Crystal field and origin of exchange bias in compensated rare-earth ferrimagnets

•The unidirectional anisotropy is induced by an applied magnetic field the direction of which is collinear to quantization axis.•An applied magnetic field causes a slight canting of the metal magnetic moments, disrupting the balance of energies of exchange interactions.•The effect of spins reversal on temperature dependences of the total magnetization during crossing the compensation point for different applied fields has been investigated. Mechanism of exchange bias (EB) and spin reversal (SR) in the vicinity of compensation point, Tcomp, was considered in a framework of quantum–mechanical mean field theory. Specific differences between EB and SR phenomena in compensated ferrimagnets, associated with an impact of the crystal field, have been considered, and characteristic single crystals of GdCrO3 and ErFeO3 were studied. It was shown that an applied magnetic field induces an additional weak canting of the transition metal M3+ magnetic moments in the vicinity of Tcomp, disturbing the energy balance between isotropic and anisotropic exchange interactions in the system of transition metal and rare-earth ions. This is a source of unidirectional anisotropy associated with the orientation of uncompensated ferromagnetic moment of transition metal ion with respect to the direction of magnetic field. It was demonstrated that a thermodynamic behavior of ErFeO3 in the vicinity of Tcomp, can be described using the concept of effective spin. The parameters of microscopic interactions were determined and the temperature dependences of the canting angles, effective exchange fields, temperatures of spin flips, coercivity fields, and exchange bias fields were calculated, for both GdCrO3 and ErFeO3.