Temperature dependence of the normal and inverse magnetoresistance in magnetic multilayers

The temperature dependence of the giant magnetoresistance (GMR) in M₁/N/M₂ multilayers consisting of magnetic Mᵢ (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, {Δ}R/R, shows a variety of behaviors depending on the values of a₁ and a₂ where aᵢ=Δ_i↑/Δ_i↓ and Δᵢₛ is the imaginary part of the coherent potential of an s-spin electron at the interface of the Mᵢ layer. In the normal MR where a₁>1 and a₂>1 (or a₁1 and a₂1), {Δ}R/R decreases as the temperature is raised. On the contrary, in the inverse MR where a₁>1,a₂1 (or vice versa) and {Δ}R/R0, it increases although its absolute magnitude decreases. In a multilayer where normal and inverse MR's coexist, {Δ}R/R may show a maximum or almost constant behavior in a fairly wide temperature range.