Theory of giant magnetoresistance caused by magnetic-ion pairs embedded in paramagnetic metals

Abstract

To clarify a mechanism of a giant magnetoresistance (MR), we study the resistivity of a paramagnetic metal in which a magnetic-ion pair is embedded as impurities. In this pair, magnetic ions at the positions ${\mathbf{r}}_{1}$ and ${\mathbf{r}}_{2}$, respectively, are assumed to have localized spins ${\mathbf{S}}_{1}$ and ${\mathbf{S}}_{2}$, which are called $d$ spins. Conducting electrons, on the other hand, are assumed to have a light mass, being called $s$ electrons. The $s$ electrons are scattered by both the $d$ spins through the $s\ensuremath{-}d$ exchange interaction. Since interferences occur in the wave functions of electrons scattered by both the $d$ spins, transition probabilities between different electronic states are shown to depend strongly on $\mathbf{R}={\mathbf{r}}_{2}\ensuremath{-}{\mathbf{r}}_{1}$ and the spin configuration in the pair $({\mathbf{S}}_{1}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathbf{S}}_{2})$. The steady state of the $s$ electron system under an external electric field is obtained on the basis of the Boltzmann equation and the relaxation-time approximation. By using the obtained relaxation times, the resistivity of the metal is calculated to find its $\mathbf{R}$ and $({\mathbf{S}}_{1}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathbf{S}}_{2})$ dependencies. MRs are shown to appear when an antiparallel spin configuration realized by the Ruderman-Kittel-Kasuya-Yoshida interaction is changed to be a parallel one by a magnetic field. The maximum MR ratio ${[({\ensuremath{\rho}}_{\mathrm{ap}}\ensuremath{-}{\ensuremath{\rho}}_{\mathrm{p}})/{\ensuremath{\rho}}_{\mathrm{p}}]}_{\mathrm{MR}}$ is found to give a giant MR (GMR) of the order of ${10}^{2}\phantom{\rule{4pt}{0ex}}%, {\ensuremath{\rho}}_{\mathrm{ap}}$ and ${\ensuremath{\rho}}_{\mathrm{p}}$ being the resistivities in the metals with the antiparallel and parallel spin pairs, respectively. These results are extensively applied to the GMR in the metallic magnetic multilayers by taking into account possible magnetic-ion pairs in their nonmagnetic layers. This application shows that Mott's two-fluid model can exhibit a GMR of magnetic multilayers also in the case of the current in planes (CIP).