Spin-wave spectrum and magnetic phase diagram of hexagonal HoMnO$_{3}$

We present neutron scattering measurements of the magnetic order and spin-wave dynamics in single crystals of hexagonal HoMnO$_{3}$, an antiferromagnetic ferroelectric material. Ferroelectric ordering of Ho$^{3+}$ ions along the c axis occurs around 875K, and the triangular lattice of S=2 moments on Mn$^{3+}$ ions order in a 120$^{\circ}$ antiferromagnetic structure below 72K. Below 40K, these moments undergo a spin reorientation transition to another 120$^{\circ}$ structure, with significant coupling between the two order parameters observable at the transition. We have mapped out the spin-wave spectrum, and our results are well-described by a Heisenberg model on a triangular lattice with a nearest-neighbor exchange of 2.44 meV and a temperature-dependent anisotropy. Measurements of the spin structure in a magnetic field applied along the ferroelectric ordering direction reveal multiple spin-reorientation transitions along with significant hysteresis. Applied electric field results will also be discussed.