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 TsTs and the saturation magnetization MsMs. In the case of γ>0γ>0, both MsMs and TsTs 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 MgB2 thin films. By contrast, for γ>0γ>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 NiFe2O4 ultra-thin films, where a very strong enhancement of MsMs is observed.