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

Abstract

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 $\chi(T) \sim \exp \bigr{(}B/(T/T_{KT}-1)^a\bigl{)}$, where $a=0.50\pm0.03$ and $B=3.48\pm0.16$, in quantitative agreement with KT theory. Below the finite-size transition temperature $T_C(L)$, 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. In these, the temperature interval between the fitted Kosterlitz-Thouless transition temperature and the finite-size transition temperature is $T_C(L)/T_{KT} -1=0.065\pm0.016$. This yeids 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, does not give reasonable results. The effective critical exponent $\gamma_{eff} \approx 3.7 \pm 0.7$ does not correspond to a known universality class, and the fitted transition temperature is much further below the peak in the susceptibility than is reasonable.