Transport properties of spin-glasses. Effect of including Kondo-like terms

Abstract

Transport properties in spin-glasses have been studied for the $s\ensuremath{-}d$ model using the method of the double-time Green's function. The higher-order Green's functions have been decoupled to lower orders using Nagaoka's decoupling scheme. The self-energy has been obtained in a multiple-scattering approximation. A self-consistent expression for the $t$ matrix has been obtained using Hamann's approach, and the temperature ${T}_{m}$, at which the resistivity is maximum, has been calculated. An expression for the Lorenz number has been obtained, following the procedure of Nam and Fullenbaum. The relative contribution to the Lorenz number ($\frac{\ensuremath{\Delta}L}{{L}_{0}}$), where $L$ is the contribution to the Lorenz number due to the exchange interaction $J$, is lower in the spin-glass system as compared to the Kondo system. The thermoelectric power has been calculated using the perturbation expansion of the self-energy to order ${J}^{3}$. It is found to contain values ${V}_{0}{J}^{2}$ and ${V}_{0}{J}^{3}$, where the second term is very large and dominates over the first term at low temperature, and the sign of the thermoelectric power is therefore decided by the sign of ${V}_{0}$ and $J$. The thermoelectric power involves a term such as $Q+\ensuremath{\chi}$, where $Q$ is the spin-glass order parameter and $\ensuremath{\chi}$ is the spin-deviation correlation function. No abrupt change in the calculation of the thermoelectric power is found around ${T}_{f}$, which is supported by the experimental data. The thermoelectric power calculation agrees well with the experimental data at low temperatures but there is a systematic discrepancy between the two at high temperatures due to the neglect of the electron-phonon interaction in the present calculation.