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

• Published in: Journal of magnetism and magnetic materials Vol. 598; p. 172040
• Main Authors: Courtès, Clémentine, Boileau, Matthieu, Côte, Raphaël, Hervieux, Paul-Antoine, Manfredi, Giovanni
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.05.2024; Elsevier
• Subjects: Condensed Matter; Curie temperature; Finite-size effect; Landau-Lifshitz-Gilbert equation; Mathematics; Micromagnetism; Nanolayer; Nanowire; Numerical Analysis; Physics; Strongly Correlated Electrons; Nanowire; Micromagnetism; Landau-Lifshitz-Gilbert equation; Finite-size effect; Nanolayer; Curie temperature; Finite-size effects
• ISSN: 0304-8853; 1873-4766; 1873-4766
• DOI: 10.1016/j.jmmm.2024.172040

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. •Simulation of temperature effects using a stochastic Landau-Lifshitz-Gilbert equation.•Accurate determination of the Curie temperature for Cobalt, Nickel, and Iron.•Determination of the scaling law of the Curie temperature with the size of the system, for nanowire and nanolayer geometries.