Finite-size Kosterlitz-Thouless transition in 2DXY Fe/W(001) ultrathin films

Magnetic susceptibility measurements of 3–4 ML Fe/W(001) ferromagnetic films demonstrate that this is a 2DXY system in which a finite-size Kosterlitz-Thouless (KT) transition occurs. The films are grown in ultrahigh vacuum and their magnetic response is measured using the magneto-optic Kerr effect (MOKE). The analysis of many independently grown films shows that the paramagnetic tail of the susceptibility is described by χ(T)=χ0exp[B/(T/TKT−1)a], where a=0.50±0.03 and B=3.48±0.16, in quantitative agreement with KT theory. Below the finite size L transition temperature TC(L), the behavior is complicated by dissipation (likely related to the re-emergence of fourfold anisotropy and magnetic domains). A subset of measurements with very small dissipation most closely represents the idealized system treated by theory. For these measurements, there is a temperature interval of order tens of K between the fitted Kosterlitz-Thouless transition temperature and the finite-size transition temperature, in agreement with theory. The normalized interval TC(L)/TKT−1=0.065±0.016 yields an estimate of the finite size L affecting the film of order micrometers. This gives experimental support to the idea that even a mesoscopic limitation of the vortex-antivortex gas results in a substantial finite-size effect at the KT transition. In contrast, fitting the paramagnetic tail to a power law, appropriate to a second-order critical transition, gives unphysical parameters. The effective critical exponent γeff≈3.7±0.7 does not correspond to a known universality class, and the fitted transition temperature Tγ is much further below the peak in the susceptibility than is physically reasonable.