Interplay between crystal-field splitting and superexchange interaction in the t 2g orbital Mott insulator

Physical Review B - Condensed Matter and Materials Physics

Volumn 85, Issue 6, 2012, Pages

  Krivenko, Sergey ^a  

^a KAZAN FEDERAL UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84857751831     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.85.064406     Document Type: Article

References (81)

1. M. Imada, A. Fujimori, and Y. Tokura, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.70.1039 70, 1039 (1998). (Pubitemid 128159247)
2. Y. Tokura and N. Nagaosa, Science SCIEAS 0036-8075 10.1126/science.288. 5465.462 288, 462 (2000); (Pubitemid 30236021)
3. Y. Tokura, Phys. Today 0031-9228 10.1063/1.1603080 56, 50 (2003).
4. K. I. Kugel and D. I. Khomskii, Usp. Fiz. Nauk UFNAAG 0042-1294 10.3367/UFNr.0136.198204c.0621 136, 621 (1982);
5. K. I. Kugel and D. I. Khomskii, Sov. Phys. Usp. SOPUAP 0038-5670 10.1070/PU1982v025n04ABEH004537 25, 231 (1982)].
6. S. Maekawa, T. Tohyama, S. E. Barnes, S. Ishihara, W. Koshibae, and G. Khaliullin, Physics of Transition Metal Oxides, Springer Series in Solid State Sciences, Vol. 144 (Springer-Verlag, Heidelberg, 2004).
7. M. Mochizuki and M. Imada, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/6/1/154 6, 154 (2004). (Pubitemid 39587891)
8. G. Khaliullin, Prog. Theor. Phys. Suppl. PTPSAL 0375-9687 10.1143/PTPS.160.155 160, 155 (2005). (Pubitemid 43608149)
9. L. F. Feiner and A. M. Ole, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.59.3295 59, 3295 (1999);
10. S.Okamoto, S. Ishihara, and S. Maekawa, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.65.144403 65, 144403 (2002).
11. T. Mizokawa, D. I. Khomskii, and G. A. Sawatzky, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.60.7309 60, 7309 (1999).
12. S. Ishihara, T. Hatakeyama, and S. Maekawa, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.65.064442 65, 064442 (2002).
13. G. Khaliullin and S. Maekawa, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.3950 85, 3950 (2000). (Pubitemid 32027224)
14. G. Khaliullin, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.64.212405 64, 212405 (2001).
15. K. Kikoin, O. Entin-Wohlman, V. Fleurov, and A. Aharony, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.67.214418 67, 214418 (2003).
16. A. M. Ole, P. Horsch, L. F. Feiner, and G. Khaliullin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.147205 96, 147205 (2006).
17. A. M. Ole, P. Horsch, and G. Khaliullin, Phys. Status Solidi B PSSBBD 0370-1972 10.1002/pssb.200674619 244, 2378 (2007).
18. P. Horsch, A. M. Ole, L. F. Feiner, and G. Khaliullin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.167205 100, 167205 (2008). (Pubitemid 351585524)
19. G. Khaliullin, P. Horsch, and A. M. Ole, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.3879 86, 3879 (2001); (Pubitemid 32425355)
20. P. Horsch, G. Khaliullin, and A. M. Ole, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.257203 91, 257203 (2003);
21. A. M. Ole, P. Horsch, and G. Khaliullin, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.75.184434 75, 184434 (2007).
22. G. Khaliullin and S. Okamoto, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.167201 89, 167201 (2002).
23. G. Khaliullin and S. Okamoto, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.68.205109 68, 205109 (2003).
24. M. Mochizuki and M. Imada, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.167203 91, 167203 (2003).
25. M. Mochizuki and M. Imada, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.73.1833 73, 1833 (2004). (Pubitemid 40803685)
26. M. Cwik, T. Lorenz, J. Baier, R. Müller, G. André, F. Bourée, F. Lichtenberg, A. Freimuth, R. Schmitz, E. Müller-Hartmann, and M. Braden, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.68.060401 68, 060401 (2003).
27. E. Pavarini, S. Biermann, A. Poteryaev, A. I. Lichtenstein, A. Georges, and O. K. Andersen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92. 176403 92, 176403 (2004).
28. R. M. Eremina, M. V. Eremin, V. V. Iglamov, J. Hemberger, H.-A. Krug von Nidda, F. Lichtenberg, and A. Loidl, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.70.224428 70, 224428 (2004). (Pubitemid 40267759)
