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 Néel temperature ${\mathit{T}}_{\mathit{N}}$. 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 Néel temperature of the spin-density-wave (SDW) state. Like SM, we find that the SDW is commensurate with the lattice when the energy mismatch ${\mathit{z}}_0$ between the electron and hole Fermi surfaces is smaller than the critical value ${\mathit{z}}_0^{\mathrm{*}}$≊365 meV, which may be achieved with the addition of a small fraction of manganese impurities, as observed experimentally. In the incommensurate state above ${\mathit{z}}_0^{\mathrm{*}}$, the susceptibility contains two peaks on either side of the wave vector G/2=2π/a for small frequency and close to ${\mathit{T}}_{\mathit{N}}$. In the commensurate state below ${\mathit{z}}_0^{\mathrm{*}}$, the susceptibility contains only a single peak at G/2. Because ${\mathit{z}}_0^{\mathrm{*}}$ decreases with the damping energy Γ, this central peak may split into sidepeaks with the addition of isoelectric impurities such as molybdenum or tungsten. As Γ increases, ${\mathit{z}}_0^{\mathrm{*}}$ reaches a minimum value of about 185 meV. When ${\mathit{z}}_0$ is below this minimum value, the SDW is always commensurate for any value of the damping. If Γ exceeds the critical damping ${\mathrm{\Gamma }}_{\mathrm{cr}}$, then the Néel temperature vanishes but the susceptibility still contains peaks near the wave vectors of the SDW with Γ=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 Γ.