Disordered substitutional magnets in a magnetic field

Disordered binary magnetic alloys in a magnetic field are investigated in the Heisenberg–Mattis model. The Green's function is calculated for arbitrary wave vectors and energies in the case of a weakly dilute ferromagnet. It is shown that the presence of the magnetic field leads in this case only to the appearance of a gap in the spectrum of the elementary excitations. The equation of motion for the generalized coordinates of the model is used to obtain the long-wavelength spectrum of the elementary excitations for arbitrary concentrations of one of the components. In the case of complete disorder, the magnetic field strongly changes the spectrum of the elementary excitations. It is shown that for ${\mathbf k}=0$ the energy spectrum is analogous to the spectrum of a ferromagnet.