29. R. Schmitz, O. Entin-Wohlman, A. Aharony, A. B. Harris, and E. Müller-Hartmann, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.71.144412 71, 144412 (2005). (Pubitemid 41755468)
30. R. Schmitz, O. Entin-Wohlman, A. Aharony, A. B. Harris, and E. Müller-Hartmann, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.71.214438 71, 214438 (2005). (Pubitemid 41703010)
31. E. Pavarini, A. Yamasaki, J. Nuss, and O. K. Andersen, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/7/1/188 7, 188 (2005). (Pubitemid 41261656)
32. I. V. Solovyev, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.69.134403 69, 134403 (2004).
33. S. V. Streltsov, A. S. Mylnikova, A. O. Shorikov, Z. V. Pchelkina, D.I. Khomskii, and V. I. Anisimov, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.71. 245114 71, 245114 (2005). (Pubitemid 41702911)
34. I. V. Solovyev, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.74.054412 74, 054412 (2006). (Pubitemid 44215658)
35. M. Mochizuki and M. Imada, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.70.2872 70, 2872 (2001).
36. V. V. Iglamov and M. V. Eremin, Phys. Solid State PSOSED 1063-7834 10.1134/S1063783407020084 49, 229 (2007).
37. A. A. Mozhegorov, A. E. Nikiforov, A. V. Larin, A. V. Efremov, L. E. Gontchar, and P. A. Agzamova, Phys. Solid State PSOSED 1063-7834 10.1134/S1063783408090400 50, 1795 (2008);
38. A. A. Mozhegorov, A. V. Larin, A. E. Nikiforov, L. E. Gontchar, and A. V. Efremov, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.79.054418 79, 054418 (2009).
39. B. Keimer, D. Casa, A. Ivanov, J. W. Lynn, M. v. Zimmermann, J.P. Hill, D. Gibbs, Y. Taguchi, and Y. Tokura, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.3946 85, 3946 (2000). (Pubitemid 32027223)
40. D. A. MacLean, H. N. Ng, and J. E. Greedan, J. Solid State Chem. JSSCBI 0022-4596 10.1016/0022-4596(79)90127-0 30, 35 (1979); (Pubitemid 10418854)
41. M. Eitel and J. E. Greedan, J. Less-Common Met. JCOMAH 0022-5088 10.1016/0022-5088(86)90220-1 116, 95 (1986). (Pubitemid 16522764)
42. T. Kiyama and M. Itoh, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.167202 91, 167202 (2003).
43. M. W. Haverkort, Z. Hu, A. Tanaka, G. Ghiringhelli, H. Roth, M. Cwik, T. Lorenz, C. Schüßler-Langeheine, S. V. Streltsov, A.S. Mylnikova, V. I. Anisimov, C. de Nadai, N. B. Brookes, H. H. Hsieh, H.-J. Lin, C. T. Chen, T. Mizokawa, Y. Taguchi, Y. Tokura, D. I. Khomskii, and L. H. Tjeng, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.056401 94, 056401 (2005). (Pubitemid 40620867)
44. M. Reedyk, D. A. Crandles, M. Cardona, J. D. Garrett, and J. E. Greedan, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.55.1442 55, 1442 (1997).
45. C. Ulrich, A. Gössling, M. Grüninger, M. Guennou, H. Roth, M. Cwik, T. Lorenz, G. Khaliullin, and B. Keimer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.157401 97, 157401 (2006). (Pubitemid 44537103)
46. C. Ulrich, L. J. P. Ament, G. Ghiringhelli, L. Braicovich, M. M. Sala, N. Pezzotta, T. Schmitt, G. Khaliullin, J. van den Brink, H. Roth, T. Lorenz, and B. Keimer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.107205 103, 107205 (2009).
47. T. Kiyama, H. Saitoh, M. Itoh, K. Komada, H. Ichikawa, and J. Akimitsu, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.74.1123 74, 1123 (2005). (Pubitemid 41282615)
48. S. Miyasaka, Y. Okimoto, M. Iwama, and Y. Tokura, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.68.100406 68, 100406 (R) (2003);
49. S. Miyasaka, J. Fujioka, M. Iwama, Y. Okimoto, and Y. Tokura, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.73.224436 73, 224436 (2006). (Pubitemid 43962756)
50. C. Ulrich, G. Khaliullin, J. Sirker, M. Reehuis, M. Ohl, S. Miyasaka, Y. Tokura, and B. Keimer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91. 257202 91, 257202 (2003).
51. S. Miyasaka, S. Onoda, Y. Okimoto, J. Fujioka, M. Iwama, N. Nagaosa, and Y. Tokura, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.076405 94, 076405 (2005). (Pubitemid 40620731)
52. P. W. Anderson, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.115.2 115, 2 (1959).
