Dzyaloshinskii-Moriya interactions in valence-bond systems

Physical Review B - Condensed Matter and Materials Physics

Volumn 79, Issue 2, 2009, Pages

  Tovar, Mayra ^a   Raman, Kumar S ^a   Shtengel, Kirill ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 58949101855     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.024405     Document Type: Article

References (84)

1. F. Wegner, J. Math. Phys. 2259, 12 (1971).
2. P. W. Anderson, Mater. Res. Bull. 8, 153 (1973). 10.1016/0025-5408(73) 90167-0
3. N. Read and S. Sachdev, Phys. Rev. Lett. 62, 1694 (1989). 10.1103/PhysRevLett.62.1694
4. X. G. Wen, Phys. Rev. B 44, 2664 (1991). 10.1103/PhysRevB.44.2664
5. D. S. Rokhsar and S. A. Kivelson, Phys. Rev. Lett. 61, 2376 (1988). 10.1103/PhysRevLett.61.2376
6. G. Misguich, C. Lhuillier, B. Bernu, and C. Waldtmann, Phys. Rev. B 60, 1064 (1999). 10.1103/PhysRevB.60.1064
7. R. Moessner and S. L. Sondhi, Phys. Rev. Lett. 86, 1881 (2001). 10.1103/PhysRevLett.86.1881
8. L. Balents, M. P. A. Fisher, and S. M. Girvin, Phys. Rev. B 65, 224412 (2002). 10.1103/PhysRevB.65.224412
9. G. Misguich, D. Serban, and V. Pasquier, Phys. Rev. Lett. 89, 137202 (2002). 10.1103/PhysRevLett.89.137202
10. K. S. Raman, R. Moessner, and S. L. Sondhi, Phys. Rev. B 72, 064413 (2005). 10.1103/PhysRevB.72.064413
11. K. S. D. Beach and A. W. Sandvik, Nucl. Phys. B 750, 142 (2006). 10.1016/j.nuclphysb.2006.05.032
12. S. A. Kivelson, D. S. Rokhsar, and J. P. Sethna, Phys. Rev. B 35, 8865 (1987). 10.1103/PhysRevB.35.8865
13. P. W. Anderson, Science 235, 1196 (1987). 10.1126/science.235.4793.1196
14. D. A. Huse, W. Krauth, R. Moessner, and S. L. Sondhi, Phys. Rev. Lett. 91, 167004 (2003). 10.1103/PhysRevLett.91.167004
15. M. Freedman, C. Nayak, and K. Shtengel, Phys. Rev. B 78, 174411 (2008). 10.1103/PhysRevB.78.174411
16. M. P. Shores, E. A. Nytko, B. M. Bartlett, and D. G. Nocera, J. Am. Chem. Soc. 127, 13462 (2005). 10.1021/ja053891p
17. J. S. Helton, Phys. Rev. Lett. 98, 107204 (2007). 10.1103/PhysRevLett.98. 107204
18. O. Ofer, A. Keren, E. A. Nytko, M. P. Shores, B. M. Bartlett, D. G. Nocera, C. Baines, and A. Amato, arXiv:cond-mat/0610540 (unpublished).
19. P. Mendels, F. Bert, M. A. de Vries, A. Olariu, A. Harrison, F. Duc, J. C. Trombe, J. S. Lord, A. Amato, and C. Baines, Phys. Rev. Lett. 98, 077204 (2007). 10.1103/PhysRevLett.98.077204
20. T. Imai, E. A. Nytko, B. M. Bartlett, M. P. Shores, and D. G. Nocera, Phys. Rev. Lett. 100, 077203 (2008). 10.1103/PhysRevLett.100.077203
21. The frustration of the classical triangular Heisenberg antiferromagnet is partially relieved by having the spins arrange in a noncollinear 120° pattern which turns out to closely model the ground state of the quantum model (Ref.), despite initial thoughts that it was a spin liquid (Ref.). In contrast, for the classical kagomé Heisenberg model, the ground state is highly degenerate (Ref.) and there is no obvious reason we are aware of for why quantum fluctuations should favor one of them, though a particular set of them are apparently favored classically due to "order by disorder" (Ref.).
