Effect of impurities and temperature on singularities of the magnetic susceptibility of metals

Impurity- and temperature-induced broadening of the magnetic susceptibility singularities at extreme points of the energy spectrum is considered. Assuming that the electron damping Γ in the vicinity of the extreme points is independent of the electron momentum, an equation is obtained expressing the thermodynamic potential Ω of a system with impurities in terms of Ω0, the thermodynamic potential of the pure metal. This equation makes it possible to derive expressions describing the impurity broadening of singularities of any electronic properties of the system. The example of the two-band model is used to show that the expansion of the susceptibility in powers of T and Γ at critical points starts with terms proportional to T1/2 and T1/2, respectively. A numerical calculation of the impurity broadening of the orbital susceptibility anomalies at critical points in the given model also indicates that for small Γ(Γ ≪ Δ, where 2Δ is the energy gap) this broadening can be described by introducing an effective temperature.