Dynamical mean-field approach to materials with strong electronic correlations

European Physical Journal: Special Topics

Volumn 180, Issue 1, 2009, Pages 5-28

  Kunes J ^a   Leonov, I ^b   Kollar, M ^b   Byczuk, K ^c   Anisimov, V I ^d   Vollhardt, D ^b  

^a INSTITUTE OF PHYSICS   (Czech Republic)

^b UNIVERSITY OF AUGSBURG   (Germany)

^c UNIVERSITY OF WARSAW   (Poland)

^d INSTITUTE OF METAL PHYSICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77954402279     PISSN: 19516355     EISSN: 19516401     Source Type: Journal    
DOI: 10.1140/epjst/e2010-01209-0     Document Type: Review

References (149)

1. M. Imada, A. Fujimori, Y. Tokura, Rev. Mod. Phys. 70, 1039 (1998).
2. Y. Tokura, N. Nagaosa, Science 288, 462 (2000).
3. E. Dagotto, Science 309, 257 (2005).
4. R. O. Jones, O. Gunnarsson, Rev. Mod. Phys. 61, 689 (1989).
5. J. P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).
6. F. Tran, P. Blaha, Phys. Rev. Lett. 102, 226401 (2009).
7. V. I. Anisimov, J. Zaanen, O. K. Andersen, Phys. Rev. B 44, 943 (1991).
8. A. I. Liechtenstein, V. I. Anisimov, J. Zaanen, Phys. Rev. B 52, R5467 (1995).
9. V. I. Anisimov, F. Aryasetiawan, A. I. Lichtenstein, J. Phys.: Condens. Matter 9, 767 (1997).
10. S. Baroni, S. de Gironcoli, A. Dal Corso, P. Giannozzi, Rev. Mod. Phys. 73, 515 (2001).
11. P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. Fabris, G. Fratesi, S. de Gironcoli, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P. Umari, R. M. Wentzcovitch, J. Phys. Condens. Matter 21, 395502 (2009).
12. P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, J. Luitz, WIEN2k, An Augmented Plane Wave + Local Orbitals Program for Calculating Crystal Properties (Karlheinz Schwarz, Techn. Universität Wien, Austria, 2001).
13. G. Kresse, J. Hafner, Phys. Rev. B 47, 558 (1993).
14. W. Metzner, D. Vollhardt, Phys. Rev. Lett. 62, 324 (1989).
15. A. Georges, G. Kotliar, W. Krauth, M. J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996).
16. G. Kotliar, D. Vollhardt, Phys. Today 57, 53 (2004).
17. G. Kotliar, S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet, C. A. Marianetti, Rev. Mod. Phys. 78, 865 (2006).
18. M. I. Katsnelson, V. Yu. Irkhin, L. Chioncel, A. I. Lichtenstein, R. A. de Groot, Rev. Mod. Phys. 80, 315 (2008).
19. V. I. Anisimov, A. I. Poteryaev, M. A. Korotin, A. O. Anokhin, G. Kotliar, J. Phys. Condens. Matt. 9, 7359 (1997).
20. A. I. Lichtenstein, M. I. Katsnelson, Phys. Rev. B 57, 6884 (1998).
21. A. I. Lichtenstein, M. I. Katsnelson, G. Kotliar, in Electron Correlations and Materials Properties 2nd ed., edited by A. Gonis, N. Kioussis, M. Ciftan (Kluwer Academic/Plenum, New York, 2002), p. 428.
22. K. Held, I. A. Nekrasov, G. Keller, V. Eyert, N. Blümer, A. K. McMahan, R. T. Scalettar, Th. Pruschke, V. I. Anisimov, D. Vollhardt, Psi-k Newsletter 56, 65 (2003).
23. K. Held, I. A. Nekrasov, G. Keller, V. Eyert, N. Blümer, A. K. McMahan, R. T. Scalettar, Th. Pruschke, V. I. Anisimov, D. Vollhardt, Phys. Status Solidi B 243, 2599 (2006).
