Temperature Dependence of the Spin Resistivity in Ferromagnetic Thin Films

TL;DR

This paper investigates how temperature affects spin resistivity in ferromagnetic thin films through Monte Carlo simulations and a Boltzmann equation-based theory, analyzing effects of film properties and magnetic domains near phase transition.

Contribution

It combines extensive Monte Carlo simulations with a Boltzmann equation approach to explain the temperature dependence of spin resistivity in ferromagnetic films, including effects of impurities and surface interactions.

Findings

Resistivity peaks near the magnetic phase transition due to magnetic domains.

Film thickness and impurities significantly influence resistivity behavior.

Theoretical results agree well with Monte Carlo simulations and experimental discussions.

Abstract

The magnetic phase transition is experimentally known to give rise to an anomalous temperature-dependence of the electron resistivity in ferromagnetic crystals. Phenomenological theories based on the interaction between itinerant electron spins and lattice spins have been suggested to explain these observations. In this paper, we show by extensive Monte Carlo (MC) simulation the behavior of the resistivity of the spin current calculated as a function of temperature ($T$) from low-$T$ ordered phase to high-$T$ paramagnetic phase in a ferromagnetic film. We analyze in particular effects of film thickness, surface interactions and different kinds of impurities on the spin resistivity across the critical region. The origin of the resistivity peak near the phase transition is shown to stem from the existence of magnetic domains in the critical region. We also formulate in this paper a theory based on the Boltzmann's equation in the relaxation-time approximation. This equation can be solved using numerical data obtained by our simulations. We show that our theory is in a good agreement with our MC results. Comparison with experiments is discussed.