Hidden symmetries of the extended Kitaev-Heisenberg model: Implications for the honeycomb-lattice iridates A2IrO3

Physical Review B - Condensed Matter and Materials Physics

Volumn 92, Issue 2, 2015, Pages

  Chaloupka, Jiří ^a   Khaliullin, Giniyat ^b  

^a MASARYK UNIVERSITY   (Czech Republic)

^b MAX PLANCK INSTITUT FÜR FESTKÖRPERFORSCHUNG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84938217345     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.92.024413     Document Type: Article

References (79)

1. W. J. L. Buyers, T. M. Holden, E. C. Svensson, R. A. Cowley, and M. T. Hutchings, J. Phys. C: Solid State Phys. 4, 2139 (1971). JPSOAW 0022-3719 10.1088/0022-3719/4/14/028
2. R. J. Elliott and M. F. Thorpe, J. Appl. Phys. 39, 802 (1968). JAPIAU 0021-8979 10.1063/1.2163622
3. A. Abragam and B. Bleaney, Electron Paramagnetic Resonance of Transition Ions (Clarendon Press, Oxford, 1970).
4. K. I. Kugel and D. I. Khomskii, Sov. Phys. Usp. 25, 231 (1982). SOPUAP 0038-5670 10.1070/PU1982v025n04ABEH004537
5. G. Khaliullin and S. Okamoto, Phys. Rev. Lett. 89, 167201 (2002) PRLTAO 0031-9007 10.1103/PhysRevLett.89.167201;
6. G. Khaliullin and S. Okamoto, Phys. Rev. B 68, 205109 (2003). PRBMDO 0163-1829 10.1103/PhysRevB.68.205109
7. G. Khaliullin, Prog. Theor. Phys. Suppl. 160, 155 (2005). PTPSAL 0375-9687 10.1143/PTPS.160.155
8. G. Khaliullin, W. Koshibae, and S. Maekawa, Phys. Rev. Lett. 93, 176401 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.93.176401
9. G. Chen and L. Balents, Phys. Rev. B 78, 094403 (2008). PRBMDO 1098-0121 10.1103/PhysRevB.78.094403
10. G. Jackeli and G. Khaliullin, Phys. Rev. Lett. 102, 017205 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.102.017205
11. A. Shitade, H. Katsura, J. Kuneš, X.-L. Qi, S.-C. Zhang, and N. Nagaosa, Phys. Rev. Lett. 102, 256403 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.102.256403
12. J. Chaloupka, G. Jackeli, and G. Khaliullin, Phys. Rev. Lett. 105, 027204 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.105.027204
13. S. Okamoto, Phys. Rev. Lett. 110, 066403 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.110.066403
14. W. Witczak-Krempa, G. Chen, Y. B. Kim, and L. Balents, Annu. Rev. Condens. Matter Phys. 5, 57 (2014). 1947-5454 10.1146/annurev-conmatphys-020911-125138
15. Z. Nussinov and J. van den Brink, Rev. Mod. Phys. 87, 1 (2015). RMPHAT 0034-6861 10.1103/RevModPhys.87.1
16. G. Khaliullin and S. Maekawa, Phys. Rev. Lett. 85, 3950 (2000). PRLTAO 0031-9007 10.1103/PhysRevLett.85.3950
17. G. Khaliullin, Phys. Rev. B 64, 212405 (2001). PRBMDO 0163-1829 10.1103/PhysRevB.64.212405
18. G. Chen, L. Balents, and A. P. Schnyder, Phys. Rev. Lett. 102, 096406 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.102.096406
19. G. Khaliullin, Phys. Rev. Lett. 111, 197201 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.111.197201
20. O. N. Meetei, W. S. Cole, M. Randeria, and N. Trivedi, Phys. Rev. B 91, 054412 (2015). PRBMDO 1098-0121 10.1103/PhysRevB.91.054412