53. K. I. Kugel and D. I. Khomskii, Sov. Phys. Solid State 17, 285 (1975).
54. 2g triplet splitting.
55. A. B. Harris, T. Yildirim, A. Aharony, O. Entin-Wohlman, and I.Ya. Korenblit, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.087206 91, 087206 (2003).
56. N. D. Mermin and H. Wagner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.17.1133 17, 1133 (1966).
57. For introduction to the order-from-disorder phenomena in frustrated systems, see, for example, A. M. Tsvelik, Quantum Field Theory in Condensed Matter Physics (Cambridge University Press, Cambridge, 1995), Chap. 17;
58. and Frustrated Spin Systems, edited by H. T. Diep (World Scientific, Singapore, 2005).
59. G. Khaliullin and V. Oudovenko, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.56.R14243 56, R14243 (1997);
60. G. Khaliullin and R. Kilian, J. Phys. Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/11/48/333 11, 9757 (1999).
61. g -orbital frustration of the KK SE model remains an intricate problem; in the cubic lattice its exact solution is unknown. The chainlike orbital order represents the likely ground state, when the Hund-exchange is neglected (see Ref.). The phase diagram of the generalized model was deduced to contain transitions into various alternative spin-orbital states, including entangled ones;
62. see the articles L. F. Feiner, A. M. Ole, and J. Zaanen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.2799 78, 2799 (1997);
63. L. F. Feiner, A. M. Ole, and J. Zaanen, J. Phys. Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/10/32/001 10, L555 (1998);
64. for the resent progress in this research see W. Brzezicki and A. M. Ole, Phys. Rev. B 1098-0121 PRBMDO 10.1103/PhysRevB.83.214408 83, 214408 (2011).
65. Y. Q. Li, M. Ma, D. N. Shi, and F. C. Zhang, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.3527 81, 3527 (1998).
66. Y. Q. Li, M. Ma, D. N. Shi, and F. C. Zhang, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.60.12781 60, 12781 (1999).
67. B. Frischmuth, F. Mila, and M. Troyer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.835 82, 835 (1999).
68. F. Mila, B. Frischmuth, A. Deppeler, and M. Troyer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.3697 82, 3697 (1999).
69. S.-Q. Shen, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.64.132411 64, 132411 (2001).
70. P. W. Anderson, Mater. Res. Bull. MRBUAC 0025-5408 10.1016/0025-5408(73) 90167-0 8, 153 (1973);
71. P. W. Anderson, Science SCIEAS 0036-8075 10.1126/science.235.4793.1196 235, 1196 (1987).
72. H represents a challenge for future studies, particularly in a regime of the spin-orbital entanglement.
73. int (2) for the orbital state, see the discussion in Sec. also.
74. It has been similarly argued in Ref., that the Izing-magnon approximation is appropriate to resolve the spin-orbital coupling problem even in the pure-SE model, which corresponds to the case of the gapless orbitons, Δ = 0, in my study.
75. For the lowest-energy orbital excitations ω 1, k - - the functions ρ -, 1, k - m m and σ -, 1, k - m m possess divergence along the three axes α = x, y, z in the reciprocal space, when m = 2; for m = 3 it arises only for α = x, y, while along z the residues are zero. For the next branch ω 2, k - - of the dispersion the functions ρ -, 2, k - m m and σ -, 2, k - m m obtain only an isolated singularity in the origin Γ, which is not important.
76. SE.
77. SE.
78. C. P. Slichter, Principles of Magnetic Resonance (Springer-Verlag, New York, 1980), Chap. 5.
79. L. J. P. Ament and G. Khaliullin, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.81.125118 81, 125118 (2010).
80. C. Ulrich, G. Ghiringhelli, A. Piazzalunga, L. Braicovich, N. B. Brookes, H. Roth, T. Lorenz, and B. Keimer, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.77.113102 77, 113102 (2008).
81. For a discussion of Raman-active orbital effects, see, e.g., R. Rückamp, E. Benckiser, M. W. Haverkort, H. Roth, T. Lorenz, A. Freimuth, L. Jongen, A. Möller, G. Meyer, P. Reutler, B. Büchner, A. Revcolevschi, S.-W. Cheong, C. Sekar, G. Krabbes, and M. Grüninger, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/7/1/144 7, 144 (2005).