22. P. W. Leung and V. Elser, Phys. Rev. B 47, 5459 (1993). 10.1103/PhysRevB.47.5459
23. C. Waldtmann, H.-U. Everts, B. Bernu, C. Lhuillier, P. Sindzingre, P. Lecheminant, and L. Pierre, Eur. Phys. J. B 2, 501 (1998). 10.1007/s100510050274
24. F. Mila, Phys. Rev. Lett. 81, 2356 (1998). 10.1103/PhysRevLett.81.2356
25. J. B. Marston and C. Zeng, J. Appl. Phys. 69, 5962 (1991). 10.1063/1.347830
26. P. Nikolic and T. Senthil, Phys. Rev. B 68, 214415 (2003). 10.1103/PhysRevB.68.214415
27. R. R. P. Singh and D. A. Huse, Phys. Rev. B 76, 180407 (R) (2007). 10.1103/PhysRevB.76.180407
28. A. Olariu, P. Mendels, F. Bert, F. Duc, J. C. Trombe, M. A. de Vries, and A. Harrison, Phys. Rev. Lett. 100, 087202 (2008). 10.1103/PhysRevLett.100. 087202
29. Y. Ran, M. Hermele, P. A. Lee, and X.-G. Wen, Phys. Rev. Lett. 98, 117205 (2007). 10.1103/PhysRevLett.98.117205
30. F. Bert, S. Nakamae, F. Ladieu, D. L'Hote, P. Bonville, F. Duc, J.-C. Trombe, and P. Mendels, Phys. Rev. B 76, 132411 (2007). 10.1103/PhysRevB.76. 132411
31. K. Gregor and O. I. Motrunich, Phys. Rev. B 77, 184423 (2008). 10.1103/PhysRevB.77.184423
32. O. Ofer and A. Keren, arXiv:0804.4781 (unpublished).
33. M. Rigol and R. R. P. Singh, Phys. Rev. Lett. 98, 207204 (2007). 10.1103/PhysRevLett.98.207204
34. M. Rigol and R. R. P. Singh, Phys. Rev. B 76, 184403 (2007). 10.1103/PhysRevB.76.184403
35. I. E. Dzyaloshinskii, Zh. Eksp. Teor. Fiz. 32, 1547 (1957)
36. I. E. Dzyaloshinskii, [Sov. Phys. JETP 5, 1259 (1957)].
37. I. Dzyaloshinsky, J. Phys. Chem. Solids 4, 241 (1958). 10.1016/0022-3697(58)90076-3
38. T. Moriya, Phys. Rev. 120, 91 (1960). 10.1103/PhysRev.120.91
39. M. Elhajal, B. Canals, and C. Lacroix, Phys. Rev. B 66, 014422 (2002). 10.1103/PhysRevB.66.014422
40. In fact, a careful microscopic derivation shows that the a full bilinear interaction between the spins is akin to the familiar Heisenberg interaction: H=∑ JSi·Sj′, where S′ has been rotated about Dij by a certain angle (Refs.). While experimentally confirmed (Ref.), and undoubtfully important in discussions of a spontaneous ferromagnetism, this observation is not essential for the lowest-order calculations of the uniform susceptibility in the absence of magnetic order-the subject of this manuscript.
41. Z. Nussinov, C. D. Batista, B. Normand, and S. A. Trugman, Phys. Rev. B 75, 094411 (2007). 10.1103/PhysRevB.75.094411
42. V. Elser and C. Zeng, Phys. Rev. B 48, 13647 (1993). 10.1103/PhysRevB.48. 13647
43. G. Misguich, D. Serban, and V. Pasquier, Phys. Rev. B 67, 214413 (2003). 10.1103/PhysRevB.67.214413
44. D. J. Klein, J. Phys. A 15, 661 (1982). 10.1088/0305-4470/15/2/032
45. I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, Phys. Rev. Lett. 59, 799 (1987). 10.1103/PhysRevLett.59.799
46. Of course, the fluctuation-dissipation theorem will still be true. However, the relationship between the uniform susceptibility and spin-spin correlation will now involve more than just the equal-time correlator (Ref.).
