Large magneto-dielectric coupling in orthorhombic YMnO$_3$ and HoMnO$_3$

We have found a remarkable increase (up to 60 {\%}) of the dielectric constant with the onset of magnetic order at 42 K in the metastable orthorhombic structures of YMnO$_{3}$ and HoMnO$_{3}$ that proves the existence of a strong magneto-dielectric coupling in the compounds. Magnetic, dielectric, and thermodynamic properties show distinct anomalies at the onset of the incommensurate magnetic order and thermal hysteresis effects are observed around the lock-in transition temperature at which the incommensurate magnetic order locks into a temperature independent wave vector. The orders of Mn$^{3+}$ spins and Ho$^{3+}$ moments both contribute to the magneto-dielectric coupling. A large magneto-dielectric effect was observed in HoMnO$_{3}$ at low temperature where the dielectric constant can be tuned by an external magnetic field resulting in a decrease of up to 8 {\%} at 7 Tesla. By comparing data for YMnO$_{3}$ and HoMnO$_{3}$ the contributions to the coupling between the dielectric response and Mn and Ho magnetic orders is separated.