Colloquium: Spontaneous magnon decays

Reviews of Modern Physics

Volumn 85, Issue 1, 2013, Pages 219-243

  Zhitomirsky, M E ^a   Chernyshev, A L ^b  

^a UNIV GRENOBLE ALPES   (France)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL RESULTS; ANHARMONIC PHONONS; ANTIFERROMAGNETS; EXPERIMENTAL OBSERVATION; FIELD-INDUCED; HEISENBERG ANTIFERROMAGNETS; KINEMATIC CONDITION; MAGNON INTERACTIONS; MAGNONS; MANY-BODY EFFECT; NUMERICAL DATA; QUANTUM ANTIFERROMAGNETS; QUANTUM SPIN SYSTEMS; SPONTANEOUS DECAY; ZERO FIELDS; ZERO TEMPERATURES;

ANTIFERROMAGNETIC MATERIALS;

DECAY (ORGANIC);

EID: 84873583227     PISSN: 00346861     EISSN: 15390756     Source Type: Journal    
DOI: 10.1103/RevModPhys.85.219     Document Type: Article

References (148)

1. Affleck, I., 1989, Phys. Rev. Lett. 62, 474. PRLTAO 0031-9007 10.1103/PhysRevLett.62.474
2. Affleck, I., 1991, Phys. Rev. B PRBMDO 0163-1829 43, 3215. 10.1103/PhysRevB.43.3215
3. Affleck, I., and G. F. Wellman, 1992, Phys. Rev. B PRBMDO 0163-1829 46, 8934. 10.1103/PhysRevB.46.8934
4. Akhiezer, A. I., V. G. Bar'yakhtar, and S. V. Peletminskii, 1968, Spin Waves (North-Holland, Amsterdam).
5. Ament, L. J. P., M. van Veenendaal, T. P. Devereaux, J. P. Hill, and J. van den Brink, 2011, Rev. Mod. Phys. 83, 705. RMPHAT 0034-6861 10.1103/RevModPhys.83.705
6. Anderson, P. W., 1952, Phys. Rev. 86, 694. PHRVAO 0031-899X 10.1103/PhysRev.86.694
7. Anderson, P. W., 1973, Mater. Res. Bull. 8, 153. MRBUAC 0025-5408 10.1016/0025-5408(73)90167-0
8. Anderson, P. W., 1984, Basic Notions of Condensed Matter Physics (Benjamin-Cummings, Menlo Park).
9. Andreev, A. F., and V. I. Marchenko, 1980, Usp. Fiz. Nauk 130, 39 UFNAAG 0042-1294 10.3367/UFNr.0130.198001b.0039
10. [Andreev, A. F. V. I. Marchenko Sov. Phys. Usp. 23, 21 1980]. SOPUAP 0038-5670 10.1070/PU1980v023n01ABEH004859
11. Balents, L., 2010, Nature (London) NATUAS 0028-0836 464, 199. 10.1038/nature08917
12. Batyev, E. G., and L. S. Braginskii, 1984, Zh. Eksp. Teor. Fiz. ZETFA7 0044-4510 87, 1361
13. [Batyev, E. G. L. S. Braginskii Sov. Phys. JETP 60, 781 1984] [http://www.jetp.ac.ru/cgi-bin/e/index/e/60/4/p781?a=list]. SPHJAR 0038-5646
14. Bayrakci, S. P., T. Keller, K. Habicht, and B. Keimer, 2006, Science 312, 1926. SCIEAS 0036-8075 10.1126/science.1127756 (Pubitemid 43993714)
15. Beaurepaire, E., 2006, Ed., Magnetism: A Synchrotron Radiation Approach (Springer, Berlin).
16. Beliaev, S. T., 1958, Zh. Eksp. Teor. Fiz. ZETFA7 0044-4510 34, 433
17. [Beliaev, S. T. Sov. Phys. JETP 7, 299 1958]. SPHJAR 0038-5646
18. Bernu, B., P. Lecheminant, C. Lhuillier, and L. Pierre, 1994, Phys. Rev. B PRBMDO 0163-1829 50, 10 048. 10.1103/PhysRevB.50.10048