21. 2+ ions, where the ground state has S = 0 (due to large covalency and crystal field effects) while the S ≠ 0 levels are not too high; for details, see the recent work [21] and references therein.
22. J. Chaloupka and G. Khaliullin, Phys. Rev. Lett. 110, 207205 (2013) PRLTAO 0031-9007 10.1103/PhysRevLett.110.207205;
23. J. Chaloupka and G. Khaliullin, Prog. Theor. Phys. Suppl. 176, 50 (2008). PTPSAL 0375-9687 10.1143/PTPS.176.50
24. B. J. Kim, H. Ohsumi, T. Komesu, S. Sakai, T. Morita, H. Takagi, and T. Arima, Science 323, 1329 (2009). 10.1126/science.1167106
25. J. Kim, D. Casa, M. H. Upton, T. Gog, Y.-J. Kim, J. F. Mitchell, M. van Veenendaal, M. Daghofer, J. van den Brink, G. Khaliullin, and B. J. Kim, Phys. Rev. Lett. 108, 177003 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.108.177003
26. S. Fujiyama, H. Ohsumi, T. Komesu, J. Matsuno, B. J. Kim, M. Takata, T. Arima, and H. Takagi, Phys. Rev. Lett. 108, 247212 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.108.247212
27. A. Kitaev, Ann. Phys. 321, 2 (2006). APNYA6 0003-4916 10.1016/j.aop.2005.10.005
28. X. Liu, T. Berlijn, W.-G. Yin, W. Ku, A. Tsvelik, Y.-J. Kim, H. Gretarsson, Y. Singh, P. Gegenwart, and J. P. Hill, Phys. Rev. B 83, 220403(R) (2011). PRBMDO 1098-0121 10.1103/PhysRevB.83.220403
29. F. Ye, S. Chi, H. Cao, B. C. Chakoumakos, J. A. Fernandez-Baca, R. Custelcean, T. F. Qi, O. B. Korneta, and G. Cao, Phys. Rev. B 85, 180403(R) (2012). PRBMDO 1098-0121 10.1103/PhysRevB.85.180403
30. S. K. Choi, R. Coldea, A. N. Kolmogorov, T. Lancaster, I. I. Mazin, S. J. Blundell, P. G. Radaelli, Y. Singh, P. Gegenwart, K. R. Choi, S.-W. Cheong, P. J. Baker, C. Stock, and J. Taylor, Phys. Rev. Lett. 108, 127204 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.108.127204
31. R. Coldea, presentation at SPORE13, Dresden, 2013 (unpublished);
32. S. Choi, R. Coldea et al. (unpublished).
33. I. Kimchi and Y.-Z. You, Phys. Rev. B 84, 180407(R) (2011). PRBMDO 1098-0121 10.1103/PhysRevB.84.180407
34. J. Reuther, R. Thomale, and S. Rachel, Phys. Rev. B 90, 100405(R) (2014). PRBMDO 1098-0121 10.1103/PhysRevB.90.100405
35. J. Chaloupka, G. Jackeli, and G. Khaliullin, Phys. Rev. Lett. 110, 097204 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.110.097204
36. Y. Yu, L. Liang, Q. Niu, and S. Qin, Phys. Rev. B 87, 041107(R) (2013). PRBMDO 1098-0121 10.1103/PhysRevB.87.041107
37. S. Okamoto, Phys. Rev. B 87, 064508 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.87.064508
38. S. Bhattacharjee, S.-S. Lee, and Y. B. Kim, New J. Phys. 14, 073015 (2012). NJOPFM 1367-2630 10.1088/1367-2630/14/7/073015
39. Katukuri, V.M. , Nishimoto, S., Yushankhai, V., Stoyanova, A., Kandpal, H., Choi, S., Coldea, R., Rousochatzakis, I., Hozoi, L., Brink, J.V.D.Kitaev interactions between j = 1/2 moments in honeycomb Na 2IrO3 are large and ferromagnetic: Insights from ab initio quantum chemistry calculations , New Journal of Physics, 16, Article number 013056, 2014
40. J. G. Rau, E. K.-H. Lee, and H.-Y. Kee, Phys. Rev. Lett. 112, 077204 (2014). PRLTAO 0031-9007 10.1103/PhysRevLett.112.077204
41. J. G. Rau and H.-Y. Kee, arXiv:1408.4811.
