Non-Landau damping of magnetic excitations in systems with localized and itinerant electrons

We discuss the form of the damping of magnetic excitations in a metal near a ferromagnetic instability. The paramagnon theory predicts that the damping term should have the form $\Omega/\Gamma (q)$ with $\Gamma (q) \propto q$ (the Landau damping). However, the experiments on uranium metallic compounds UGe$_2$ and UCoGe showed that $\Gamma (q)$ tends to a constant value at vanishing $q$. A non-zero $\Gamma (0)$ is impossible in systems with one type of carriers (either localized or itinerant) because it would violate the spin conservation. It has been conjectured recently that a non-zero $\Gamma (q)$ in UGe$_2$ and UCoGe may be due to the presence of both localized and itinerant electrons in these materials, with ferromagnetism involving predominantly localized spins. We present microscopic analysis of the damping of near-critical localized excitations due to interaction with itinerant carriers. We show explicitly how the presence of two types of electrons breaks the cancellation between the contributions to $\Gamma (0)$ from self-energy and vertex correction insertions into the spin polarization bubble and discuss the special role of the Aslamazov-Larkin processes. We show that $\Gamma (0)$ increases with $T$ both in the paramagnetic and ferromagnetic regions, but in-between it has a peak at $T_c$. We compare our theory with the available experimental data.