:141, 1999.
[54] A. S. Alexandrov and A. M. Bratkovsky. J. Phys.: Condens. Matter., 11:1989, 1999.
[55] G. M. Zhao. Phys. Rev. B, 62:11639, 2000.
[56] J.-H. Park, E. Vescovo, H.-J. Kim, C. Kwon, R. Ramesh, and T. Venkatesan. Nature (London), 392:794, 1998.
[57] For example, see A. Gupta, X. W. Li, and G. Xiao. J. Appl. Phys., 87:6073, 2000.
[58] P. A. Stampe, R. J. Kennedy, S. M. Watts, and S. von. Monar. J. Appl. Phys., 89:2001, 2001.
[59] H. Brandle, D. Weller, S. S. P. Parkin, J. C. Scott, P. Fumagalli, W. Reim, R. J. Gambino, R. Ruf, and G. Guntherodt. Phys. Rev. B, 46:13889, 1992.
[60] K. Suzuki and P.M. Tedrow. Solid State Commun., 107:583, 1998.
[61] Nicolas Martin, Christrophe Rousselot, Daniel Rondot, Frank Palmino, and Rene Mercier. Thin Solid Films, 300:113, 1997.
[62] L. M. Williams and D. W. Hess. J. Vac. Sci. Technol. A, 1:1810, 1983.
[63] Ji-Hoon Kim, Seonghoon Lee, and Hong-Sun Im. Appl. Sur. Sci., 151:6, 1999.
[64] P. I. Lin, C. W. Liu, C. C. Hsieh, K. H. Wu, J. Y. Juang, T. M. Uen, and Y. S. Gou. Jpn. J. Appl. Lett. Part 2, 40:L377, 2001.
[65] S. Ishibashi, T. Namikawa, and M. Satou. Jpn. J. Appl. Phys. Part 1, 17:249, 1978.
[66] H. Y. Hwang and S.-W. Cheong. Science, 278:1607, 1997.
[67] K. Suzuki and P.M. Tedrow. Phys. Rev. B, 58:11597, 1998.
[68] N. Furukawa. J. Phys. Soc. Jpn., 69:1954, 2000.
[69] A. Barry, J. M. D. Coey, L. Ranno, and K. Ounadjela. J. Appl. Phys., 83:7166, 1998.
[70] H. Y. Hwang, S-W. Cheng, N. P. Ong, and B. Batlogg. Phys. Rev. Lett., 77:2041, 1996.
[71] X. W. Li, A. Gupta, G. Xiao, and G. Q. Gong. Appl. Phys. Lett., 71:1997, 1124.
[72] J. S. Helman and B. Abeles. Phys. Rev. Lett., 37:1429, 1979.
[73] J. Q. Xiao, J. S. Jiang, and C. L. Chien. Phys. Rev. Lett., 68:3749, 1992.
[74] J. Inoue and S. Maekawa. Phys. Rev. B, 53:R11927, 1996.
[75] G. A. Prinz. Science, 282:1660, 1998.
[76] G. A. Prinz. Phys. Today, 48:58, 1995.
[77] G. Srinivasan, V. S. Babu, and M. S. Seehra. Appl. Phys. Lett., 67:2090, 1995.
[78] W. Zhang, I. W. Boyd, M. Elliott, and W. Herrenden-Harkerand. Appl. Phys. Lett., 69:1154, 1996.
[79] P. J. Kung, D. B. Fenner, D. M. Potrepka, and J. I. Budick. Appl. Phys. Lett., 69:427, 1996.
[80] E. S. Vlakhov, K. Dorr, K.-H. Muller, K. A. Nenkov, A. Handstein, T. I. Donchev, A. Y. Spasov, and G. D. Beshkov. Vacuum, 58:364, 2000.
[81] K. H. Wang and Y. S. Leung. Thin Solid Films, 354:55, 1999.
[82] D. Kumar, S. Chattopadhyay, W. M. Gilmore, C. B. Lee, J. Sankar, A. Kvit, A. K. Sharma, J. Narayan, S. V. Pietambaram, and R. K. Singh. Appl. Phys. Lett., 78:1098, 2001.
