Magnetotransport in nearly antiferromagnetic metals

Abstract

We present a theory of the magnetotransport in weakly disordered metals close to an antiferromagnetic quantum-critical point. The anisotropic scattering from critical spin fluctuations is strongly influenced by weak but isotropic scattering from small amounts of disorder. This leads to a large regime where the resistivity obeys a scaling form $\rho ={\rho }_0+\Delta \rho \approx {\rho }_0{+T}^{3/2}f[T/{\rho }_0,(p-p_c)/{\rho }_0,B/{\rho }_0^{3/2}],$ where ${\rho }_0$ is the residual resistivity, B the magnetic field, and $p-p_c>0\mathrm{}$ measures the distance from the quantum-critical point on the paramagnetic side of the phase diagram. Orbital effects of the magnetic field are most pronounced in very clean samples for not too low temperatures, where the resistivity for increasing magnetic field crosses over from a linear temperature dependence $\Delta \rho \sim T\sqrt{{\rho }_0}$ to a resistivity linear in B and independent of T and ${\rho }_0.$ At higher magnetic fields, $\Delta \rho$ saturates at a value proportional to $T^{1.5}$ or $T^2/\left(p-p_c\right).\mathrm{}$ Deviations from scaling, the interplay of orbital and spin contributions of the magnetic field, and experimental test of the spin-fluctuation model are discussed in detail.