Two-dimensional percolation transition in two atomic layers of Fe on W(110): Direct measurement of a static percolation critical exponent in a two-dimensional Ising system

When the coverage of the second atomic layer of Fe in an Fe/W(110) ultrathin film reaches a critical value, the system moves suddenly from a frustrated magnetic state without long-range order to an in-plane ferromagnetic state with long-range order, and displays many features of a percolation transition. Measurements of the magnetic susceptibility as the films are grown at 255 K show power law scaling that is limited by noise at low deposition, and by the dynamics of the paramagnetic, frustrated state at high deposition. Because the measurements represent a system driven by a finite field oscillating at a finite frequency, it is demonstated that the threshold deposition for percolation is bounded by the depositions where the real and imaginary components of the susceptibility have maxima. Fitting for the critical exponent of the static susceptibility at these bounds gives a bounded value for $\gamma_p=2.39\pm0.04$, in agreement with theory.