19. Bibikov, P. N., 2007, Phys. Rev. B PRBMDO 1098-0121 76, 174431. 10.1103/PhysRevB.76.174431
20. Bloch, F., 1930, Z. Phys. ZEPYAA 0044-3328 61, 206. 10.1007/BF01339661
21. Borovik-Romanov, A. S., and S. K. Sinha, 1988, Eds., Spin-Waves and Magnetic Excitations (Elsevier, Amsterdam).
22. Brockhouse, B. N., 1995, Rev. Mod. Phys. 67, 735. RMPHAT 0034-6861 10.1103/RevModPhys.67.735 (Pubitemid 126031140)
23. Capriotti, L., A. E. Trumper, and S. Sorella, 1999, Phys. Rev. Lett. 82, 3899. PRLTAO 0031-9007 10.1103/PhysRevLett.82.3899
24. Chakravarty, S., B. I. Halperin, and D. R. Nelson, 1989, Phys. Rev. B PRBMDO 0163-1829 39, 2344. 10.1103/PhysRevB.39.2344
25. Chernyshev, A. L., 2012, Phys. Rev. B PRBMDO 1098-0121 86, 060401(R). 10.1103/PhysRevB.86.060401
26. Chernyshev, A. L., and M. E. Zhitomirsky, 2006, Phys. Rev. Lett. 97, 207202. PRLTAO 0031-9007 10.1103/PhysRevLett.97.207202 (Pubitemid 44759868)
27. Chernyshev, A. L., and M. E. Zhitomirsky, 2009 a, Phys. Rev. B PRBMDO 1098-0121 79, 144416. 10.1103/PhysRevB.79.144416
28. Chernyshev, A. L., and M. E. Zhitomirsky, 2009 b, Phys. Rev. B PRBMDO 1098-0121 79, 174402. 10.1103/PhysRevB.79.174402
29. Chernyshev, A. L., M. E. Zhitomirsky, N. Martin, and L.-P. Regnault, 2012, Phys. Rev. Lett. 109, 097201. PRLTAO 0031-9007 10.1103/PhysRevLett.109. 097201
30. Chubukov, A. V., 1984, J. Phys. C 17, L991. JPSOAW 0022-3719 10.1088/0022-3719/17/36/008
31. Chubukov, A. V., 1989, Pis'ma Zh. Eksp. Teor. Fiz. 49, 108 PZETAB 0370-274X
32. [Chubukov, A. V. Sov. Phys. JETP Lett. 49, 129 1989] [http://www. jetpletters.ac.ru/ps/1113/article-16848.shtml].
33. Chubukov, A. V., S. Sachdev, and T. Senthil, 1994, J. Phys. Condens. Matter 6, 8891. JCOMEL 0953-8984 10.1088/0953-8984/6/42/019
34. Coldea, R., D. A. Tennant, A. M. Tsvelik, and Z. Tylczynski, 2001, Phys. Rev. Lett. 86, 1335. PRLTAO 0031-9007 10.1103/PhysRevLett.86.1335 (Pubitemid 32188317)
35. Coldea, R., D. A. Tennant, E. M. Wheeler, E. Wawrzynska, D. Prabhakaran, M. Telling, K. Habicht, P. Smeibidl, and K. Kiefer, 2010, Science 327, 177. SCIEAS 0036-8075 10.1126/science.1180085
36. Coomer, F. C., 2007, Phys. Rev. B PRBMDO 1098-0121 75, 094424. 10.1103/PhysRevB.75.094424
