Quantum statistical theory of giant magnetoresistance in magnetic heterogeneous alloys

We present a quantum-statistical theory of giant magnetoresistance in magnetic heterogeneous alloys, consisting of small particles of ferromagnetic metal embedded in a nonmagnetic conducting matrix. The paper focuses on the spin-dependent size-effect on the conductivity of the system, i.e. the influence of the relative orientation of the magnetization in neighboring particles on their conductivity as a function of the size and distance between the particles. It is shown that the conductivity of heterogeneous alloys is not self-averaging when the particle sizes and/or distances are comparable to the mean-free paths. As for current in-plane giant magnetoresistance, the electron mean-free paths are the relevant length scale parameters. When the size-effects due to the bulk and interfacial spin-dependent electron scattering are taken into account, the giant magnetoresistance amplitude exhibits a maximum as a function of the average radius of the particles. The optimum radius value is determined by a balance between the interfacial and bulk scattering.