24. K. Held, Adv. Phys. 56, 829 (2007).
25. K. Held, G. Keller, V. Eyert, D. Vollhardt, V. I. Anisimov, Phys. Rev. Lett. 86, 5345 (2001).
26. E. Pavarini, S. Biermann, A. Poteryaev, A. I. Lichtenstein, A. Georges, O. K. Andersen, Phys. Rev. Lett. 92, 176403 (2004).
27. A. I. Poteryaev, A. I. Lichtenstein, G. Kotliar, Phys. Rev. Lett. 93, 086401 (2004).
28. S. Biermann, A. Poteryaev, A. I. Lichtenstein, A. Georges, Phys. Rev. Lett. 94, 026404 (2005).
29. L. Chioncel, Ph. Mavropoulos, M. Lezaić, S. Blügel, E. Arrigoni, M. I. Katsnelson, A. I. Lichtenstein, Phys. Rev. Lett. 96, 197203 (2006).
30. K. Held, A. K. McMahan, R. T. Scalettar, Phys. Rev. Lett. 87, 276404 (2001).
31. A. K. McMahan, K. Held, R. T. Scalettar, Phys. Rev. B 67, 075108 (2003).
32. B. Amadon, S. Biermann, A. Georges, F. Aryasetiawan, Phys. Rev. Lett. 96, 066402 (2006); see alsoL. V. Pourovskii, B. Amadon, S. Biermann, A. Georges, Phys. Rev. B 76, 235101 (2007) where the authors discuss the problem of full self-consistency over the charge density in Γ-Ce and Ce2O3.
33. S. Y. Savrasov, G. Kotliar, E. Abrahams, Nature (London) 410, 793 (2001).
34. X. Dai, S. Y. Savrasov, G. Kotliar, A. Migliori, H. Ledbetter, E. Abrahams, Science 300, 953 (2003).
35. S. Y. Savrasov, G. Kotliar, Phys. Rev. B 69, 245101 (2004).
36. M. I. KatsnelsonA. I. Lichtenstein, Phys. Rev. B 61, 8906 (2000).
37. A. I. Lichtenstein, M. I. Katsnelson, G. Kotliar, Phys. Rev. Lett. 87, 067205 (2001).
38. J. Braun, J. Minár, H. Ebert, M. I. Katsnelson, A. I. Lichtenstein, Phys. Rev. Lett. 97, 227601 (2006).
39. A. Grechnev, I. Di Marco, M. I. Katsnelson, A. I. Lichtenstein, J. Wills, O. Eriksson, Phys. Rev. B 76, 035107 (2007).
40. S. Chadov, J. Minár, M. I. Katsnelson, H. Ebert, D. Ködderitzsch, A. I. Lichtenstein, Europhys. Lett. 82, 37001 (2008).
41. J. Kuneš, V. I. Anisimov, A. V. Lukoyanov, D. Vollhardt, Phys. Rev. B 75, 165115 (2007).
42. J. Kuneš, V. I. Anisimov, S. L. Skornyakov, A. V. Lukoyanov, D. Vollhardt, Phys. Rev. Lett. 99, 156404 (2007).
43. J. Kuneš, A. V. Lukoyanov, V. I. Anisimov, R. T. Scalettar, W. E. Pickett, Nature Materials 7, 198 (2008).
44. J. Kuneš, Dm. M. Korotin, M. A. Korotin, V. I. Anisimov, P. Werner, Phys. Rev. Lett. 102, 146402 (2009).
45. J. Zaanen, G. A. Sawatzky, J. W. Allen, Phys. Rev. Lett. 55, 418 (1985).
46. G. A. Sawatzky, J. W. Allen, Phys. Rev. Lett. 53, 2339 (1984).
47. D. E. Eastman, J. L. Freeouf, Phys. Rev. Lett. 34, 395 (1975).
48. Z.-X. Shen, C. K. Shih, O. Jepsen, W. E. Spicer, I. Lindau, J. W. Allen, Phys. Rev. Lett. 64, 2442 (1990).
49. Z.-X. Shen, R. S. List, D. S. Dessau, B. O. Wells, O. Jepsen, A. J. Arko, R. Barttlet, C. K. Shih, F. Parmigiani, J. C. Huang, P. A. P. Lindberg, Phys. Rev. B 44, 3604 (1991).
