Momentum Signatures of Site Percolation in Disordered 2D Ferromagnets

TL;DR

This paper investigates how spin-wave excitations propagate in disordered 2D ferromagnets with site percolation, revealing signatures of Anderson localization and cluster formation through momentum distribution analysis.

Contribution

It introduces a novel spectroscopic approach to detect cluster formation in disordered 2D ferromagnets via momentum distribution signatures.

Findings

Identification of CBS and CFS peaks at low defect density

Observation of oscillating CFS peaks at higher defect densities

Linking oscillation frequencies to eigenenergy differences in small clusters

Abstract

In this work, we consider a two-dimensional square lattice of pinned magnetic spins with nearest-neighbour interactions and we randomly replace a fixed proportion of spins with nonmagnetic defects carrying no spin. We focus on the linear spin-wave regime and address the propagation of a spin-wave excitation with initial momentum $k_0$. We compute the disorder-averaged momentum distribution obtained at time $t$ and show that the system exhibits two regimes. At low defect density, typical disorder configurations only involve a single percolating magnetic cluster interspersed with single defects essentially and the physics is driven by Anderson localization. In this case, the momentum distribution features the emergence of two known emblematic signatures of coherent transport, namely the coherent backscattering (CBS) peak located at $-k_0$ and the coherent forward scattering (CFS) peak located at $k_0$. At long times, the momentum distribution becomes stationary. However, when increasing the defect density, site percolation starts to set in and typical disorder configurations display more and more disconnected clusters of different sizes and shapes. At the same time, the CFS peak starts to oscillate in time with well defined frequencies. These oscillation frequencies represent eigenenergy differences in the regular, disorder-immune, part of the Hamiltonian spectrum. This regular spectrum originates from the small-size magnetic clusters and its weight grows as the system undergoes site percolation and small clusters proliferate. Our system offers a unique spectroscopic signature of cluster formation in site percolation problems.