Modelling the magnetic properties of thin metallic films using Monte-Carlo simulation
In this thesis, Monte Carlo studies of the static critical behaviour of metallic magnetic thin-films are presented. The studies make use of a finite size scaling method designed for anisotropic shaped structures. This finite size scaling method is based on an assumption that a single correlation length is required to describe a thin-film close to its critical temperature and has lead to the derivation of formulae from which thin-film critical temperatures and exponents can be extracted. Monte Carlo simulations for Ising thin-films are carried out in order to verify the validity of the assumption and hence the formulae. Various algorithms and seed numbers for a random number generator are tested to minimise statistical errors. These studies also show the evolution from 2D to 3D-like behaviours as the films' thicknesses are increased. Critical temperatures and exponents are investigated for simple cubic (SC), body centred cubic (BCC) and face centred cubic (FCC) thin-films. Our Ising 2D and 3D results are also shown to give good agreement with previous Monte Carlo work. We then move on to study in a more realistic model of a magnetic thin-film in which the 'exchange parameters' and anisotropic constants are extracted from 'first principles' electronic structure calculations, and used in Monte Carlo simulations of a classical Heisenberg model. We model thin-films of Fe grown on a W(OOl) substrate which have been subjected to extensive experimental investigation. In line with the Mermin-Wagner theorem, we find a slow convergence for the magnetisation with the system size L in 2D which is consistent with expected absence of finite magnetisation in the finite temperatures in the thermodynamic limit. From the thin-film results in finite size systems, the magnetisation in the surface layers is weaker than those in the inner layers and a similar trend is found for the susceptibility. Slow magnetisation convergence with size is also observed for all thin-films (thickness varying from 2 to 8 layers). Because of this and the sensitivity to statistical errors, only critical temperatures and 'susceptibility critical exponents' can be extracted from the susceptibility functions. The results again show a crossover from 2D towards 3D-like behaviour. The critical temperatures are lower than those calculated from mean-field approximations and are in good agreement with experimental values where available. The differences in results between isotropic and anisotropic systems in which the anisotropic constants are very small in comparison to 'exchange interactions' are not significant.