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

TL;DR

This study investigates the 2D percolation transition in ultrathin Fe/W(110) films, revealing how island percolation induces in-plane ferromagnetism and mapping the phase boundary through magnetic susceptibility measurements.

Contribution

It provides the first experimental observation and quantitative analysis of the 2D percolation transition's phase boundary in ultrathin magnetic films, linking percolation to magnetic order.

Findings

Percolation induces long-range in-plane ferromagnetism.

Magnetic susceptibility peaks at the phase transition.

Quantitative agreement with critical scaling theory.

Abstract

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.