Possible phase transition of anisotropic frustrated Heisenberg model at finite temperature

Abstract

The frustrated spin-1/2 J_1a–J_1b–J₂ antiferromagnet with anisotropy on the two-dimensional square lattice was investigated, where the parameters J_1aand J_1b represent the nearest neighbor exchanges and along the x and y directions, respectively. J₂ represents the next-nearest neighbor exchange. The anisotropy includes the spatial and exchange anisotropies. Using the double-time Green’s function method, the effects of the interplay of exchanges and anisotropy on the possible phase transition of the Néel state and stripe state were discussed. Our results indicated that, in the case of anisotropic parameter 0≤η<1, the Néel and stripe states can exist and have the same critical temperature as long as J₂ = J_1b/2. Under such parameters, a first-order phase transformation between the Néel and stripe states can occur below the critical point. For J₂ ≠J_1b/2, our results indicate that the Néel and stripe states can also exist, while their critical temperatures differ. When J₂>J_1b/2, a first-order phase transformation between the two states may also occur. However, for J₂<J_1b/2, the Néel state is always more stable than the stripe state.

Keywords

frustrated Heisenberg model / quantum phase transition / magnetic anisotropy / antiferromagnetics

References

[1] G. Misguich and C. Lhuillier, Frustrated Spin Systems, 2nd Ed., edited by H. T. Diep, World Scientific, 2013

[2] J. R. Viana and J. R. deSousa, Anisotropy effects in frustrated Heisenberg antiferromagnets on a square lattice, Phys. Rev. B75(5), 052403 (2007)

[3] Y. Z. Ren, N. H. Tong, and X. C. Xie, Cluster meanfield theory study of J₁–J₂ Heisenberg model on a square lattice, J. Phys.: Condens. Matter26(11), 115601 (2014)

[4] S. S. Gong, W. Zhu, D. N. Sheng, O. I. Motrunich, and M. P. A. Fisher, Plaquette ordered phase and quantum phase diagram in the spin-1/2 J₁–J₂ Square Heisenberg Model, Phys. Rev. Lett.113(2), 027201 (2014)

[5] H. C. Jiang, H. Yao, and L. Balents, Spin liquid ground state of the spin-1/2 square J₁–J₂ Heisenberg model, Phys. Rev. B86(2), 024424 (2012)

[6] B. Schmidt, M. Siahatgar, and P. Thalmeier, Ordered moment in the anisotropic and frustrated square lattice Heisenberg model, Phys. Rev. B83(7), 075123 (2011)

[7] R. Darradi, O. Derzhko, R. Zinke, J. Schulenburg, S. E. Krüger, and J. Richter, Ground state phases of the spin-1/2 J₁–J₂ Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment, Phys. Rev. B78(21), 214415 (2008)

[8] R. L. Doretto, Plaquette valence-bond solid in the squarelattice J₁–J₂ antiferromagnet Heisenberg model: A bond operator approach, Phys. Rev. B89(10), 104415 (2014)

[9] T. Roscilde, A. Feiguin, A. L. Chernyshev, S. Liu, and S. Haas, Anisotropy-induced ordering in the quantum J₁–J₂ antiferromagnet, Phys. Rev. Lett.93(1), 017203 (2004)

[10] J. F. Yu and Y. J. Kao, Spin-1/2 J₁–J₂ Heisenberg antiferromagnet on a square lattice: A plaquette renormalized tensor network study, Phys. Rev. B85(9), 094407 (2012)

[11] R. F. Bishop, P. H. Y. Li, D. J. J. Farnell, and C. E. Campbell, Magnetic order in a spin-1/2 interpolating square-triangle Heisenberg antiferromagnet, Phys. Rev. B79(17), 174405 (2009)

[12] R. F. Bishop, P. H. Y. Li, R. Darradi, J. Schulenburg, and J. Richter, Effect of anisotropy on the ground-state magnetic ordering of the spin-half quantum J1XXZ−J2XXZ model on the square lattice, Phys. Rev. B78(5), 054412 (2008)

[13] L. Wang, Z. C. Gu, F. Verstraete, and X. G. Wen, Tensorproduct state approach to spin-12 square J₁–J₂ antiferromagnetic Heisenberg model: Evidence for deconfined quantum criticality, Phys. Rev. B94(7), 075143 (2016)

[14] N. D. Mermin and H. Wagner, Absence of ferromagnetism or antiferro-magnetism in one- or two-dimensional isotropic Heisenberg models, Phys. Rev. Lett.17(22), 1133 (1966)

[15] A. A. Nersesyan and A. M. Tsvelik, Spinons in more than one dimension: Resonance valence bond state stabilized by frustration, Phys. Rev. B67(2), 024422 (2003)

[16] K. Majumdar, Second-order quantum corrections for the frustrated spatially anisotropic spin-1/2 Heisenberg antiferromagnet on a square lattice, Phys. Rev. B82(14), 144407 (2010)

[17] K. Majumdar, Magnetic phase diagram of a spatially anisotropic, frustrated spin-1/2 Heisenberg antiferromagnet on a stacked square lattice, J. Phys.: Condens. Matter23(4), 046001 (2011)

[18] A. A. Tsirlin and H. Rosner, Extension of the spin-1/2 frustrated square lattice model: The case of layered vanadium phosphates, Phys. Rev. B79(21), 214417 (2009)

[19] O. Volkova, I. Morozov, V. Shutov, E. Lapsheva, P. Sindzingre, O. Cépas, M. Yehia, V. Kataev, R. Klingeler, B. Büchner, and A. Vasiliev, Realization of the Nersesyan–Tsvelik model in (NO)(Cu(NO₃)₃), Phys. Rev. B82(5), 054413 (2010)

[20] O. Janson, A. A. Tsirlin, and H. Rosner, Antiferromagnetic spin-1/2 chains in (NO)Cu(NO₃)₃: A microscopic study, Phys. Rev. B82(18), 184410 (2010)

[21] H. Y. Wang, Green’s Function in Condensed Matter Physics, Alpha Science International Ltd. and Science Press, 2012

[22] P. Fröbrich and P. J. Kuntz, Many-body Green’s function theory of Heisenberg films, Phys. Rep.432(5–6), 223 (2006)

[23] A. Y. Hu and Q. Wang, The magnetic properties of three-dimensional spin-1 easy-axis single-ion anisotropic antiferromagnets, Solid State Commun.150(13–14), 568 (2010)

[24] A. Y. Hu and H. Y. Wang, The exchange interaction values of perovskite-type materials EuTiO3 and EuZrO₃, J. Appl. Phys.116(19), 193903 (2014)

[25] H. Y. Wang, L. J. Zhai, and M. Qian, The internal energies of Heisenberg magnetic systems, J. Magn. Magn. Mater.354(3), 309 (2014)

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