37. Dagotto, E., and T. M. Rice, 1996, Science 271, 618. SCIEAS 0036-8075 10.1126/science.271.5249.618
38. Dalidovich, D., R. Sknepnek, A. J. Berlinsky, J. Zhang, and C. Kallin, 2006, Phys. Rev. B PRBMDO 1098-0121 73, 184403. 10.1103/PhysRevB.73.184403 (Pubitemid 43660024)
39. de Groot, H. J. M., and L. J. de Jongh, 1986, Physica (Amsterdam) 141B+C, 1. 10.1016/0378-4363(86)90346-3 PHBCDQ 0378-4363
40. de Jongh, L. J., and A. R. Miedema, 1974, Adv. Phys. 23, 1. ADPHAH 0001-8732 10.1080/00018739700101558
41. Dombre, T., and N. Read, 1989, Phys. Rev. B PRBMDO 0163-1829 39, 6797. 10.1103/PhysRevB.39.6797
42. Dyson, F. J., 1956 a, Phys. Rev. 102, 1217. PHRVAO 0031-899X 10.1103/PhysRev.102.1217
43. Dyson, F. J., 1956 b, Phys. Rev. 102, 1230. PHRVAO 0031-899X 10.1103/PhysRev.102.1230
44. Fazekas, P., and P. W. Anderson, 1974, Philos. Mag. PHMAA4 0031-8086 30, 423. 10.1080/14786439808206568
45. Fischer, T., S. Duffe, and G. S. Uhrig, 2010, New J. Phys. NJOPFM 1367-2630 12, 033048. 10.1088/1367-2630/12/3/033048
46. Fischer, T., S. Duffe, and G. S. Uhrig, 2011, Europhys. Lett. 96, 47 001. EULEEJ 0295-5075 10.1209/0295-5075/96/47001
47. Fritz, L., R. L. Doretto, S. Wessel, S. Wenzel, S. Burdin, and M. Vojta, 2011, Phys. Rev. B PRBMDO 1098-0121 83, 174416. 10.1103/PhysRevB.83.174416
48. Fuhrman, W. T., M. Mourigal, M. E. Zhitomirsky, and A. L. Chernyshev, 2012, Phys. Rev. B PRBMDO 1098-0121 85, 184405. 10.1103/PhysRevB.85.184405
49. Garlea, V. O., 2007, Phys. Rev. Lett. 98, 167202. PRLTAO 0031-9007 10.1103/PhysRevLett.98.167202 (Pubitemid 46633696)
50. Giamarchi, T., C. Ruegg, and O. Tchernyshyov, 2008, Nat. Phys. 4, 198. NPAHAX 1745-2473 10.1038/nphys893
51. Giamarchi, T., and A. M. Tsvelik, 1999, Phys. Rev. B PRBMDO 0163-1829 59, 11 398. 10.1103/PhysRevB.59.11398
52. Glazkov, V. N., A. I. Smirnov, A. Zheludev, and B. C. Sales, 2010, Phys. Rev. B PRBMDO 1098-0121 82, 184406. 10.1103/PhysRevB.82.184406
53. Gluzman, S., 1993, Z. Phys. B ZPCMDN 0722-3277 90, 313. 10.1007/BF01433054
54. Glyde, H. R., M. R. Gibbs, W. G. Stirling, and M. A. Adams, 1998, Europhys. Lett. 43, 422. EULEEJ 0295-5075 10.1209/epl/i1998-00375-2
55. Graf, E. H., V. J. Minkiewicz, H. B. Moller, and L. Passell, 1974, Phys. Rev. A PLRAAN 0556-2791 10, 1748. 10.1103/PhysRevA.10.1748
