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Magnetic susceptibility measurements of 3-4 ML Fe/W(001) ferromagnetic filmsdemonstrate that this is a 2DXY system in which a finite-sizeKosterlitz-Thouless (KT) transition occurs. The films are grown in ultrahighvacuum and their magnetic response is measured using the magneto-optic Kerreffect (MOKE). The analysis of many independently grown films shows that theparamagnetic 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 transitiontemperature $T_C(L)$, the behavior is complicated by dissipation (likelyrelated to the re-emergence of fourfold anisotropy and magnetic domains). Asubset of measurements with very small dissipation most closely represents theidealized system treated by theory. In these, the temperature interval betweenthe fitted Kosterlitz-Thouless transition temperature and the finite-sizetransition temperature is $T_C(L)/T_{KT} -1=0.065\pm0.016$. This yeids anestimate of the finite size $L$ affecting the film of order micrometers. Thisgives experimental support to the idea that even a mesoscopic limitation of thevortex-antivortex gas results in a substantial finite-size effect at the KTtransition. In contrast, fitting the paramagnetic tail to a power law,appropriate to a second order critical transition, does not give reasonableresults. The effective critical exponent $\gamma_{eff} \approx 3.7 \pm 0.7$does not correspond to a known universality class, and the fitted transitiontemperature is much further below the peak in the susceptibility than isreasonable.

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