50. O. Tjernberg, S. Söderholm, G. Chiaia, R. Girard, U. O. Karlsson, H. Nylén, I. Lindau, Phys. Rev. B 54, 10245 (1996).
51. N. Marzari, D. Vanderbilt, Phys. Rev. B 56, 12847 (1997).
52. V. I. Anisimov, D. E. Kondakov, A. V. Kozhevnikov, I. A. Nekrasov, Z. V. Pchelkina, J. W. Allen, S.-K. Mo, H.-D. Kim, P. Metcalf, S. Suga, A. Sekiyama, G. Keller, I. Leonov, X. Ren, D. Vollhardt, Phys. Rev. B 71, 125119 (2005).
53. J. E. Hirsch, R. M. Fye, Phys. Rev. Lett. 56, 2521 (1986).
54. M. Jarrell, J. E. Gubernatis, Phys. Rep. 269, 133 (1996).
55. A. Fujimori, F. Minami, S. Sugano, Phys. Rev. B 29, 5225 (1984).
56. J. van Elp, H. Eskes, P. Kuiper, G. A. Sawatzky, Phys. Rev. B 45, 1612 (1992).
57. S. V. Faleev, M. van Schilfgaarde, T. Kotani, Phys. Rev. Lett. 93, 126406 (2004).
58. J.-L. Li, G.-M. Rignanese, S. G. Louie, Phys. Rev. B 71, 193102 (2005).
59. S. Sharma, S. Shallcross, J. K. Dewhurst, E. K. U. Gross [arXiv: 0912. 1118].
60. S. Kobayashi, Y. Nohara, S. Yamamoto, T. Kujiwara, Phys. Rev. B 70, 155112 (2008).
61. C. Rödl, F. Fuchs, J. Furthmüller, F. Bechstedt, Phys. Rev. B 79, 235114 (2009).
62. F. Aryasetiawan, O. Gunnarsson, Phys. Rev. Lett. 74, 3221 (1995).
63. M. Cococcioni, S. De Gironcoli, Phys. Rev. B 71, 035105 (2005).
64. X. Ren, I. Leonov, G. Keller, M. Kollar, I. Nekrasov, D. Vollhardt, Phys. Rev. B 74, 195114 (2006).
65. F. Manghi, C. Calandra, S. Ossicini, Phys. Rev. Lett. 73, 3129 (1994).
66. R. Eder, Phys. Rev. B 76, 241103 (2007).
67. Q. Yin, A. Gordienko, X. Wan, S. Y. Savrasov, Phys. Rev. Lett. 100, 066404 (2008).
68. O. Miura, T. Fujiwara, Phys. Rev. B 77, 195124 (2008).
69. This conceptual picture was suggested to one of us (JK) by J. W. Allen.
70. A. Laeuchli, P. Werner, Phys. Rev. B 80, 235117 (2009).
71. H. Ishida, A. Liebsch, Phys. Rev. B 81, 054513 (2010).
72. C. S. Yoo, B. Maddox, J.-H. P. Klepeis, V. Iota, W. Evans, A. McMahan, M. Y. Hu, P. Chow, M. Somayazulu, D. Häusermann, R. T. Scalettar, W. E. Pickett, Phys. Rev. Lett. 94, 115502 (2005).
73. A. G. Gavriliuk, V. V. Struzhkin, I. S. Lyubutin, S. G. Ovchinnikov, M. Y. Hu, P. Chow, Phys. Rev. B 77, 155112 (2008).
