Thickness dependence of second-order magnetic phase transitions in films

Using a simple Landau model, we discuss the different possibilities of generating near-surface magnetic effects at a second-order transition for films. For experimental comparison, we define an order parameter averaged on the film thickness. Varying the sample size d and/or surface coupling γ, one can decrease or increase substantially the surface critical temperature T s and the saturation magnetization M s . In the case of γ > 0 , both M s and T s decrease from the bulk values as the film thickness is reduced. These theoretical results are, in particular, in nice agreement with the experimental data on superconducting MgB 2 thin films. By contrast, for γ > 0 , an enhancement of both quantities is expected. This extraordinary transition has been rarely observed experimentally and usually the situation is far from been clear. We analyze a new experiment on NiFe 2O 4 ultra-thin films, where a very strong enhancement of M s is observed.