On the theory of high-frequency properties of a ferromagnetoelectric with an “unfrozen” orbital moment

Elementary excitations of an axial ferromagnetoelectric with a weakly “unfrozen” orbital magnetic moment are considered. The magnetic subsystem is described by two moments, viz., the spin and orbital magnetic moment of an ion, which are coupled through a weak spin-orbit interaction. The spectrum of magnetic and ferroelectric excitations is determined in magnetic fields parallel and perpendicular to the easy axis. It is shown that different dependences of the spin and orbital magnetic moments on the magnetic field perpendicular to spontaneous magnetization lead to crossover of the spin and orbital branches and to a gap in the ferromagnetic resonance spectrum. The contribution of orbital excitations to the total magnetic moment is calculated; this contribution has a temperature dependence differing from that for contribution of spin waves. The obtained results are also applicable to a system with two groups of magnetic ions with magnetic moments of the first group of purely spin origin and of the second group of spin and orbital origin. In this case, the weak interaction between the magnetic moments of these groups is of the exchange type and not of the spin-orbit type.

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