74. I. S. Lyubutin, S. G. Ovchinnikov, A. G. Gavriliuk, V. V. Struzhkin, Phys. Rev. B 79, 085125 (2009).
75. R. E. Cohen, I. I. Mazin, D. G. Isaak, Science 275, 654 (1997).
76. C. G. Shull, W. A. Strauser, E. O. Wollan, Phys. Rev. 83, 333 (1951).
77. A. Fujimori, M. Saeki, N. Kimizuka, M. Taniguchi, S. Suga, Phys. Rev. B 34, 7318 (1986).
78. C.-Y. Kim, C.-Y. Kim, M. J. Bedzyk, E. J. Nelson, J. C. Woicik, L. E. Berman, Phys. Rev. B 66, 085115 (2002).
79. R. J. Lad, V. E. Henrich, Phys. Rev. B 39, 13478 (1989).
80. S. Mochizuki, Phys. Status Solidi. A 41, 591 (1977).
81. K.-H. Kim, S.-H. Lee, J.-S. Choi, J. Phys. Chem. Solids 46, 331 (1985).
82. M. P. Pasternak, G. Kh. Rozenberg, G. Yu. Machavariani, O. Naaman, R. D. Taylor, R. Jeanloz, Phys. Rev. Lett. 82, 4663 (1999).
83. G. Kh. Rozenberg, L. S. Dubrovinsky, M. P. Pasternak, O. Naaman, T. Le Bihan, R. Ahuja, Phys. Rev. B 65, 064112 (2002).
84. H. Liu, W. A. Caldwell, L. R. Benedetti, W. Panero, R. Jeanloz, Phys. Chem. Miner. 30, 582 (2003).
85. J. Badro, G. Fiquet, V. V. Struzhkin, M. Somayazulu, H.-K. Mao, G. Shen, T. Le Bihan, Phys. Rev. Lett. 89, 205504 (2002).
86. Y. Noguchi, K. Kusaba, K. Fukuoka, Y. Syono, Geophys. Res. Lett. 23, 1469 (1996).
87. Y. Mita, Y. Sakai, D. Izaki, M. Kobayashi, S. Endo, S. Mochizuki, Phys. Stat. Sol. (b) 223, 247 (2001).
88. Y. Mita, D. Izaki, M. Kobayashi, S. Endo, Phys. Rev. B 71, 100101 (2005).
89. J. R. Patterson, C. M. Aracne, D. D. Jackson, V. Malba, S. T. Weir, P. A. Baker, Y. K. Vohra, Phys. Rev. B 69, 220101 (2004).
90. C. S. Yoo, B. R. Maddox, J.-H. P. Klepeis, V. Iota, W. Evans, A. McMahan, M. Hu, P. Chow, M. Somayazulu, D. Häusermann, R. T. Scalettar, W. E. Pickett, Phys. Rev. Lett. 94, 115502 (2005).
91. J.-P. Rueff, A. Mattila, J. Badro, G. Vankò, A. Shukla, J. Phys.: Cond. Matt. 17, S717 (2005).
92. P. Werner, A. J. Millis, Phys. Rev. Lett. 99, 126405 (2007).
93. W. M. Xu, O. Naaman, G. Kh. Rozenberg, M. P. Pasternak, R. D. Taylor Phys. Rev. B 64, 094411 (2001).
94. D. J. Adams, B. Amadon, Phys. Rev. B 79, 115114 (2009).
95. The problem of the equilibrium volume of a number of simple elements has also been addressed recently in I. Di Marco, J. Minár, S. Chadov, M. I. Katsnelson, H. Ebert, A. I. Lichtenstein, Phys. Rev. B 79, 115111 (2009) and Ref. [96].
