The J1-J2 Model on the Anisotropic Triangular and the Square Lattice: 
Similarities and Differences

Schmidt, B.; Thalmeier, P.

doi:10.12693/APhysPolA.127.324

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The J₁-J₂ Model on the Anisotropic Triangular and the Square Lattice: Similarities and Differences

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Schmidt, B.
Burkhard Schmidt, Physics of Quantum Materials, Max Planck Institute for Chemical Physics of Solids, Max Planck Society;

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Thalmeier, P.
Peter Thalmeier, Physics of Correlated Matter, Max Planck Institute for Chemical Physics of Solids, Max Planck Society;

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Citation

Schmidt, B., & Thalmeier, P. (2015). The J₁-J₂ Model on the Anisotropic Triangular and the Square Lattice: Similarities and Differences. Acta Physica Polonica A, 127(2), 324-326. doi:10.12693/APhysPolA.127.324.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0026-CA08-E

Abstract

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 J(1)-J(2) 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 phi - tan(-1)(J(2)/J(1)). 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.