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 $\Delta x$ ($T\to T\Delta x/a_{\text{eff}}$, 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.

28 pages

References in corpus (3)

• Quantitative simulation of temperature dependent magnetization dynamics and equilibrium properties of elemental ferromagnets
• Dynamic approach for micromagnetics close to the Curie temperature
• Autoresonant control of the magnetization switching in single-domain nanoparticles