Micromagnetic simulations of the size dependence of the Curie temperature in ferromagnetic nanowires and nanolayers

Abstract

We solve the Landau-Lifshitz-Gilbert equation in the finite-temperature regime, where thermal fluctuations are modeled by a random magnetic field whose variance is proportional to the temperature. By rescaling the temperature proportionally to the computational cell size Δx (T→TΔx/aeff, where aeff is the lattice constant) [M. B. Hahn, J. Phys. Comm., 3:075009, 2019], we obtain Curie temperatures TC that are in line with the experimental values for cobalt, iron and nickel. For finite-sized objects such as nanowires (1D) and nanolayers (2D), the Curie temperature varies with the smallest size d of the system. We show that the difference between the computed finite-size TC and the bulk TC follows a power-law of the type: (ξ0/d)λ, where ξ0 is the correlation length at zero temperature, and λ is a critical exponent. We obtain values of ξ0 in the nanometer range, also in accordance with other simulations and experiments. The computed critical exponent is close to λ=2 for all considered materials and geometries. This is the expected result for a mean-field approach, but slightly larger than the values observed experimentally.