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.