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

TL;DR

This paper provides an exact solution for the ground state phase diagram of frustrated classical Heisenberg and XY models with nearest-neighbor exchange in 2D, revealing diverse magnetic states relevant to manganites.

Contribution

It offers the first exact determination of the ground state phase diagram for these frustrated models, including novel states and their relevance to experimental materials.

Findings

Identified multiple magnetic ground states including ferromagnetic, spiral, uudd, and vortex lattices.

Connected the uudd state to the E-type state observed in manganites.

Showed the model likely contains the mechanism behind the uudd state.

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.