[83] W. Zhang, X. Wang, and I. W. Boyd. Appl. Surf. Sci., 138-139:563, 1999.
[84] Z. Trajavonic, C. Kwon, M. C. Robson, K.-C. Kim, M. Rajeswari, R. Ramesh, T. Venkatesan, S. E. Lo and, S. M. Bhagat, and D. Fork. Appl. Phys. Lett., 69:1005, 1996.
[85] S. J. Liu, J. Y. Juang, K. H. Wu, T. M. Uen, Y. S. Gou, and J.-Y. Lin. Appl. Phys. Lett., 80:4202, 2002.
[86] J. C. Chen, S. C. Law, L. C. Tung, C. C. Chi, and Weiyan Guan. Phys. Rev. B, 60:12143, 1999.
[87] A. Gupta, G. Q. Gong, G. Xiao, P. R. Duncombe, P. Lecoeur, P. Trouilloud, Y. Y. Wang, V. P. Dravid, and J. Z. Sun. Phys. Rev. B, 54:R15629, 1996.
[88] K. Kubo and N. Ohata. J. Phys. Soc. Jpn., 33:1972, 21.
[89] H. L. Ju, J. Gopalakrishnan, J. L. Peng, Q. Li, G. C. Xiong, T. Venkatesan, and R. L. Greene. Phys. Rev. B, 51:6143, 1995.
[90] Z. L. Wang, J. S. Yin, Y. D. Jiang, and J. Zhang. Appl. Phys. Lett., 70:3362, 1997.
[91] C. Ritter, M. R. Ibarra, J. M. D. Teresa, P. A.
Algarabel, C. Marquina, J. Blasco, J. Garcia, S. Osero, and S-W. Cheong. Phys. Rev. B, 56:8902, 1997.
[92] N. Malde, P. S. I. de Silva, A. K. M. A. Hossain, L. F. Cohen, K. A. Thomas, J. L. MacManus-Driscoll, N. D. Mathur, and M. G. Blamire. Solid State Commun., 105:643, 1998.
[93] M. Rajeswari, R. Shreekala, A. Goyal, S. E. Lo
and, S. M. Bhagat, K. Ghosh, R. P. Sharma, R. L. Greene, R. Ramesh, and T. Venkatesan. Appl. Phys. Lett., 73:2672, 1998.
[94] K. Dorr, J. M. D. Teresa, K.-H. Muller, D. Eckert, T. Walter, E. Vlakhov, K. Nenkov, and L. Schultz. J. Phys.: Conden. Matter, 12:7099, 2000.
[95] R. Cauro1, A. Gilabert, J. P. Contour, R. Lyonnet, M.-G. Medici, J.-C. Grenet, C. Leighton, and I. K. Schuller. Phys. Rev. B, 63:174423-1, 2001.
[96] J. H. Zhao, H. P. Kunkel, X. Z. Zhou, and G. Williams. J. Phys.: Conden. Matter, 13:5785, 2001.
[97] Y. G. Zhao, W. Cai, J. Zhao, X. P. Zhang, B. S. Cao, M. H. Zhu, L. W. Zhang, S. B. Ogale, T. Wu, T. Venkatesan, L. Lu, T. K. Mandal, and J. Gopalakrishnan. Phys. Rev. B, 65:144406-1, 2002.
[98] J. Li, C. K. Ong, J.-M. Liu, Q. Huang, and S. J. Wang. Appl. Phys. Lett., 76:1051, 2000.
[99] A. Biswas, M. Rajeswari, R. C. Srivastava, T. Venkatesan, R. L. Greene, Q. Lu, A. L. de Lozanne, and A. J. Millis. Phys. Rev. B, 63:184424-1, 2001.
[100] J. W. Cai, C. Wang, B. G. Shen, J. G. Zhao, and W. S. Zhan. Appl. Phys. Lett., 71:1727, 1997.
[101] J. M. De Teresa, M. R. Ibarra, J. Garcia, J. Blasco, P. A. Algarabel, C. Marquina, and A. del Moral. Phys. Rev. Lett., 76:3392, 1996.
