Direct and inverse magnetoelectric effect in orthorhombic single crystals of Dy$_{1-x}$Ho$_x$MnO$_3$

In this work, the magnetoelectric response in a series of Dy$_{1-x}$Ho$_x$MnO$_3$ crystals with substitution $x$ from 0 to 0.4 was investigated. The measurement results showed that, as $x$ increases, a decrease in both the polarization $P_a$ and the magnitude of the susceptibility of the inverse magnetoelectric effect $\alpha_{ba}$ is observed. In addition, the field $H_b$ increases, at which the $P_c\to P_a$ transition is observed, and the temperature range of the existence of the magnetoelectric response decreases. Thus, an increase in the substitution x suppresses the magnetoelectric effect in this series of compounds. The measurement results also indirectly indicate the prolongation of the $P_a$ state and, consequently, of the magnetic state with a cycloid lying in the ab-plane by an external electric field $E_a$.