42. Y. Yamaji, Y. Nomura, M. Kurita, R. Arita, and M. Imada, Phys. Rev. Lett. 113, 107201 (2014). PRLTAO 0031-9007 10.1103/PhysRevLett.113.107201
43. Y. Sizyuk, C. Price, P. Wölfle, and N. B. Perkins, Phys. Rev. B 90, 155126 (2014). PRBMDO 1098-0121 10.1103/PhysRevB.90.155126
44. K. Shinjo, S. Sota, and T. Tohyama, Phys. Rev. B 91, 054401 (2015). PRBMDO 1098-0121 10.1103/PhysRevB.91.054401
45. I. Kimchi, R. Coldea, and A. Vishwanath, Phys. Rev. B 91, 245134 (2015). 10.1103/PhysRevB.91.245134
46. E. Sela, H.-C. Jiang, M. H. Gerlach, and S. Trebst, Phys. Rev. B 90, 035113 (2014). PRBMDO 1098-0121 10.1103/PhysRevB.90.035113
47. I. I. Mazin, H. O. Jeschke, K. Foyevtsova, R. Valentí, and D. I. Khomskii, Phys. Rev. Lett. 109, 197201 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.109.197201
48. H. Gretarsson, J. P. Clancy, Y. Singh, P. Gegenwart, J. P. Hill, J. Kim, M. H. Upton, A. H. Said, D. Casa, T. Gog, and Y.-J. Kim, Phys. Rev. B 87, 220407(R) (2013). PRBMDO 1098-0121 10.1103/PhysRevB.87.220407
49. S. H. Chun, J.-W. Kim, Jungho Kim, H. Zheng, C. Stoumpos, C. Malliakas, J. F. Mitchell, K. Mehlawat, Y. Singh, Y. Choi, T. Gog, A. Al-Zein, M. Moretti Sala, M. Krisch, J. Chaloupka, G. Jackeli, G. Khaliullin, and B. J. Kim, Nat. Phys. 11, 462 (2015). 1745-2473 10.1038/nphys3322
50. I. Kimchi and A. Vishwanath, Phys. Rev. B 89, 014414 (2014). PRBMDO 1098-0121 10.1103/PhysRevB.89.014414
51. I. Rousochatzakis, U. K. Rössler, J. van den Brink, and M. Daghofer, arXiv:1209.5895.
52. M. Becker, M. Hermanns, B. Bauer, M. Garst, and S. Trebst, Phys. Rev. B 91, 155135 (2015). PRBMDO 1098-0121 10.1103/PhysRevB.91.155135
53. K. Li, S.-L. Yu, and J.-X. Li, New J. Phys. 17, 043032 (2015). NJOPFM 1367-2630 10.1088/1367-2630/17/4/043032
54. K. W. Plumb, J. P. Clancy, L. J. Sandilands, V. V. Shankar, Y. F. Hu, K. S. Burch, H.-Y. Kee, and Y.-J. Kim, Phys. Rev. B 90, 041112(R) (2014). PRBMDO 1098-0121 10.1103/PhysRevB.90.041112
55. T. Takayama, A. Kato, R. Dinnebier, J. Nuss, H. Kono, L. S. I. Veiga, G. Fabbris, D. Haskel, and H. Takagi, Phys. Rev. Lett. 114, 077202 (2015). PRLTAO 0031-9007 10.1103/PhysRevLett.114.077202
56. A. Biffin, R. D. Johnson, S. Choi, F. Freund, S. Manni, A. Bombardi, P. Manuel, P. Gegenwart, and R. Coldea, Phys. Rev. B 90, 205116 (2014). PRBMDO 1098-0121 10.1103/PhysRevB.90.205116
57. K. A. Modic, T. E. Smidt, I. Kimchi, N. P. Breznay, A. Biffin, S. Choi, R. D. Johnson, R. Coldea, P. Watkins-Curry, G. T. McCandless, J. Y. Chan, F. Gandara, Z. Islam, A. Vishwanath, A. Shekhter, R. D. McDonald, and J. G. Analytis, Nat. Commun. 5, 4203 (2014). 2041-1723 10.1038/ncomms5203
58. A. Biffin, R. D. Johnson, I. Kimchi, R. Morris, A. Bombardi, J. G. Analytis, A. Vishwanath, and R. Coldea, Phys. Rev. Lett. 113, 197201 (2014). PRLTAO 0031-9007 10.1103/PhysRevLett.113.197201
59. M. Hermanns and S. Trebst, Phys. Rev. B 89, 235102 (2014). PRBMDO 1098-0121 10.1103/PhysRevB.89.235102
60. B. N. Figgis and M. A. Hitchman, Ligand Field Theory and Its Applications (Wiley-VCH, New York, 2000).
