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2015 | 127 | 2 | 324-326
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The J₁-J₂ Model on the Anisotropic Triangular and the Square Lattice: Similarities and Differences

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The Heisenberg model on a triangular lattice is a prime example for a geometrically frustrated spin system. However most experimentally accessible compounds have spatially anisotropic exchange interactions. As a function of this anisotropy, ground states with different magnetic properties can be realized. On the other hand, the J₁-J₂ model on the square lattice is a well-known example for frustration induced by competing exchange. The classical phase diagrams of the two models are related in a broad range of the control parameter ϕ=^{-1}(J₂/J₁). In both cases three different types of ground states are realized, each model having a ferromagnetic and an antiferromagnetic region in the phase diagram, and a third phase with columnar magnetic order for the square lattice and an in general incommensurate spiral structure for the triangular lattice. Quantum effects lift degeneracies in the non-FM phases and lead to additional nonmagnetic regions in the phase diagrams. The contribution of zero point fluctuations to ground state energy, wave vector, and ordered moment is discussed.
  • Max-Planck-Institut für Chemische Physik fester Stoffe, 01187 Dresden, Germany
  • Max-Planck-Institut für Chemische Physik fester Stoffe, 01187 Dresden, Germany
  • [1] T. Jolicoeur, J.C. Le Guillou, Phys. Rev. B 40, 2727 (1989), doi: 10.1103/PhysRevB.40.2727
  • [2] A.V. Chubukov, S. Sachdev, T. Senthil, J. Phys. Condens. Matter 6, 8891 (1994), doi: 10.1088/0953-8984/6/42/019
  • [3] H. Kawamura, S. Miyashita, J. Phys. Soc. Jpn. 53, 4138 (1984), doi: 10.1143/JPSJ.53.4138
  • [4] B. Bernu, P. Lecheminant, C. Lhuillier, L. Pierre, Phys. Rev. B 50, 10048 (1994), doi: 10.1103/PhysRevB.50.10048
  • [5] S.R. White, A.L. Chernyshev, Phys. Rev. Lett. 99, 127004 (2007), doi: 10.1103/PhysRevLett.99.127004
  • [6] J. Merino, R.H. McKenzie, J.B. Marston, C.H. Chung, J. Phys. Condens. Matter 11, 2965 (1999), doi: 10.1088/0953-8984/11/14/012
  • [7] A.E. Trumper, Phys. Rev. B 60, 2987 (1999), doi: 10.1103/PhysRevB.60.2987
  • [8] M.Y. Veillette, J.T. Chalker, R. Coldea, Phys. Rev. B 71, 214426 (2005), doi: 10.1103/PhysRevB.71.214426
  • [9] M.Y. Veillette, A.J.A. James, F.H.L. Essler, Phys. Rev. B 72, 134429 (2005), doi: 10.1103/PhysRevB.72.134429
  • [10] J. Reuther, R. Thomale, Phys. Rev. B 83, 024402 (2011), doi: 10.1103/PhysRevB.83.024402
  • [11] Z. Weihong, R.H. McKenzie, R.R.P. Singh, Phys. Rev. B 59, 14367 (1999), doi: 10.1103/PhysRevB.59.14367
  • [12] M.Q. Weng, D.N. Sheng, Z.Y. Weng, R.J. Bursill, Phys. Rev. B 74, 012407 (2006), doi: 10.1103/PhysRevB.74.012407
  • [13] P. Hauke, Phys. Rev. B 87, 014415 (2013), doi: 10.1103/PhysRevB.87.014415
  • [14] G. Misguich, C. Lhuillier, in: Frustrated Spin Systems, Ed. H.T. Diep, World Sci., 2004
  • [15] S. Sorella, Phys. Rev. Lett. 80, 4558 (1998), doi: 10.1103/PhysRevLett.80.4558
  • [16] R.R.P. Singh, W. Zheng, C.J. Hamer, J. Oitmaa, Phys. Rev. B 60, 7278 (1999), doi: 10.1103/PhysRevB.60.7278
  • [17] H.J. Schulz, T.A.L. Ziman, D. Poilblanc, J. Phys. I (France) 6, 675 (1996), doi: 10.1051/jp1:1996236
  • [18] B. Schmidt, M. Siahatgar, P. Thalmeier, Phys. Rev. B 81, 165101 (2010), doi: 10.1103/PhysRevB.81.165101
  • [19] N. Shannon, B. Schmidt, K. Penc, P. Thalmeier, Eur. Phys. J. B 38, 599 (2004), doi: 10.1140/epjb/e2004-00156-3
  • [20] I. Affleck, J. Phys. A Math. Gen. 31, 4573 (1998), doi: 10.1088/0305-4470/31/20/002
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