Magnetoresistance in canonical spin-glasses

The transverse magnetoresistance (TMR) $\frac{\Delta \rho }{\rho }$ has been measured in $\mathrm{Au}\mathrm{Fe}$, $\mathrm{Au}\mathrm{Mn}$, $\mathrm{Cu}\mathrm{Mn}$, and $\mathrm{Ag}\mathrm{Mn}$ spin-glasses in the temperature range 1.5 to 77 K and magnetic fields up to 18 kG. All the alloys exhibit a negative TMR at all temperatures and fields and changes with field $H$ as $H^n$, where $n\simeq 2$ at low fields and $1<n<\mathrm{}2\mathrm{}$ at higher fields. Below the spin-glass freezing temperature $T_0$ and at higher fields, the TMR is nearly independent of temperature. This behavior is very similar to that of the Hall resistivity. At low fields it varies smoothly around $T_0$ without showing any anomaly. However, below $T_0$ the TMR shows a somewhat stronger temperature dependence in a few alloys. Above $T_0$, $\left|\frac{\Delta \rho }{\rho }\right|$ decreases with temperature and becomes undetectable beyond $T_m$, the temperature of the resistance maximum of the alloy. Also, $\left|\frac{\Delta \rho }{\rho }\right|$ increases with the impurity concentration $c$ in $\mathrm{Au}\mathrm{Fe}$ while decreasing with it in $\mathrm{Au}\mathrm{Mn}$, $\mathrm{Cu}\mathrm{Mn}$, and $\mathrm{Ag}\mathrm{Mn}$. However, $\left|\Delta \rho \right|$ increases monotonically with $c$ in all the systems. A recent theory of magnetoresistance, based on an Edwards-Anderson-type model for a spin-glass, explains most of the above characteristic features. This theory has been applied to compute the values of the $s-d$ exchange parameter "$J$." They are in reasonable agreement with those found by earlier authors. Effects of field cooling, remanence, aging, and annealing on the TMR are discussed. A fresh annealing and quenching of $\mathrm{Au}\mathrm{Fe}$ alloys significantly reduces $\left|\frac{\Delta \rho }{\rho }\right|$.