56. Grenier, B., and T. Ziman, 2007, C.R. Physique CRPOBN 1631-0705 8, 717. 10.1016/j.crhy.2007.09.016
57. Gurevich, A. G., and G. A. Melkov, 1996, Magnetization Oscillations and Waves (CRC Press, Boca Raton).
58. Hagiwara, M., 2005, Phys. Rev. Lett. 94, 177202. PRLTAO 0031-9007 10.1103/PhysRevLett.94.177202 (Pubitemid 41508814)
59. Hamer, C. J., Zheng Weihong, and P. Arndt, 1992, Phys. Rev. B PRBMDO 0163-1829 46, 6276. 10.1103/PhysRevB.46.6276
60. Harris, A. B., 1973, Phys. Rev. B PLRBAQ 0556-2805 7, 3166. 10.1103/PhysRevB.7.3166
61. Harris, A. B., D. Kumar, B. I. Halperin, and P. C. Hohenberg, 1971, Phys. Rev. B PLRBAQ 0556-2805 3, 961. 10.1103/PhysRevB.3.961
62. Hase, M., I. Terasaki, and K. Uchinokura, 1993, Phys. Rev. Lett. 70, 3651. PRLTAO 0031-9007 10.1103/PhysRevLett.70.3651
63. Hoddeson, L., G. Baym, and M. Eckert, 1987, Rev. Mod. Phys. 59, 287. RMPHAT 0034-6861 10.1103/RevModPhys.59.287
64. Holstein, T., and H. Primakoff, 1940, Phys. Rev. 58, 1098. PHRVAO 0031-899X 10.1103/PhysRev.58.1098
65. Igarashi, J.-I., 1992, Phys. Rev. B PRBMDO 0163-1829 46, 10763. 10.1103/PhysRevB.46.10763
66. Igarashi, J.-I., and T. Nagao, 2005, Phys. Rev. B PRBMDO 1098-0121 72, 014403. 10.1103/PhysRevB.72.014403
67. Ishii, R., 2011, Europhys. Lett. 94, 17 001. EULEEJ 0295-5075 10.1209/0295-5075/94/17001
68. Jaime, M., 2004, Phys. Rev. Lett. 93, 087203. PRLTAO 0031-9007 10.1103/PhysRevLett.93.087203
69. Jolicoeur, Th., and J. C. Le Guillou, 1989, Phys. Rev. B PRBMDO 0163-1829 40, 2727. 10.1103/PhysRevB.40.2727
70. Kats, E. I., and A. R. Muratov, 2005, J. Phys. Condens. Matter JCOMEL 0953-8984 17, 6849. 10.1088/0953-8984/17/43/006 (Pubitemid 41483215)
71. Kohama, Y., 2011, Phys. Rev. Lett. 106, 037203. PRLTAO 0031-9007 10.1103/PhysRevLett.106.037203
72. Kohno, M., O. A. Starykh, and L. Balents, 2007, Nat. Phys. NPAHAX 1745-2473 3, 790. 10.1038/nphys749
73. Kolezhuk, A., and S. Sachdev, 2006, Phys. Rev. Lett. 96, 087203. PRLTAO 0031-9007 10.1103/PhysRevLett.96.087203 (Pubitemid 43327442)
74. Kosevich, A. M., 2005, The Crystal Lattice: Phonons, Solitons, Dislocations, Superlattices (Wiley Verlag, Weinheim).
75. Kreisel, A., F. Sauli, N. Hasselmann, and P. Kopietz, 2008, Phys. Rev. B PRBMDO 1098-0121 78, 035127. 10.1103/PhysRevB.78.035127
76. Kubo, R., 1952, Phys. Rev. 87, 568. PHRVAO 0031-899X 10.1103/PhysRev.87. 568
77. Kulik, Y., and O. P. Sushkov, 2011, Phys. Rev. B PRBMDO 1098-0121 84, 134418. 10.1103/PhysRevB.84.134418
78. Lancaster, T., 2007, Phys. Rev. B PRBMDO 1098-0121 75, 094421. 10.1103/PhysRevB.75.094421
79. Leuenberger, B., H. U. Güdel, R. Feile, and J. K. Kjems, 1983, Phys. Rev. B PRBMDO 0163-1829 28, 5368(R). 10.1103/PhysRevB.28.5368
80. Lhuillier, C., and G. Misguich, 2011, in Introduction to Frustrated Magnetism, edited by, C. Lacroix, (Springer, Berlin).