47. B. S. Shastry and B. Sutherland, Physica B&C 108, 1069 (1981). 10.1016/0378-4363(81)90838-X
48. H. Kageyama, K. Yoshimura, R. Stern, N. V. Mushnikov, K. Onizuka, M. Kato, K. Kosuge, C. P. Slichter, T. Goto, and Y. Ueda, Phys. Rev. Lett. 82, 3168 (1999). 10.1103/PhysRevLett.82.3168
49. S. Miyahara and K. Ueda, Phys. Rev. Lett. 82, 3701 (1999). 10.1103/PhysRevLett.82.3701
50. We might view a valence-bond solid as "exotic" if it occurs spontaneously due to quantum frustration. However, in the SS model, and experimentally in spin-dimer materials (Ref.), the valence-bond solid phase occurs because some links have a stronger interaction than others. The discussion in the introduction where we counted the valence-bond solid as an example of an exotic nonmagnetic phase was in reference to the first scenario.
51. O. Cépas, K. Kakurai, L. P. Regnault, T. Ziman, J. P. Boucher, N. Aso, M. Nishi, H. Kageyama, and Y. Ueda, Phys. Rev. Lett. 87, 167205 (2001). 10.1103/PhysRevLett.87.167205
52. S. Miyahara, F. Mila, K. Kodama, M. Takigawa, M. Horvatic, C. Berthier, H. Kageyama, and Y. Ueda, J. Phys.: Condens. Matter 16, S911 (2004). 10.1088/0953-8984/16/11/048
53. The experiments we are referring to (Ref.) were actually done in a magnetometer with a static field of H=1.0 T, which for spin 1/2 corresponds to an energy scale g μB H∼1.3 K. The temperature range of the experiment is from 1.7 to 400 K, so the results can be interpreted by a zero-field theory except for perhaps the very lowest temperature points.
54. H. Nojiri, H. Kageyama, K. Onizuka, Y. Ueda, and M. Motokawa, J. Phys. Soc. Jpn. 68, 2906 (1999). 10.1143/JPSJ.68.2906
55. Measurements of the NMR relaxation rate (Ref.) determined the gap to the lowest magnetic state to be Δ1 =30 K, consistent with the value of Δ1 =35 K given in Ref.. Fitting the susceptibility data gave a slightly lower value of Δ=19 K but these and other authors (Ref.) have interpreted the ≈30 K values as the "spin gap." Therefore, we use this value for our estimate.
56. S. Miyahara and F. Mila, Prog. Theor. Phys. 159, 33 (2005). 10.1143/PTPS.159.33
57. K. Kodama, S. Miyahara, M. Takigawa, M. Horvatic, C. Berthier, F. Mila, H. Kageyama, and Y. Ueda, J. Phys.: Condens. Matter 17, L61 (2005). 10.1088/0953-8984/17/4/L02
58. The spin gap scale is ∼Δ/g μB ∼20 T while the onset of a uniform magnetization is seen at around 18 T. We point out that these interesting field dependencies occur at fields much higher than the 1.0 T field of the magnetometer used in Ref., the results of which we interpret with our zero-field calculation.
59. S. T. Bramwell and M. J. P. Gingras, Science 294, 1495 (2001). 10.1126/science.1064761
60. C. D. Batista and S. A. Trugman, Phys. Rev. Lett. 93, 217202 (2004). 10.1103/PhysRevLett.93.217202
61. C. K. Majumdar and D. K. Ghosh, J. Math. Phys. 10, 1388 (1969). 10.1063/1.1664978
62. W. J. Caspers, K. M. Emmett, and W. Magnus, J. Phys. A 17, 2687 (1984). 10.1088/0305-4470/17/13/020
63. One situation where the expansion might not work so well is if the wave function were a liquid state of the Rokhsar-Kivelson type (Ref.). In this case, the error made in keeping only leading terms might be quite large because of the cumulative effect of many small terms.
