Extension of the spin- 1 2 frustrated square lattice model: The case of layered vanadium phosphates

Physical Review B - Condensed Matter and Materials Physics

Volumn 79, Issue 21, 2009, Pages

  Tsirlin, Alexander A ^a,b   Rosner, Helge ^a  

^a MAX PLANCK INSTITUTE FOR CHEMICAL PHYSICS OF SOLIDS   (Germany)

^b MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 67650076991     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.79.214417     Document Type: Article

References (66)

1. P. A. Lee, Rep. Prog. Phys. 71, 012501 (2008). 10.1088/0034-4885/71/1/ 012501
2. K. P. Schmidt, J. Dorier, A. M. Läuchli, and F. Mila, Phys. Rev. Lett. 100, 090401 (2008). 10.1103/PhysRevLett.100.090401
3. A. P. Ramirez, Annu. Rev. Mater. Sci. 24, 453 (1994).
4. J. E. Greedan, J. Mater. Chem. 11, 37 (2001). 10.1039/b003682j
5. M. P. Shores, E. A. Nytko, B. M. Bartlett, and D. G. Nocera, J. Am. Chem. Soc. 127, 13462 (2005). 10.1021/ja053891p
6. M. A. de Vries, K. V. Kamenev, W. A. Kockelmann, J. Sanchez-Benitez, and A. Harrison, Phys. Rev. Lett. 100, 157205 (2008). 10.1103/PhysRevLett.100.157205
7. O. Janson, J. Richter, and H. Rosner, Phys. Rev. Lett. 101, 106403 (2008). 10.1103/PhysRevLett.101.106403
8. G. Misguich and C. Lhuillier, in Frustrated spin systems, edited by, H. T. Diep, (World Scientific, Singapore, 2004) (and references therein).
9. N. Shannon, B. Schmidt, K. Penc, and P. Thalmeier, Eur. Phys. J. B 38, 599 (2004). 10.1140/epjb/e2004-00156-3
10. A. A. Nersesyan and A. M. Tsvelik, Phys. Rev. B 67, 024422 (2003). 10.1103/PhysRevB.67.024422
11. O. A. Starykh and L. Balents, Phys. Rev. Lett. 93, 127202 (2004). 10.1103/PhysRevLett.93.127202
12. P. Sindzingre, Phys. Rev. B 69, 094418 (2004). 10.1103/PhysRevB.69.094418
13. S. Moukouri, J. Stat. Mech. (2006) P02002. 10.1088/1742-5468/2006/02/ P02002
14. R. F. Bishop, P. H. Y. Li, R. Darradi, and J. Richter, J. Phys.: Condens. Matter 20, 255251 (2008). 10.1088/0953-8984/20/25/255251
15. In Refs., the model has been considered for the case of antiferromagnetic J1 and J2 only. Therefore, the results refer to the narrowing and disappearance of the critical region at J2 / J1 =0.5. Yet one can expect a similar behavior for the critical region at J2 / J1 =-0.5, see Sec. 6.
16. R. Melzi, P. Carretta, A. Lascialfari, M. Mambrini, M. Troyer, P. Millet, and F. Mila, Phys. Rev. Lett. 85, 1318 (2000). 10.1103/PhysRevLett.85.1318
17. R. Melzi, S. Aldrovandi, F. Tedoldi, P. Carretta, P. Millet, and F. Mila, Phys. Rev. B 64, 024409 (2001). 10.1103/PhysRevB.64.024409
18. H. Rosner, R. R. P. Singh, W. H. Zheng, J. Oitmaa, S.-L. Drechsler, and W. E. Pickett, Phys. Rev. Lett. 88, 186405 (2002). 10.1103/PhysRevLett.88.186405
19. H. Rosner, R. R. P. Singh, W. H. Zheng, J. Oitmaa, and W. E. Pickett, Phys. Rev. B 67, 014416 (2003). 10.1103/PhysRevB.67.014416
20. G. Misguich, B. Bernu, and L. Pierre, Phys. Rev. B 68, 113409 (2003). 10.1103/PhysRevB.68.113409
21. A. Bombardi, J. Rodriguez-Carvajal, S. Di Matteo, F. de Bergevin, L. Paolasini, P. Carretta, P. Millet, and R. Caciuffo, Phys. Rev. Lett. 93, 027202 (2004). 10.1103/PhysRevLett.93.027202
22. P. Carretta, N. Papinutto, C. B. Azzoni, M. C. Mozzati, E. Pavarini, S. Gonthier, and P. Millet, Phys. Rev. B 66, 094420 (2002). 10.1103/PhysRevB.66. 094420