81. Lifshitz, E. M., and L. P. Pitaevskii, 1980, Statistical Physics II (Pergamon, Oxford).
82. Lüscher, A., and A. M. Läuchli, 2009, Phys. Rev. B PRBMDO 1098-0121 79, 195102. 10.1103/PhysRevB.79.195102
83. Mahan, G. D., 2000, Many-Particle Physics (Kluwer, New York).
84. Majlis, N., 2007, The Quantum Theory of Magnetism (World Scientific, Singapore).
85. Manousakis, E., 1991, Rev. Mod. Phys. 63, 1. RMPHAT 0034-6861 10.1103/RevModPhys.63.1
86. Masuda, T., S. Kitaoka, S. Takamizawa, N. Metoki, K. Kaneko, K. C. Rule, K. Kiefer, H. Manaka, and H. Nojiri, 2010, Phys. Rev. B PRBMDO 1098-0121 81, 100402(R). 10.1103/PhysRevB.81.100402
87. Masuda, T., A. Zheludev, H. Manaka, L.-P. Regnault, J.-H. Chung, and Y. Qiu, 2006, Phys. Rev. Lett. 96, 047210. PRLTAO 0031-9007 10.1103/PhysRevLett.96. 047210 (Pubitemid 43270920)
88. Matan, K., D. Grohol, D. G. Nocera, T. Yildirim, A. B. Harris, S. H. Lee, S. E. Nagler, and Y. S. Lee, 2006 Phys. Rev. Lett. 96, 247201. PRLTAO 0031-9007 10.1103/PhysRevLett.96.247201 (Pubitemid 43926992)
89. Matsubara, T., and H. Matsuda, 1956, Prog. Theor. Phys. 16, 569. PTPKAV 0033-068X 10.1143/PTP.16.569
90. Matsumoto, M., B. Normand, T. M. Rice, and M. Sigrist, 2004, Phys. Rev. B PRBMDO 0163-1829 69, 054423. 10.1103/PhysRevB.69.054423
91. Mattis, D. C., 1981, The Theory of Magnetism (Springer, Berlin).
92. Mila, F., 1998, Eur. Phys. J. B 6, 201. EPJBFY 1434-6028 10.1007/s100510050542
93. Miyake, S. J., 1992, J. Phys. Soc. Jpn. 61, 983. JUPSAU 0031-9015 10.1143/JPSJ.61.983
94. Mourigal, M., M. E. Zhitomirsky, and A. L. Chernyshev, 2010, Phys. Rev. B PRBMDO 1098-0121 82, 144402. 10.1103/PhysRevB.82.144402
95. Náfrádi, B., T. Keller, H. Manaka, A. Zheludev, and B. Keimer, 2011, Phys. Rev. Lett. 106, 177202. PRLTAO 0031-9007 10.1103/PhysRevLett.106.177202
96. Nikuni, T., M. Oshikawa, A. Oosawa, and H. Tanaka, 2000, Phys. Rev. Lett. 84, 5868. PRLTAO 0031-9007 10.1103/PhysRevLett.84.5868
97. Notbohm, S., 2007, Phys. Rev. Lett. 98, 027403. PRLTAO 0031-9007 10.1103/PhysRevLett.98.027403 (Pubitemid 46135133)
98. Oguchi, T., 1960, Phys. Rev. 117, 117. PHRVAO 0031-899X 10.1103/PhysRev.117.117
99. Ohyama, T., and H. Shiba, 1993, J. Phys. Soc. Jpn. 62, 3277. JUPSAU 0031-9015 10.1143/JPSJ.62.3277
100. Oosawa, A., M. Fujisawa, T. Osakabe, K. Kakurai, and H. Tanaka, 2003, J. Phys. Soc. Jpn. 72, 1026. JUPSAU 0031-9015 10.1143/JPSJ.72.1026
101. Osano, K., H. Shiba, and Y. Endoh, 1982, Prog. Theor. Phys. 67, 995. PTPKAV 0033-068X 10.1143/PTP.67.995
102. Pappas, C., G. Ehlers, and F. Mezei, 2006, in Neutron Scattering From Magnetic Materials, edited by, T. Chatterji, (Elsevier, Amsterdam).
103. Pethick, C. J., and H. Smith, 2008, Bose-Einstein Condensation in Dilute Gases (Cambridge University Press, Cambridge).
