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Novel phases in a square-lattice frustrated ferromagnet : 1/3-magnetisation plateau, helicoidal spin-liquid and vortex crystal

A large part of the interest in magnets with frustrated antiferromagnetic interactions comes from the many new phases found in applied magnetic field. In this Article, we explore some of the new phases which arise in a model with frustrated ferromagnetic interactions, the $J_1-J_2-J_3$ Heisenberg model on a square lattice. Using a combination of classical Monte-Carlo simulation and spin-wave theory, we uncover behaviour reminiscent of some widely-studied frustrated antiferromagnets, but with a number of new twists. We first demonstrate that, for a suitable choice of parameters, the phase diagram as a function of magnetic field and temperature is nearly identical to that of the Heisenberg antiferromagnet on a triangular lattice, including the celebrated 1/3-magnetisation plateau. We then examine how this phase diagram changes when the model is tuned to a point where the classical ground--state is highly degenerate. In this case, two new phases emerge; a classical, finite-temperature spin-liquid, characterised by a "ring" in the spin structure--factor $\mathcal{S}({\mathbf q})$; and a vortex crystal, a multiple-Q state with finite magnetisation, which can be viewed as an ordered lattice of magnetic vortices. All of these new phases persist for a wide range of magnetic field. We discuss the relationship between these results and published studies of frustrated antiferromagnets, together with some of the materials where these new phases might be observed in experiment.