Self-consistent Gaussian approximation study of classical J1-J2 Heisenberg model in honeycomb and diamond lattices

Rahimipour, N; Shahbazi, F

doi:10.18869/acadpub.ijpr.15.1.81

Self-consistent Gaussian approximation study of classical J1-J2 Heisenberg model in honeycomb and diamond lattices

Authors

N Rahimipour

F Shahbazi

https://doi.org/10.18869/acadpub.ijpr.15.1.81

Abstract

The classical J1-J2 Heisenberg model on bipartite lattice exhibits "Neel" order. However if the AF interactions between the next nearest neighbor(nnn) are increased with respect to the nearest neighbor(nn), the frustration effect arises. In such situations, new phases such as ordered phases with coplanar or spiral ordering and disordered phases such as spin liquids can arise. In this paper we use the self-consistent Gaussian approximation to study the J1-J2 Heisenberg model in honeycomb and diamond lattices. We find the spin liquid phases such as ring-liquid and pancake-liquid in honeycomb lattice.Also for diamond lattice we show that the degeneracy of ground state can be lifted by thermal fluctuations through the order by disorder mechanism.

Keywords

Heisenberg model

frustration

spiral ordering

spin liquid

1. J T Chalker, “Introduction to Frustrated Magnetism”, edited by C Lacroix, p. Mendels and F Mila, Springer (2010).
2. P H Conlon, “Aspects of Frustrated Magnetism”, PhD Thesis, University of Oxford (2010).
3. S Okumura, H Kawamura, T Okubo, and Y Motomo, , J. Phys. Soc. Jpn. 79 (2010) 114705.
4. A Mulder, R Ganesh, L Capriotti, and A Paramekanti, Phys. Rev. B 81 (2010) 214419.
5. F Mezzacapo and M Boninsegni, Phys. Rev. B 85 (2012) 060402.
6. H Mosadeq, F shahbazi, and S A Jafari, J. Phys. Condens Matter 23 (2011) 226006.
7. J Bernier, M J Lawler, and Yong Beak Kim, Phys. Rev. Lett. 101, (2008) 047201.
8. D Bergman, J Alicea, E Gull, S Trebest, and L Balents, Nature Physics 3 (2007) 487.
9. T Suzuky et al., J. Phys. Condens. Matter 19 (2007) 145265.
10. J Villain, R Bidaux, J P Carton, and R Conte, J. de Phys. 41(1980) 1263.
11. E Rastelli and A Tassi, Journal of Physics C, Solid State Physics 20 (1987) L303.
12. C L Henley, Phys. Rev. Lett. 62 (1989) 2056.
13. J S Smart, “Effectiv Field Theories of Magnetism”, W B Saunders Company, Philadelphia, Pennsylvania, (1966).