104. Pitaevskii, L. P., 1959, Zh. Eksp. Teor. Fiz. ZETFA7 0044-4510 36, 1168
105. [Pitaevskii, L. P. Sov. Phys. JETP 9, 830 1959]. SPHJAR 0038-5646
106. Pomeranchuk, I., 1941, J. Phys. (USSR) IV, 357.
107. Regnault, L.-P., I. Zaliznyak, J. P. Renard, and C. Vettier, 1994, Phys. Rev. B PRBMDO 0163-1829 50, 9174. 10.1103/PhysRevB.50.9174
108. Regnault, L.-P., A. Zheludev, M. Hagiwara, and A. Stunault, 2006, Phys. Rev. B PRBMDO 1098-0121 73, 174431. 10.1103/PhysRevB.73.174431 (Pubitemid 43782076)
109. Rößler, U. K., A. N. Bogdanov, and C. Pfleiderer, 2006, Nature (London) NATUAS 0028-0836 442, 797. 10.1038/nature05056 (Pubitemid 44261900)
110. Ruëgg, Ch., B. Normand, M. Matsumoto, A. Furrer, D. F. McMorrow, K. W. Krämer, H.-U. Güdel, S. N. Gvasaliya, H. Mutka, and M. Boehm, 2008, Phys. Rev. Lett. 100, 205701. PRLTAO 0031-9007 10.1103/PhysRevLett.100.205701 (Pubitemid 351725963)
111. Sachdev, S., 2008, Nat. Phys. 4, 173. NPAHAX 1745-2473 10.1038/nphys894
112. Sachdev, S., and R. N. Bhatt, 1990, Phys. Rev. B PRBMDO 0163-1829 41, 9323. 10.1103/PhysRevB.41.9323
113. Sandvik, A. W., 1997, Phys. Rev. B PRBMDO 0163-1829 56, 11 678. 10.1103/PhysRevB.56.11678
114. Sandvik, A. W., and R. R. P. Singh, 2001, Phys. Rev. Lett. 86, 528. PRLTAO 0031-9007 10.1103/PhysRevLett.86.528 (Pubitemid 32136499)
115. Schmidiger, D., S. Mühlbauer, S. N. Gvasaliya, T. Yankova, and A. Zheludev, 2011, Phys. Rev. B PRBMDO 1098-0121 84, 144421. 10.1103/PhysRevB.84. 144421
116. Schulz, H. J., 1996, Phys. Rev. Lett. 77, 2790. PRLTAO 0031-9007 10.1103/PhysRevLett.77.2790
117. Shirata, Y., H. Tanaka, A. Matsuo, and K. Kindo, 2012, Phys. Rev. Lett. 108, 057205. PRLTAO 0031-9007 10.1103/PhysRevLett.108.057205
118. Slater, J. C., 1930, Phys. Rev. 35, 509. PHRVAO 0031-899X 10.1103/PhysRev.35.509
119. Sluckin, T. J., and R. M. Bowley, 1974, J. Phys. C 7, 1779. JPSOAW 0022-3719 10.1088/0022-3719/7/10/006
120. Starykh, O. A., A. V. Chubukov, and A. G. Abanov, 2006, Phys. Rev. B PRBMDO 1098-0121 74, 180403(R). 10.1103/PhysRevB.74.180403 (Pubitemid 44748677)
121. Stephanovich, V. A., and M. E. Zhitomirsky, 2011, Europhys. Lett. 95, 17 007. EULEEJ 0295-5075 10.1209/0295-5075/95/17007
122. Stone, M. B., I. A. Zaliznyak, T. Hong, C. L. Broholm, and D. H. Reich, 2006, Nature (London) NATUAS 0028-0836 440, 187. 10.1038/nature04593 (Pubitemid 43372092)
123. Syljuåsen, O. F., 2008, Phys. Rev. B PRBMDO 1098-0121 78, 180413(R). 10.1103/PhysRevB.78.180413
124. Syromyatnikov, A. V., 2009, Phys. Rev. B PRBMDO 1098-0121 79, 054413. 10.1103/PhysRevB.79.054413
125. Syromyatnikov, A. V., 2010, J. Phys. Condens. Matter JCOMEL 0953-8984 22, 216003. 10.1088/0953-8984/22/21/216003
126. Takatsu, K., W. Shiramura, and H. Tanaka, 1997, J. Phys. Soc. Jpn. 66, 1611. JUPSAU 0031-9015 10.1143/JPSJ.66.1611
127. Toth, S., 2011, Phys. Rev. B PRBMDO 1098-0121 84, 054452. 10.1103/PhysRevB.84.054452
