Core Concepts
The Curie temperature of ferromagnetic nanowires and nanolayers varies with their smallest dimension according to a power-law scaling, with a critical exponent close to 2.
Abstract
The authors solve the Landau-Lifshitz-Gilbert equation in the finite-temperature regime to study the size dependence of the Curie temperature in ferromagnetic nanowires and nanolayers. They use a temperature scaling approach to account for the mismatch between the computational cell size and the lattice constant.
The key highlights and insights are:
The computed Curie temperatures are in line with experimental values for cobalt, iron, and nickel, thanks to the temperature scaling approach.
For finite-sized objects, the Curie temperature varies with the smallest size d according to a power-law of the type: (ξ0/d)^λ, where ξ0 is the correlation length at zero temperature and λ is the critical exponent.
The computed correlation length ξ0 is in the nanometer range, consistent with other simulations and experiments.
The critical exponent λ is close to 2 for all materials and geometries, slightly larger than the values observed experimentally but in agreement with atomistic mean-field models.
Size effects are more pronounced for lower-dimensional structures, with greater variability in the magnetization curve observed for nanowires compared to nanolayers.
The time-dependent approach allows investigating not only the equilibrium properties, but also the nonequilibrium dynamics near the Curie temperature, where large statistical fluctuations are observed.
Stats
The Curie temperatures (in Kelvin) obtained from the numerical simulations for nanowires and nanolayers of different sizes and materials are listed in Table 3.
Quotes
"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."
"Size effects then appear to be stronger for lower-dimensional structures."