Phase Diagram and Magnetic Dynamics in Er$_{1-x}$Y$_{x}$MnO$_{3}$

We have grown single-crystal samples of the hexagonal multiferroic Er$_{1-x}$Y$_{x}$MnO$_{3}$ at different compositions. YMnO$_{3}$ orders in a P6'$_{3}$cm' phase, while ErMnO$_{3}$ orders in a P6'$_{3}$c'm phase. The boundary between these phases is of interest because of the strong coupling between ferroelectricity and magnetism observed at the spin reorientation transition between these phases in HoMnO$_{3}$. We find that Er$_{1-x}$Y$_{x}$MnO$_{3}$ transitions completely from the P6'$_{3}$cm' to the P6'$_{3}$c'm phase over a very narrow composition range on the Y-rich side of the phase diagram. We have also performed inelastic neutron scattering measurements on these samples, and find quasielastic scattering similar to that found in YMnO$_{3}$. However, as for Ho$_{1-x}$Y$_{x}$MnO$_{3}$, this scattering exhibits out-of-plane correlations and is centered at locations other than the fundamental magnetic Bragg peak.