Combinatorial parametric excitation of spin waves under conditions of a combined resonance

The combinatorial parametric resonance in the case of transverse microwave pumping in the presence of a longitudinal rf field is studied theoretically. In the absence of a combined resonance the instability threshold is the same as that in the case of longitudinal pumping studied previously experimentally and theoretically. Under the conditions of a combined resonance, however, the threshold is described by a substantially different formula. This determines the characteristic features of the dependences of the threshold of parametric instability of the magnon system on the external parameters.