Probing multiferroicity and spin-spin interactions via dielectric measurements on Y-doped HoMnO$_{3}$ in high magnetic fields

The magnetic field dependent phase diagram of the ferroelectric material ${\rm Ho}_{1-x}Y_{x}MnO_{3}$ has been investigated for x = 0, 0.6, and 0.8 for fields directed along both the ab in-plane and c-axis basal plane directions. Dielectric measurements are used to map out the re-entrant temperature-magnetic field phase transitions which involve in-plane Mn spin rotations in the antiferromagnetic state below the N$\acute{e}$el temperature. We show through the alloy study that the Ho sublattice plays a major role in all transitions, and that the phase diagram for $Ho_{1-x}Y_{x}MnO_{3}$ is dependent on magnetic field direction. We describe this behavior in terms of the interaction of the Ho sublattice spin system with the underlying, robust $YMnO_{3}$ antiferromagnetic triangular lattice, where the Ho-Y spin interactions are highly sensitive to concentration and field direction.