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

• Published in: arXiv.org
• Main Authors: Courtès, Clémentine, Boileau, Matthieu, Côte, Raphaël, Paul-Antoine Hervieux, Manfredi, Giovanni
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 25.04.2024
• Subjects: Computation; Computer Science - Numerical Analysis; Curie temperature; Electrons; Ferromagnetism; Lattice parameters; Mathematics - Numerical Analysis; Nanowires; Physics - Mesoscale and Nanoscale Physics; Rescaling; Temperature; Temperature dependence
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2401.05722

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 \(\Delta x\) (\(T \to T\,\Delta x/a_{\text{eff}}\), 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: \((\xi_0/d)^\lambda\), where \(\xi_0\) is the correlation length at zero temperature, and \(\lambda\) is a critical exponent. We obtain values of \(\xi_0\) in the nanometer range, also in accordance with other simulations and experiments. The computed critical exponent is close to \(\lambda=2\) for all considered materials and geometries. This is the expected result for a mean-field approach, but slightly larger than the values observed experimentally.