Micromagnetic simulations of the size dependence of the Curie temperature in ferromagnetic nanowires and nanolayers - Courtès, Clémentine; Boileau, Matthieu; Côte, Raphaël; Paul-Antoine Hervieux; Manfredi, Giovanni (arXiv.org, 2024)
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 \(Δ x\) (\(T → T\,Δ x/a_{\text{eff}}\), where \(a_{\text{eff}}\) is the lattice constant) [M. B. Hahn, J. Phys. Comm., 3:075009, 2019], we obtain Curie temperatures \(T_{\text{C}}\) 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 \(T_{\text{C}}\) and the bulk \(T_{\text{C}}\) follows a power-law of the type: \((ξ_0/d)^λ\), where \(ξ_0\) is the correlation length at zero temperature, and \(λ\) is a critical exponent. We obtain values of \(ξ_0\) 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.