Two-dimensional percolation transition at finite temperature: Phase boundary for in-plane magnetism in films with two atomic layers of Fe on W(110)

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 percolation using the magnetic susceptibility χ(θ) 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 χ(T) in the critical region of the paramagnetic state to provide an excellent, independent representation of the experimental measurements.