61. H. Gretarsson, J. P. Clancy, X. Liu, J. P. Hill, E. Bozin, Y. Singh, S. Manni, P. Gegenwart, J. Kim, A. H. Said, D. Casa, T. Gog, M. H. Upton, H.-S. Kim, J. Yu, V. M. Katukuri, L. Hozoi, J. van den Brink, and Y.-J. Kim, Phys. Rev. Lett. 110, 076402 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.110.076402
62. ab| ≃ 1.9 [74].
63. 0 = 0.
64. M. Kamfor, S. Dusuel, J. Vidal, and K. P. Schmidt, J. Stat. Mech: Theory Exp. (2010) P08010. 1742-5468 10.1088/1742-5468/2010/08/P08010
65. M. Kamfor, S. Dusuel, J. Vidal, and K. P. Schmidt, J. Stat. Mech: Theory Exp. (2010) P08010. 1742-5468 10.1088/1742-5468/2010/08/P08010
66. E. Quinn, S. Bhattacharjee, and R. Moessner, Phys. Rev. B 91, 134419 (2015). PRBMDO 1098-0121 10.1103/PhysRevB.91.134419
67. 3 rotation rules in Fig. 1 (c).
68. J. Lou, L. Liang, Y. Yu, and Y. Chen, arXiv:1501.06990.
69. J. Chaloupka, G. Jackeli, and G. Khaliullin, presentation at SPORE13, Dresden, 2013 (unpublished).
70. A. M. Tsvelik, Quantum Field Theory in Condensed Matter Physics (Cambridge University Press, Cambridge, 1995), Chap. 17, and references therein.
71. Regarding the terminology used here, we have in mind that the compass-type and Kitaev-type interactions are very distinct in their physical appearance and origin. While the compass-spins (pseudodipoles) as introduced in Ref. [4] align themselves along the bond direction as real compasses do (hence the name), the spins in the Kitaev honeycomb model tend rather to avoid the bond directions. Placed on a honeycomb lattice, the bond-directional compasses would feel much less frustrated than the Kitaev spins, and show "order-from-disorder" behavior instead. As to the physical origin, the compass-type and Kitaev-type spin anisotropy terms arise in compounds with distinct chemical bonding geometries-corner-shared [16,9] and edge-shared [6,9] structures, correspondingly.
72. 3 is a manifestation of the other anisotropy terms beyond the "Heisenberg plus Kitaev" spin model.
73. H.-C. Jiang, Z.-C. Gu, X.-L. Qi, and S. Trebst, Phys. Rev. B 83, 245104 (2011). PRBMDO 1098-0121 10.1103/PhysRevB.83.245104
74. Ref. [46] has estimated the angle a ≃ 44° based on the fits that did not account for a trigonal field splitting. Positive (negative) Δ values may decrease (increase) the actual value of a from this estimate.
75. J. M. Luttinger and L. Tisza, Phys. Rev. 70, 954 (1946). PHRVAO 0031-899X 10.1103/PhysRev.70.954
76. D. B. Litvin, Physica 77, 205 (1974). PHYSAG 0031-8914 10.1016/0031-8914(74)90257-2
77. K. Foyevtsova, H. O. Jeschke, I. I. Mazin, D. I. Khomskii, and R. Valentí, Phys. Rev. B 88, 035107 (2013). PRBMDO 1098-0121 10.1103/PhysRevB.88.035107
78. Y. Singh and P. Gegenwart, Phys. Rev. B 82, 064412 (2010). PRBMDO 1098-0121 10.1103/PhysRevB.82.064412
79. Y. Singh, S. Manni, J. Reuther, T. Berlijn, R. Thomale, W. Ku, S. Trebst, and P. Gegenwart, Phys. Rev. Lett. 108, 127203 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.108.127203
80. J.-H. Kim, A. Jain, M. Reehuis, G. Khaliullin, D. C. Peets, C. Ulrich, J. T. Park, E. Faulhaber, A. Hoser, H. C. Walker, D. T. Adroja, A. C. Walters, D. S. Inosov, A. Maljuk, and B. Keimer, Phys. Rev. Lett. 113, 147206 (2014). PRLTAO 0031-9007 10.1103/PhysRevLett.113.147206