Magnetic irreversibilities and nonreciprocity of the microwave absorption of FeCr$_2$O$_4$ spinel

A FeCr$_2$O$_4$ single crystal with the spinel structure is grown by the zone melting method with optical heating. The critical temperatures of establishing the orbital ordering $T_{OO} = 138$ K, the formation of the collinear ferrimagnetic state $T_N = 65$ K, and the formation of the spiral modulation of the magnetic structure $T_s = 38$ K are determined from the temperature dependences of the heat capacity and magnetic susceptibility. An anomaly of the susceptibility at $T \sim 21$ K, below which the hysteresis curves become butterfly-like is probably caused by a change in the magnetic anisotropy. It is established that the magnetic resonance spectrum in the microwave X-band ($\sim9.4$ GHz) at $T = 30$ K changes under the reversal of the direction of the external magnetic field (nonreciprocity phenomenon). Magnetic and induced electric dipole transitions are considered theoretically. The detected nonreciprocity is explained by the interference of these transitions.