96. A. Kutepov, S. Y. Savrasov, G. Kotliar, Phys. Rev. B 80, 041103 (2009).
97. H. A. Jahn, E. Teller, Proc. R. Soc. London Ser. A 161, 220 (1937).
98. D. I. Khomskii, K. I. Kugel, Solid State Comm. 13, 763 (1973).
99. K. I. Kugel, D. I. Khomskii, Sov. Phys. Solid State 17, 285 (1975).
100. K. I. Kugel, D. I. Khomskii, Sov. Phys. JETP 52, 501 (1981).
101. K. I. Kugel, D. I. Khomskii, Sov. Phys. Usp. 25, 231 (1982).
102. O. K. Andersen, Phys. Rev. B 12, 3060 (1975).
103. O. K. Andersen, T. Saha-Dasgupta, Phys. Rev. B 62, R16219 (2000).
104. I. Leonov, N. Binggeli, Dm. Korotin, V. I. Anisimov, N. Stojić, D. Vollhardt, Phys. Rev. Lett. 101, 096405 (2008).
105. I. Leonov, Dm. Korotin, N. Binggeli, V. I. Anisimov, D. Vollhardt, Phys. Rev. B 81, 075109 (2010).
106. G. Trimarchi, I. Leonov, N. Binggeli, Dm. Korotin, V. I. Anisimov, J. Phys.: Condens. Matter 20, 135227 (2008).
107. Dm. Korotin, A. V. Kozhevnikov, S. L. Skornyakov, I. Leonov, N. Binggeli, V. I. Anisimov, G. Trimarchi, Eur. Phys. J. B 65, 91 (2008).
108. B. Amadon, F. Lechermann, A. Georges, F. Jollet, T. O. Wehling, A. I. Lichtenstein, Phys. Rev. B 77, 205112 (2008).
109. For a formulation of LDA+D MFT within a mixed-basis pseudopotential approach seeF. Lechermann, A. Georges, A. Poteryaev, S. Biermann, M. Posternak, A. Yamasaki, O. K. Andersen, Phys. Rev. B 74, 125120 (2006).
110. To describe the thermodynamics of solids one must, in principle, also compute the entropy, consider the electronic, magnetic and lattice (vibrational) contributions in the Gibbs free energy. The first two contributions are generally small and can be neglected in the paramagnetic phase of a wide-band insulator, whereas the lattice entropy may have an influence on a structural phase transition. To estimate its contribution would require to perform molecular dynamics calculations for a correlated system. This is a very demanding project which we plan to do in the future.
111. S. Kadota, I. Yamada, S. Yoneyama, K. Hirakawa, J. Phys. Soc. Jpn. 23, 751 (1967).
112. R. H. Buttner, E. N. Maslen, N. Spadaccini, Acta Cryst. B 46, 131 (1990).
113. J. B. Goodenough, Magnetism and the Chemical Bond (Interscience, New York, 1963).
114. J. E. Medvedeva, M. A. Korotin, V. I. Anisimov, A. J. Freeman, Phys. Rev. B 65, 172413 (2002).
115. E. Pavarini, E. Koch, A. I. Lichtenstein, Phys. Rev. Lett. 101, 266405 (2008).
116. N. Binggeli, M. Altarelli, Phys. Rev. B 70, 085117 (2004).
117. In general, GGA tends to give better results than LDA for the electronic and structural properties of complex oxides and related materials. SeeD. R. Hamann, Phys. Rev. Lett. 76, 660 (1996) and Ref. [118].
118. H. Sawada, Y. Morikawa, K. Terakura, N. Hamada, Phys. Rev. B 56, 12154 (1997).
119. M. T. Hutchings, E. J. Samuelsen, G. Shirane, K. Hirakawa, Phys. Rev. 188, 919 (1969).
120. T. Ueda, K. Sugawara, T. Kondo, I. Yamada, Solid State Commun. 80, 801 (1991).
121. I. Yamada, H. Fujii, M. Hidaka, J. Phys. Condens. Matter 1, 3397 (1989).
122. M. V. Eremin, D. V. Zakharov, H.-A. Krug von Nidda, R. M. Eremina, A. Shuvaev, A. Pimenov, P. Ghigna, J. Deisenhofer, A. Loidl, Phys. Rev. Lett. 101, 147601 (2008).
123. J. Deisenhofer, I. Leonov, M. V. Eremin, Ch. Kant, P. Ghigna, F. Mayr, V. V. Iglamov, V. I. Anisimov, D. van der Marel, Phys. Rev. Lett. 101, 157406 (2008).
124. L. Paolasini, R. Caciuffo, A. Sollier, P. Ghigna, M. Altarelli, Phys. Rev. Lett. 88, 106403 (2002).
125. R. Caciuffo, L. Paolasini, A. Sollier, P. Ghigna, E. Pavarini, J. van den Brink, M. Altarelli, Phys. Rev. B 65, 174425 (2002).
