Ferronematic order in a spin-1 Heisenberg antiferromagnet

We study the field-induced ground-state phase transition of a spin-1 Heisenberg antiferromagnet with large easy-axis single-ion anisotropy $D$. Direct spin-wave treatment predicts a single first-order phase transition from an antiferromagnetic N\'{e}el phase at low magnetic fields to a fully polarized state at high magnetic fields. Mean field arguments, based on an effective spin-1/2 model that is exact in the $D\rightarrow\infty$ limit, show that this transition is preempted by an intermediate phase with double-spin-flip correlations. We call this phase the {\em ferronematic} phase, as the effective spin model for large (negative) $D$ is a spin-1/2 XXZ model with {\em ferromagnetic} transverse exchange. Using exact diagonalization and quantum Monte Carlo, we confirm the presence of the ferronematic phase. Long range order is observed in the equal-time Green's function $\langle S_{i}^{+}S_{i}^{+}S_{j}^{-}S_{j}^{-}+H.c.\rangle$, which is the correlation function for ferronematic order. We also show the rapid convergence to the effective model for large values of $D$.