Spin-fluctuation contribution to the high-frequency electrical conductivity of nearly magnetic transition metals

The high-frequency limit of the electrical conductivity of nonmagnetic transition metals is calculated. The conduction electrons are assumed to be scattered by the spin fluctuations in the partially filled $d$ bands. The frequency-dependent conductivity has a Drude-type form, in which the scattering rate is itself frequency dependent. The scattering rate is increased as the magnetic susceptibility is enhanced by the spin fluctuations. The scattering rate exhibits a complicated frequency and temperature dependence. However, in the dc limit it does follow the low-temperature $T^2$ law of electron-electron collisions followed at higher temperatures by a linear dependence on $T$. On the other hand, at $T=0\mathrm{}$, the scattering rate is proportional to ${\omega }^2$ for low frequency.