Observation of magnetic-field-induced electric polarization in terbium orthoferrite

In TbFeO$_3$ orthoferrite at temperatures below the antiferromagnetic ordering temperature for the terbium subsystem ($\sim$ 3.2 K), the electric polarization $P_a(H_b)$ induced by a magnetic field $H_b$ along the a axis is found. Such polarization is accompanied by anomalies related to metamagnetic (for Tb) and spin-reorientation (for Fe) transitions. At low magnetic fields $|H| < H_{\text{cr1}}\sim5\,$ kOe, the $P_a(H_b)$ dependence exhibits a strong hysteresis and has a “butterfly” shape, while in intermediate-field magnetic configurations, $|H_{\text{cr1}}| < |H| < |H_{\text{cr2}}|\sim18\,$ kOe, the sign of the polarization is determined by the sign of an applied electric field, and the $P_a(H_b)$ dependence turns out to be nonmonotonic. A qualitative explanation of the observed effects is given in the framework of a symmetry analysis of the allowed magnetoelectric interactions in the field-induced magnetic structures.