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

Dielectric measurements are used to characterize magnetic phase transitions in the doped ferrielectric oxides \textit{Ho}$_{1-x}Y_{x}$\textit{MnO}$_{3}$ ($x$ = 0, 0.4, 0.5, 0.6, 0.7, 0.8, 1). The \textit{T-B-$\theta $} phase diagram of the ferrielectric material \textit{Ho}$_{1-x}Y_{x}$\textit{MnO}$_{3}$ has been determined from the dielectric constant angular dependence between the crystallographic $c$-axis and applied magnetic field. The re-entrant temperature-magnetic field phase transitions which involve in- plane \textit{Mn} spin rotations in the antiferromagnetic state below the N\'{e}el temperature are driven by the interaction with the \textit{Ho} subsystem. We describe this behavior in terms of the interaction of the \textit{Ho} sublattice spin system with the underlying, robust \textit{YMnO}$_{3}$ antiferromagnetic triangular lattice, where the \textit{Ho}-spin interactions are highly sensitive to $Y$ concentration and field direction. The magnetic field anisotropy study is an important step towards understanding of magnetic and electric phase competition in the diluted $4f$ system by non-magnetic Yttrium($Y)$.