23. A. Bombardi, L. C. Chapon, I. Margiolaki, C. Mazzoli, S. Gonthier, F. Duc, and P. G. Radaelli, Phys. Rev. B 71, 220406 (R) (2005). 10.1103/PhysRevB.71.220406
24. E. E. Kaul, H. Rosner, N. Shannon, R. V. Shpanchenko, and C. Geibel, J. Magn. Magn. Mater. 272-276, 922 (2004). 10.1016/j.jmmm.2003.12.002
25. E. E. Kaul, Ph.D. thesis, Technical University Dresden, 2005. Electronic version available at: http://hsss.slub-dresden.de/documents/1131439690937-4924/ 1131439690937-4924.pdf.
26. M. Skoulatos, J. P. Goff, N. Shannon, E. E. Kaul, C. Geibel, A. P. Murani, M. Enderle, and A. R. Wildes, J. Magn. Magn. Mater. 310, 1257 (2007). 10.1016/j.jmmm.2006.10.379
27. M. Skoulatos, Ph.D. thesis, University of Liverpool, 2008.
28. A. A. Tsirlin, A. A. Belik, R. V. Shpanchenko, E. V. Antipov, E. Takayama-Muromachi, and H. Rosner, Phys. Rev. B 77, 092402 (2008). 10.1103/PhysRevB.77.092402
29. K. Oka, I. Yamada, M. Azuma, S. Takeshita, K. H. Satoh, A. Koda, R. Kadono, M. Takano, and Y. Shimakawa, Inorg. Chem. 47, 7355 (2008). 10.1021/ic800649a
30. R. Nath, A. A. Tsirlin, H. Rosner, and C. Geibel, Phys. Rev. B 78, 064422 (2008). 10.1103/PhysRevB.78.064422
31. P. Thalmeier, M. E. Zhitomirsky, B. Schmidt, and N. Shannon, Phys. Rev. B 77, 104441 (2008). 10.1103/PhysRevB.77.104441
32. H. Kageyama, T. Kitano, N. Oba, M. Nishi, S. Nagai, K. Hirota, L. Viciu, J. B. Wiley, J. Yasuda, Y. Baba, Y. Ajiro, and K. Yoshimura, J. Phys. Soc. Jpn. 74, 1702 (2005). 10.1143/JPSJ.74.1702
33. M. Yoshida, N. Ogata, M. Takigawa, J. Yamaura, M. Ichihara, T. Kitano, H. Kageyama, Y. Ajiro, and K. Yoshimura, J. Phys. Soc. Jpn. 76, 104703 (2007). 10.1143/JPSJ.76.104703
34. A. A. Tsirlin and H. Rosner, Phys. Rev. B 10.1103/PhysRevB.79.214416 79, 214416 (2009).
35. H. A. Eick and L. Kihlborg, Acta Chem. Scand. 20, 722 (1966). 10.3891/acta.chem.scand.20-0722
36. P. Millet and C. Satto, Mater. Res. Bull. 33, 1339 (1998). 10.1016/S0025-5408(98)00122-6
37. S. Meyer, B. Mertens, and H. Müller-Buschbaum, Z. Naturforsch. B 52, 985 (1997).
38. S. Meyer and H. Müller-Buschbaum, Z. Naturforsch. B 52, 367 (1997).
39. R. V. Shpanchenko, E. E. Kaul, C. Geibel, and E. V. Antipov, Acta Crystallogr. C 62, i88 (2006). 10.1107/S0108270106021597
40. K. Koepernik and H. Eschrig, Phys. Rev. B 59, 1743 (1999). 10.1103/PhysRevB.59.1743
41. J. P. Perdew and Y. Wang, Phys. Rev. B 45, 13244 (1992). 10.1103/PhysRevB.45.13244
42. A. A. Tsirlin, R. Nath, C. Geibel, and H. Rosner, Phys. Rev. B 77, 104436 (2008). 10.1103/PhysRevB.77.104436
43. E. E. Kaul, H. Rosner, V. Yushankhai, J. Sichelschmidt, R. V. Shpanchenko, and C. Geibel, Phys. Rev. B 67, 174417 (2003). 10.1103/PhysRevB.67. 174417
44. R. Nath, A. A. Tsirlin, E. E. Kaul, M. Baenitz, N. Büttgen, C. Geibel, and H. Rosner, Phys. Rev. B 78, 024418 (2008). 10.1103/PhysRevB.78. 024418
45. Note that the exchange constants of the order of 10 K are at least 9 orders of magnitude smaller than the total energy per unit cell.
46. N. Dupré, G. Wallez, J. Gaubicher, and M. Quarton, J. Solid State Chem. 177, 2896 (2004). 10.1016/j.jssc.2004.04.006
47. A. F. Albuquerque, F. Alet, P. Corboz, P. Dayal, A. Feiguin, S. Fuchs, L. Gamper, E. Gull, S. Gürtler, A. Honecker, R. Igarashi, M. Körner, A. Kozhevnikov, A. Läuchli, S. R. Manmana, M. Matsumoto, I. P. McCulloch, F. Michel, R. M. Noack, G. Pawłowski, L. Pollet, T. Pruschke, U. Schollwöck, S. Todo, S. Trebst, M. Troyer, P. Werner, and S. Wessel, J. Magn. Magn. Mater. 310, 1187 (2007). 10.1016/j.jmmm.2006.10.304
