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.
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