Spin dynamics of chromium .1. Formalism and commensurate alloys

The spin dynamics of chromium alloys are produced by the fluctuations about a spin-density wave (SDW) consisting of bound electron-hole pairs. While commensurate (C) alloys have a single SDW with wave vector G/2=2 pi/a, incommensurate (I) alloys have two SDW's with wave vectors on either side of G/2. Spin fluctuations with frequency omega and wave vector q correspond to possible quasiparticle transitions between the two (C) or three (I) bands of hybridized electron and hole energies with energy change omega and momentum change q. This paper develops the random-phase approximation for the spin dynamics of both C and I alloys. The collective excitations of C alloys consist of a transverse spin-wave (SW) mode with linear dispersion and a longitudinal amplitude mode. Incoherent spin fluctuations lie above the amplitude mode frequency and below the SW frequency. While the SW mode involves the rigid rotation of the local magnetic moments, the amplitude mode involves the oscillation of the SDW amplitude, which decays in time according to a power law.