Temperature dependence of the normal and inverse magnetoresistance in magnetic multilayers

The temperature dependence of the giant magnetoresistance (GMR) in ${\mathit{M}}_1$/N/${\mathit{M}}_2$ multilayers consisting of magnetic ${\mathit{M}}_{\mathit{i}}$ (i=1,2) and nonmagnetic N layers, is discussed with the use of the finite-temperature band theory in which the effect of spin fluctuations is taken into account by means of the static functional-integral method combined with the coherent potential approximation. It is shown that the temperature dependence of the MR ratio, ΔR/R, shows a variety of behaviors depending on the values of ${\mathit{a}}_1$ and ${\mathit{a}}_2$ where ${\mathit{a}}_{\mathit{i}}$=${\mathrm{\Delta }}_{\mathit{i}\mathrm{\uparrow }}$/${\mathrm{\Delta }}_{\mathit{i}\mathrm{\downarrow }}$ and ${\mathrm{\Delta }}_{\mathit{i}\mathit{s}}$ is the imaginary part of the coherent potential of an s-spin electron at the interface of the ${\mathit{M}}_{\mathit{i}}$ layer. In the normal MR where ${\mathit{a}}_1$>1 and ${\mathit{a}}_2$>1 (or ${\mathit{a}}_1$${\mathit{a}}_2$R/R decreases as the temperature is raised. On the contrary, in the inverse MR where ${\mathit{a}}_1$>1,${\mathit{a}}_2$R/RR/R may show a maximum or almost constant behavior in a fairly wide temperature range.