Interaction Correction of Conductivity Near a Ferromagnetic Quantum Critical Point

Abstract

We calculate the temperature dependence of conductivity due to interaction correction for a disordered itinerant electron system close to a ferromagnetic quantum critical point which occurs due to a spin density wave instability. In the quantum critical regime, the crossover between diffusive and ballistic transport occurs at a temperature $T^{\ast}=1/[τγ(E_{F}τ)^{2}]$, where $γ$ is the parameter associated with the Landau damping of the spin fluctuations, $τ$ is the impurity scattering time, and $E_{F}$ is the Fermi energy. For a generic choice of parameters, $T^{\ast}$ is few orders of magnitude smaller than the usual crossover scale $1/τ$. In the ballistic quantum critical regime, the conductivity has a $T^{(d-1)/3}$ temperature dependence, where $d$ is the dimensionality of the system. In the diffusive quantum critical regime we get $T^{1/4}$ dependence in three dimensions, and $\ln^2 T$ dependence in two dimensions. Away from the quantum critical regime we recover the standard results for a good metal.