Abstract
New magnetization plateaus and supersolid phases are identified in an extended Shastry–Sutherland model – with additional longer range interactions and exchange anisotropy – over a wide range of interaction parameters and an applied magnetic field. The model is appropriate for describing the low energy properties of some members of the rare earth tetraborides. Using a plaquette representation and exact mapping of ground state configurations in the Ising limit, supplemented by large scale quantum Monte Carlo simulations to include the effects of exchange interactions, we have identified several magnetization plateaus and associated spin supersolid phases. Our methods enable us to elucidate the underlying structure and mechanism of formation of the supersolid phases, thus gaining deeper understanding into their emergence from competing interactions. Additionally, in this regime we find evidence of a fractional plateau at 1∕9 saturation magnetization, which may hold the clue to understanding the fractional plateau in TmB4 that exhibits magnetic hysteresis.
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References
O. Penrose, L. Onsager, Phys. Rev. 104, 576 (1956)
M. Boninsegni, N.V. Prokof’ev, Rev. Mod. Phys. 84, 759 (2012)
D.Y. Kim, M.H.W. Chan, Phys. Rev. B 90, 064503 (2014)
A. Eyal, X. Mi, A.V. Talanov, J.D. Reppy, Proc. Natl. Acad. Sci., USA 113, E3203 (2016)
B.S. Shastry, B. Sutherland, Physica B+C 108, 1069 (1981)
H. Kageyama, K. Yoshimura, R. Stern, N. Mushnikov, K. Onizuka, M. Kato, K. Kosuge, C. Slichter, T. Goto, Y. Ueda, Phys. Rev. Lett. 82, 3168 (1999)
S. Miyahara, K. Ueda, Phys. Rev. Lett. 82, 3701 (1999)
K. Onizuka, H. Kageyama, Y. Narumi, K. Kindo, Y. Ueda, T. Goto, J. Phys. Soc. Jpn. 69, 1016 (2000)
H. Kageyama, M. Nishi, N. Aso, K. Onizuka, T. Yosihama, K. Nukui, K. Kodama, K. Kakurai, Y. Ueda, Phys. Rev. Lett. 84, 5876 (2000)
K. Kodama, M. Takigawa, M. Horvatić, C. Berthier, H. Kageyama, Y. Ueda, S. Miyahara, F. Becca, F. Mila, Science 298, 395 (2002)
S. Miyahara, K. Ueda, J. Phys.: Condens. Matter 15, R327 (2003)
S.E. Sebastian, N. Harrison, P. Sengupta, C.D. Batista, S. Francoual, E. Palm, T. Murphy, N. Marcano, H.A. Dabkowska, B.D. Gaulin, Proc. Natl. Acad. Sci., USA 105, 20157 (2008)
S. Yoshii, T. Yamamoto, M. Hagiwara, A. Shigekawa, S. Michimura, F. Iga, T. Takabatake, K. Kindo, J. Phys.: Conf. Ser. 51, 59 (2006)
S. Michimura, A. Shigekawa, F. Iga, M. Sera, T. Takabatake, K. Ohoyama, Y. Okabe, Physica B 378–380, 596 (2006)
K. Siemensmeyer, E. Wulf, H.J. Mikeska, K. Flachbart, S. Gabáni, S. Mat’aš, P. Priputen, A. Efdokimova, N. Shitsevalova, Phys. Rev. Lett. 101, 177201 (2008)
Z.Y. Meng, S. Wessel, Phys. Rev. B 78, 224416 (2008)
F. Liu, S. Sachdev, https://doi.org/arXiv:0904.3018 (2009)
M.C. Chang, M.F. Yang, Phys. Rev. B 79, 104411 (2009)
T. Suzuki, Y. Tomita, N. Kawashima, Phys. Rev. B 80, 180405 (2009)
T. Suzuki, Y. Tomita, N. Kawashima, P. Sengupta, Phys. Rev. B 82, 214404 (2010)
Y.I. Dublenych, Phys. Rev. Lett. 109, 167202 (2012)
Y.I. Dublenych, Phys. Rev. E 88, 022111 (2013)
K. Wierschem, P. Sengupta, Phys. Rev. Lett. 110, 207207 (2013)
K. Wierschem, P. Sengupta, J. Korean Phys. Soc. 63, 486 (2013)
W.C. Huang, L. Huo, G. Tian, H.R. Qian, X.S. Gao, M.H. Qin, J.M. Liu, J. Phys.: Condens. Matter 24, 386003 (2012)
P. Farkašovský, H. Čenčariková, S. Mat’aš, Phys. Rev. B 82, 054409 (2010)
T. Suzuki, Private communication
A.W. Sandvik, J. Kurkijärvi, Phys. Rev. B 43, 5950 (1991)
O.F. Syljuåsen, A.W. Sandvik, Phys. Rev. E 66, 046701 (2002)
K. Louis, C. Gros, Phys. Rev. B 70, 100410 (2004)
R.G. Melko, J. Phys.: Condens. Matter 19, 145203 (2007)
A. Dorneich, M. Troyer, Phys. Rev. E 64, 066701 (2001)
A.W. Sandvik, Phys. Rev. B 56, 11678 (1997)
E.L. Pollock, D.M. Ceperley, Phys. Rev. B 36, 8343 (1987)
W. Selke, Phys. Rep. 170, 213 (1988)
L. Balents, M.P.A. Fisher, S.M. Girvin, Phys. Rev. B 65, 224412 (2002)
A. Kalz, A. Honecker, S. Fuchs, T. Pruschke, Phys. Rev. B 83, 174519 (2011)
A. Kalz, M. Arlego, D. Cabra, A. Honecker, G. Rossini, Phys. Rev. B 85, 104505 (2012)
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Contribution to the Topical Issue “Coexistence of Long-Range Orders in Low-dimensional Systems”, edited by Sudhakar Yarlagadda, and Peter B. Littlewood.
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Wierschem, K., Zhang, Z., Wibawa, A. et al. Magnetization plateaus and supersolid phases in an extended Shastry–Sutherland model. Eur. Phys. J. B 91, 201 (2018). https://doi.org/10.1140/epjb/e2018-90356-5
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DOI: https://doi.org/10.1140/epjb/e2018-90356-5