The J_{1}-J_{2} Model on the Anisotropic Triangular and the Square Lattice: Similarities and Differences |

B. Schmidt and P. Thalmeier
Max-Planck-Institut für Chemische Physik fester Stoffe, 01187 Dresden, Germany |

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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 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 ϕ = 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. |

DOI: 10.12693/APhysPolA.127.324 PACS numbers: 75.10.Jm, 75.30.Cr, 75.30.Ds |