Magnetic Coupling in the multiferroic hexagonal ErMnO$_{3}$*

Hexagonal ErMnO$_{3}$ is one of the rare earth manganites RMnO$_{3}$ and has attracted renewed interest due to its multiferroic properties. Understanding the coupling between spin, charge, and lattice degrees of freedom is crucial to explore and design strong magnetic-ferroelectric coupled materials. We measured the crystal and magnetic structures of ErMnO$_{3}$ at selected temperatures and magnetic fields by single crystal neutron diffraction. Combined with planned inelastic neutron scattering measurements, the magnetic-magnetic and magnetic-lattice interactions will be discussed.