128. Tsujii, H., C. R. Rotundu, T. Ono, H. Tanaka, B. Andraka, K. Ingersent, and Y. Takano, 2007, Phys. Rev. B PRBMDO 1098-0121 76, 060406(R). 10.1103/PhysRevB.76.060406
129. Tsyrulin, N., T. Pardini, R. R. P. Singh, F. Xiao, P. Link, A. Schneidewind, A. Hiess, C. P. Landee, M. M. Turnbull, and M. Kenzelmann, 2009, Phys. Rev. Lett. 102, 197201. PRLTAO 0031-9007 10.1103/PhysRevLett.102.197201
130. Tsyrulin, N., F. Xiao, A. Schneidewind, P. Link, H. M. Rønnow, J. Gavilano, C. P. Landee, M. M. Turnbull, and M. Kenzelmann, 2010, Phys. Rev. B PRBMDO 1098-0121 81, 134409. 10.1103/PhysRevB.81.134409
131. Van Kranendonk, J., and J. H. Van Vleck, 1958, Rev. Mod. Phys. 30, 1. RMPHAT 0034-6861 10.1103/RevModPhys.30.1
132. Veillette, M. Y., A. J. A. James, and F. H. L. Essler, 2005, Phys. Rev. B PRBMDO 1098-0121 72, 134429. 10.1103/PhysRevB.72.134429 (Pubitemid 43028802)
133. Villain, J., 1974, J. Phys. (Paris) 35, 27. JOPQAG 0302-0738 10.1051/jphys:0197400350102700
134. Walker, C. T., and G. A. Slack, 1970, Am. J. Phys. 38, 1380. AJPIAS 0002-9505 10.1119/1.1976141
135. Weihong, Z., and C. J. Hamer, 1993, Phys. Rev. B PRBMDO 0163-1829 47, 7961. 10.1103/PhysRevB.47.7961
136. White, R. M., 1983, Quantum Theory of Magnetism (Springer, Berlin).
137. White, S. R., and A. L. Chernyshev, 2007, Phys. Rev. Lett. 99, 127004. PRLTAO 0031-9007 10.1103/PhysRevLett.99.127004 (Pubitemid 47462647)
138. Woodward, F. M., A. S. Albrecht, C. M. Wynn, C. P. Landee, and M. M. Turnbull, 2002, Phys. Rev. B PRBMDO 0163-1829 65, 144412. 10.1103/PhysRevB.65. 144412
139. Xiao, F., 2009, Phys. Rev. B PRBMDO 1098-0121 79, 134412. 10.1103/PhysRevB.79.134412
140. Zaliznyak, I. A., S.-H. Lee, and S. V. Petrov, 2001, Phys. Rev. Lett. 87, 017202. PRLTAO 0031-9007 10.1103/PhysRevLett.87.017202
141. Zheludev, A., 2007, Phys. Rev. B PRBMDO 1098-0121 76, 054450. 10.1103/PhysRevB.76.054450
142. Zheng, W., J. O. Fjaerestad, R. R. P. Singh, R. H. McKenzie, and R. Coldea, 2006 a, Phys. Rev. Lett. 96, 057201. PRLTAO 0031-9007 10.1103/PhysRevLett.96.057201 (Pubitemid 43270986)
143. Zheng, W., J. O. Fjaerestad, R. R. P. Singh, R. H. McKenzie, and R. Coldea, 2006 b, Phys. Rev. B PRBMDO 1098-0121 74, 224420. 10.1103/PhysRevB.74. 224420 (Pubitemid 44956494)
144. Zheng, W., C. J. Hamer, and R. R. P. Singh, 2006, Phys. Rev. B PRBMDO 1098-0121 74, 172407. 10.1103/PhysRevB.74.172407 (Pubitemid 44748672)
145. Zheng, W., J. Oitmaa, and C. J. Hamer, 2005, Phys. Rev. B PRBMDO 1098-0121 71, 184440. 10.1103/PhysRevB.71.184440 (Pubitemid 43292095)
146. Zhitomirsky, M. E., 2006, Phys. Rev. B PRBMDO 1098-0121 73, 100404(R). 10.1103/PhysRevB.73.100404 (Pubitemid 43389968)
147. Zhitomirsky, M. E., and A. L. Chernyshev, 1999, Phys. Rev. Lett. 82, 4536. PRLTAO 0031-9007 10.1103/PhysRevLett.82.4536
148. Zhitomirsky, M. E., and T. Nikuni, 1998, Phys. Rev. B PRBMDO 0163-1829 57, 5013. 10.1103/PhysRevB.57.5013