126. Calculations have been performed using the Quantum ESPRE SSO package, see Ref. [11, 12], http://www. quantum-espresso. org.
127. The local coordinate system is chosen with the z direction defined along the longest (in ab plane) Cu-F bond of the CuF6 octahedron.
128. Here we perform DMFT calculations for a fixed DFT Hamiltonian ĤDFT, thereby neglecting full charge self-consistency which is not expected to change the results significantly [32].
129. To simplify the computation we neglected the orbital off-diagonal elements of the local Green function by applying an additional transformation into the local basis set with a diagonal density matrix during each DMFT iteration.
130. J. B. A. A. Elemans, B. van Laar, K. R. van der Veen, B. O. Loopstra, J. Phys. Chem. Solids 3, 238 (1971).
131. J. Rodriguez-Carvajal, M. Hennion, F. Moussa, A. H. Moudden, L. Pinsard, A. Revcolevschi, Phys. Rev. B 57, R3189 (1998).
132. T. Chatterji, F. Fauth, B. Ouladdiaf, P. Mandal, B. Ghosh, Phys. Rev. B 68, 052406 (2003).
133. G. Trimarchi, N. Binggeli, Phys. Rev. B 71, 035101 (2005).
134. Th. Pruschke, M. B. Zölfl, Advances in Solid State Physics40, 251 (2000); see also R. Peters, Th. Pruschke, cond-mat/0908. 3990, where the authors discuss the interplay of orbital and spin degrees of freedom in the two orbital Hubbard model near quarter filling.
135. A. Yamasaki, M. Feldbacher, Y.-F. Yang, O. K. Andersen, K. Held, Phys. Rev. Lett. 96, 166401 (2006).
136. K. Held, O. K. Andersen, M. Feldbacher, A. Yamasaki, Y.-F. Yang, J. Phys.: Condens. Matter 20, 064202 (2008).
137. E. Pavarini, E. Koch, cond-mat/0904. 4603.
138. W.-G. Yin, D. Volja, W. Ku, Phys. Rev. Lett. 96, 116405 (2006).
139. The local coordinate system is chosen such that the GGA Mn 3d density matrix has a diagonal form.
140. A. J. Millis, B. I. Shraiman, R. Mueller, Phys. Rev. Lett. 77, 175 (1996).
141. K. Held, D. Vollhardt, Phys. Rev. Lett. 84, 5168 (2000).
142. I. A. Nekrasov, K. Held, G. Keller, D. E. Kondakov, T. Pruschke, M. Kollar, O. K. Andersen, V. I. Anisimov, D. Vollhardt, Phys. Rev. B 73, 155112 (2006).
143. O. Gunnarsson, O. K. Andersen, O. Jepsen, J. Zaanen, Phys. Rev. B 39, 1708 (1989).
144. K. Byczuk, M. Kollar, K. Held, Y.-F. Yang, I. A. Nekrasov, T. Pruschke, D. Vollhardt, Nature Physics 3, 168 (2007).
145. T. Yoshida, K. Tanaka, H. Yagi, A. Ino, H. Eisaki, A. Fujimori, Z.-X. Shen, Phys. Rev. Lett. 95, 146404 (2005).
146. M. Takizawa, M. Minohara, H. Kumigashira, D. Toyota, M. Oshima, H. Wadati, T. Yoshida, A. Fujimori, M. Lippmaa, M. Kawasaki, H. Koinuma, G. Sordi, M. Rozenberg, Phys. Rev. B 80, 235104 (2009).
147. A. Toschi, M. Capone, C. Castellani, K. Held, Phys. Rev. Lett. 102, 076402 (2009).
148. C. Raas, P. Grete, G. S. Uhrig, Phys. Rev. Lett. 102, 076406 (2009).
149. A. Hofmann, X. Y. Cui, J. Schäfer, S. Meyer, P. Höpfner, C. Blumenstein, M. Paul, L. Patthey, E. Rotenberg, J. Bünemann, F. Gebhard, T. Ohm, W. Weber, R. Claessen, Phys. Rev. Lett. 102, 187204 (2009).