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A two dimensional (2D) percolation transition in Fe/W(110) ultrathin magneticfilms occurs when islands in the second atomic layer percolate and resolve afrustrated magnetic state to produce long-range in-plane ferromagnetic order.Novel measurements of the magnetic susceptibility $\chi(\theta)$ as the filmsare deposited at a constant temperature, allow the long-range percolationtransition to be observed as a sharp peak consistent with a critical phasetransition. The measurements are used to trace theparamagnetic-to-ferromagnetic phase boundary between the $T=0$ percolationmagnetic transition and the thermal Curie magnetic transition of the undilutedfilm. A quantitative comparison to critical scaling theory is made by fittingthe functional form of the phase boundary. The fitted parameters are then usedin theoretical expressions for $\chi(T)$ in the critical region of theparamagnetic state to provide an excellent, independent representation of theexperimental measurements.

The 2D percolation transition at finite temperature: The phase boundary for in-plane ferromagnetism in $\approx$2 ML Fe/W(110) films