MAGNETIC-STRUCTURE AND PARAMAGNETIC DYNAMICS OF CHROMIUM AND ITS ALLOYS

Using mean-field theory, we study the dynamics of chromium and its alloys above the Neel temperature T(N). Starting with a three-band model of chromium, we recover the two-band model originally developed by Sato and Maki (SM). From the poles of the transverse spin susceptibility, we calculate the wave vector and Neel temperature of the spin-density-wave (SDW) state. Like SM, we find that the SDW is commensurate with the lattice when the energy mismatch z0 between the electron and hole Fermi surfaces is smaller than the critical value z0* almost-equal-to 365 meV, which may be achieved with the addition of a small fraction of manganese impurities, as observed experimentally. In the incommensurate state above z0*, the susceptibility contains two peaks on either side of the wave vector G/2=2=2pi/a for small frequency and close to T(N). In the commensurate state below z0*, the susceptibility contains only a single peak at G/2. Because z0* decreases with the damping energy GAMMA, this central peak may split into sidepeaks with the addition of isoelectric impurities such as molybdenum or tungsten. As GAMMA increases, z0* reaches a minimum value of about 185 meV. When z0 is below this minimum value, the SDW is always commensurate for any value of the damping. If GAMMA exceeds the critical damping GAMMA(cr), then the Neel temperature vanishes but the susceptibility still contains peaks near the wave vectors of the SDW with GAMMA=0. In agreement with experiments by Fawcett et al., we find that the elastic-scattering cross section for paramagnetic chromium alloys vanishes at T=0. We also predict that the elastic-scattering cross section reaches a maximum at a temperature which increases with GAMMA.