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arXiv · 1003.5622

Frustrated classical Heisenberg and XY models in 2 dimensions with nearest neighbor exchange: exact solution for the ground state phase diagram

L. X. Hayden·T. A. Kaplan·S. D. Mahanti
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Abstract

The ground state phase diagram is determined exactly for the frustrated classical Heisenberg model plus nearest-neighbor biquadratic exchange interactions on a 2-dimensional lattice. A square- and a rhombic-symmetry version are considered. There appear ferromagnetic, incommensurate-spiral, "up-up-down-down" (uudd) and canted ferromagnetic states, a non-spiral coplanar state that is an ordered vortex lattice, plus a non-coplanar ordered state (a "conical vortex lattice"). In the rhombic case, which adds biquadratic terms to the Heisenberg model used widely for insulating manganites, the uudd state found is the E-type state observed; this along with accounting essentially for the variety of ground states found in these materials, shows that this model probably contains the long-sought mechanism behind the uudd state.

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L. X. Hayden, T. A. Kaplan, S. D. Mahanti. 2010-04-08. Frustrated classical Heisenberg and XY models in 2 dimensions with nearest neighbor exchange: exact solution for the ground state phase diagram. https://doi.org/10.1103/physrevlett.105.047203

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