Theory for the first-order spin-wave instability threshold in ferromagnetic insulating thin films

Abstract

A theory for the first-order Suhl and the parallel pumping instability in thin films is presented. Significant differences for the critical microwave field and wave vector to former calculations occur, which discuss the problem in terms of bulk spin-waves neglecting boundary conditions. A coupling matrixC _kk′ is introduced, which describes the couplings between the modes and the driving microwave field. For bulk standing spin-wavesC _kk′ is always diagonal. For the true discrete standing modes of a thin filmC _kk′ changes only in case of 1. Suhl instability and if the wavevector has a non vanishing component perpendicular to the film plane. Here the diagonal bulk couplings have to be replaced in part by off diagonal terms, describing couplings between modes, which perpendicular wave vector componentk _⊥ differs byπ/d (d=film thickness). The decisive quantity, which decides if the finite thickness of the film is of importance or if the film can be treated as a bulk system, is the frequency difference δω _k of the coupled modes. For δω _k much smaller than the spin-wave damping η _k the bulk approximation is correct. For$\delta \omega _k > > \eta _k$ two experimental situations for 1. Suhl instability are discussed: For a perpendicular to the film plane magnetized film the critical microwave field is by π/2 bigger than in the bulk case. In an in-plane magnetized film the critical spin-waves propagate always in the film plane, as only hereC _kk′ remains identical to the bulk case.