[102] B. D. Cullity. Introduction to Magnetic Materials. Addison-Wesley, Canada, 1972.
[103] J. A. Souza, R. F. Jardim, R. Muccillo, E. N. S. Muccillo, M. S. Torikachvili, and J. J. Neumeier. J. Appl. Phys., 89:6636, 2001.
[104] G. M. Zhao, V. Smolyaninova, W. Prellier, and H. Keller. Phys. Rev. Lett., 84:6086, 2000.
[105] J. Philip and T. R. N. Kutty. Appl. Phys. Lett., 79:79, 2001.
[106] W. Westerburg, F. Martin, S. Friedrich, M. Maier, and G. Jakob. J. Appl. Phys., 86:2173, 1999.
[107] J. E. Evetts, M. G. Blamire, N. D. Mathur, S. P. Isaac, B.-S. Teo, L. F. Cohen, and J. L. Macmanus-Driscoll. Phil. Tran. R. Soc. Lond. A, 356:1593, 1998.
[108] M. Ziese. Phys. Rev. B, 60:R738, 1999.
[109] N. K. Todd, N. D. Mathur, S. P. Issac, J. E. Evetts, and M. G. Blamire. J. Appl. Phys., 85:7263, 1999.
[110] R. Gross, L. Al, and B. Buchner et al. J. Magn. Magn. Mater., 211:150, 2000.
[111] S. J. Liu, S. F. Chen, J. Y. Juang, K. H. Wu, T. M. Uen, Y. S. Gou, and J.-Y. Lin. (submitted to Phys. Rev. B). 2002.
[112] R.Gunnarsson, A. Kadigrobov, and Z. Ivanov. Phys. Rev. B, 66:024404, 2002.
[113] M. Merz, N. Nucker, P. Schweiss, S. Schuppler, C. T. Chen, V. Chakarian, J. Freeland, Y. U. Idzerda, M. Klaser, G. Muller-Vogt, and Th. Wolf. Phys. Rev. Lett., 80:5192, 1998.
[114] M. Merz, N. Nucker, E. Pellegrin, P. Schweiss, S. Schuppler, M. Lielwein, Knupfer, M. S. Golden, J. Fink, C. T. Chen, V. Chakarian, Y. U. Idzerda, and A. Erb. Phys.
Rev. B, 55:9160, 1997.
[115] A. Krol, Z. H. Zing, Y. H. Yao, N. Nucker, G. Roth, J. Fink, G. C. Smith, K. T.
Park, J. Yu, J. Freeman, A. Erb, G. Muller-Vogt, J. Karpinski, E. Kaldis, and K. Schonmann. Phys. Rev. B, 45:2581, 1995.
[116] S. P. Chen. The growth and characteriztion of (110)-oriented YBa2Cu3O7-yfilms. PhD thesis, National Chiao Tung University, 2000.
[117] H. Alloul, T. Ohno, and P. Mendels. Phys. Rev. Lett., 63:1700, 1989.
[118] N. Nucker, E. Pellegrin, P. Schweiss, J. Fink, S. L. Molodtsov, C. T. Simmons, G. Kaindl, W. Frentrup, A. Erb, and G. Muller-Vogt. Phys. Rev. B, 51:8529, 1995.
[119] W. M. Temmerman, Z. Szotec, and G. Y. Guo. J. Phys. C, 21:L867, 1988.
[120] A. M. Oles and W. Grzelka. Phys. Rev. B, 44:9531, 1991.
[121] R. Lawrence Comstock. Introduction to Magnetism and Magnetic Recording. John Wiley & Sons, New York, 1999.
[122] E. Dagotto. Nanoscale Phase Separation and Colossal Magnetoresistance: The Physics of Manganites and Related Compounds. Springer-Verlag, Berlin Heidelberg, 2002.
[123] T. Holstein. Ann. Phys., 8:325, 1959.
[124] William Jones and Norman H. March. Chapter 9 in "Theoretical Solid State Physics Volume 2: Non-equilibrium and Disorder". John Wiley & Sons, London, 1979.
[125] J. A. Mydosh. Spin Glasses: an Experimental Introduction. Taylor & Francis, London, 1993.