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

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