64. M. Mambrini and F. Mila, Eur. Phys. J. B 17, 651 (2000). 10.1007/PL00011071
65. R. R. P. Singh and D. A. Huse, Phys. Rev. B 77, 144415 (2008). 10.1103/PhysRevB.77.144415
66. R. Chitra and M. J. Rozenberg, Phys. Rev. B 77, 052407 (2008). 10.1103/PhysRevB.77.052407
67. M. J. Rozenberg and R. Chitra, Phys. Rev. B 78, 132406 (2008). 10.1103/PhysRevB.78.132406
68. O. Cepas, C. M. Fong, P. W. Leung, and C. Lhuillier, Phys. Rev. B 78, 140405 (2008). 10.1103/PhysRevB.78.140405
69. A. Zorko, S. Nellutla, J. van Tol, L. C. Brunel, F. Bert, F. Duc, J.-C. Trombe, M. A. de Vries, A. Harrison, and P. Mendels, Phys. Rev. Lett. 101, 026405 (2008). 10.1103/PhysRevLett.101.026405
70. This point was also made in the discussion section of Ref..
71. L. Shekhtman, O. Entin-Wohlman, and A. Aharony, Phys. Rev. Lett. 69, 836 (1992). 10.1103/PhysRevLett.69.836
72. L. Shekhtman, A. Aharony, and O. Entin-Wohlman, Phys. Rev. B 47, 174 (1993). 10.1103/PhysRevB.47.174
73. A. Zheludev, S. Maslov, I. Tsukada, I. Zaliznyak, L. P. Regnault, T. Masuda, K. Uchinokura, R. Erwin, and G. Shirane, Phys. Rev. Lett. 81, 5410 (1998). 10.1103/PhysRevLett.81.5410
74. M. Hermele, Y. Ran, P. A. Lee, and X.-G. Wen, Phys. Rev. B 77, 224413 (2008). 10.1103/PhysRevB.77.224413
75. R. Ballou, B. Canals, M. Elhajal, C. Lacroix, and A. S. Wills, J. Magn. Magn. Mater. 262, 465 (2003). 10.1016/S0304-8853(03)00079-9
76. R. Moessner, S. L. Sondhi, and P. Chandra, Phys. Rev. B 64, 144416 (2001). 10.1103/PhysRevB.64.144416
77. S. Ryu, O. I. Motrunich, J. Alicea, and M. P. A. Fisher, Phys. Rev. B 75, 184406 (2007). 10.1103/PhysRevB.75.184406
78. A. Kolezhuk, S. Sachdev, R. R. Biswas, and P. Chen, Phys. Rev. B 74, 165114 (2006). 10.1103/PhysRevB.74.165114
79. O. I. Motrunich, Phys. Rev. B 72, 045105 (2005). 10.1103/PhysRevB.72. 045105
80. B. Bernu, C. Lhuillier, and L. Pierre, Phys. Rev. Lett. 69, 2590 (1992). 10.1103/PhysRevLett.69.2590
81. R. R. P. Singh and D. A. Huse, Phys. Rev. Lett. 68, 1766 (1992). 10.1103/PhysRevLett.68.1766
82. J. T. Chalker, P. C. W. Holdsworth, and E. F. Shender, Phys. Rev. Lett. 68, 855 (1992). 10.1103/PhysRevLett.68.855
83. T. A. Kaplan, Z. Phys. B: Condens. Matter 49, 313 (1983). 10.1007/BF01301591
84. A. Auerbach, Interacting Electrons and Quantum Magnetism, Graduate Texts in Contemporary Physics (Springer-Verlag, New York, 1998).