48. To estimate the accuracy of the FD simulations for the FSL model, one should compare the magnetic susceptibility and the specific heat at α=0 with the results of quantum Monte-Carlo (QMC) simulations for the same, unfrustrated square lattice. The latter simulations are less computationally exhaustive and can be performed for sufficiently large clusters. According to the FD results of Ref., the susceptibility maximum for the unfrustrated square lattice is found at Tmax 1.1J, while the QMC results converge to Tmax 0.9J
49. [J.-K. Kim and M. Troyer, Phys. Rev. Lett. 80, 2705 (1998)]. 10.1103/PhysRevLett.80.2705
50. C. J. Ballhausen and H. B. Gray, Inorg. Chem. 1, 111 (1962). 10.1021/ic50001a022
51. Assuming similar FM contributions to all the NN couplings, one can suggest that the very small t1 in Pb2 VO (PO4) 2 implies similar (and FM) interactions along the b axis, despite two different superexchange pathways are present (see Sec. 2). This conclusion can be further supported by LSDA+U calculations (not shown) and justifies our consideration of Pb2 VO (PO4) 2 as the close analog of the other AA′ VO (PO4) 2 compounds.
52. Note that Ud, the Coulomb repulsion parameter of LSDA+U, is applied to atomic orbitals. This is different from Ueff, the effective on-site Coulomb repulsion in the mixed vanadium-oxygen band. In general, the Ud and Ueff values do not coincide.
53. M. A. Korotin, I. S. Elfimov, V. I. Anisimov, M. Troyer, and D. I. Khomskii, Phys. Rev. Lett. 83, 1387 (1999). 10.1103/PhysRevLett.83.1387
54. D. W. Boukhvalov, E. Z. Kurmaev, A. Moewes, D. A. Zatsepin, V. M. Cherkashenko, S. N. Nemnonov, L. D. Finkelstein, Y. M. Yarmoshenko, M. Neumann, V. V. Dobrovitski, M. I. Katsnelson, A. I. Lichtenstein, B. N. Harmon, and P. Kögerler, Phys. Rev. B 67, 134408 (2003). 10.1103/PhysRevB.67.134408
55. D. W. Boukhvalov, V. V. Dobrovitski, M. I. Katsnelson, A. I. Lichtenstein, B. N. Harmon, and P. Kögerler, Phys. Rev. B 70, 054417 (2004). 10.1103/PhysRevB.70.054417
56. A. Barbour, R. D. Luttrell, J. Choi, J. L. Musfeldt, D. Zipse, N. S. Dalal, D. W. Boukhvalov, V. V. Dobrovitski, M. I. Katsnelson, A. I. Lichtenstein, B. N. Harmon, and P. Kögerler, Phys. Rev. B 74, 014411 (2006). 10.1103/PhysRevB.74.014411
57. V. V. Mazurenko, F. Mila, and V. I. Anisimov, Phys. Rev. B 73, 014418 (2006). 10.1103/PhysRevB.73.014418
58. P. Carretta, M. Filibian, R. Nath, C. Geibel, and P. J. C. King, arXiv:0904.3618 (unpublished).
59. K.-H. Lii, J. Chin. Chem. Soc. (Taipei) 39, 569 (1992).
60. H. Y. Kang, W. C. Lee, S. L. Wang, and K. H. Lii, Inorg. Chem. 31, 4743 (1992). 10.1021/ic00049a007
61. D. Papoutsakis, J. E. Jackson, and D. G. Nocera, Inorg. Chem. 35, 800 (1996). 10.1021/ic950931p
62. M. Roca, M. D. Marcos, P. Amorós, J. Alamo, A. Beltrán-Porter, and D. Beltrán-Porter, Inorg. Chem. 36, 3414 (1997). 10.1021/ic970166+
63. M. Roca, P. Amorós, J. Cano, M. D. Marcos, J. Alamo, A. Beltrán-Porter, and D. Beltrán-Porter, Inorg. Chem. 37, 3167 (1998). 10.1021/ic971210o
64. E. Le Fur, O. Peña, and J. Y. Pivan, J. Alloys Compd. 285, 89 (1999). 10.1016/S0925-8388(99)00013-4
65. Le Fur, O. Peña, and J. Y. Pivan, J. Mater. Chem. 9, 1029 (1999). 10.1039/a808386j
66. E. Le Fur and J. Y. Pivan, J. Mater. Chem. 9, 2589 (1999). 10.1039/a901048c