Multifractal Magnons Around Localized Defects

Abstract

Multifractal wavefunctions fluctuate over a hierarchy of spatial scales, remaining spatially extended while exhibiting strongly nonuniform structure. We show that magnons in otherwise crystalline two-dimensional magnets can exhibit such behavior on mesoscopic scales, without disorder or quasiperiodicity. A localized defect can mix discrete groups of nearly degenerate magnon states in a finite sample, generating multiscale interference patterns and multifractal wavefunctions. We demonstrate this mechanism for both a simple spin defect and topological magnetic skyrmions. Large-scale spin-wave calculations for skyrmions in chiral and frustrated magnets reveal clear multifractal diagnostics over the full accessible range of system sizes of above-gap modes. Crucially, skyrmions make these states experimentally observable by hybridizing them with magnetically active internal deformation modes, which gives a subset of the multifractal states a nonzero magnetic dipole moment. These states can therefore be excited by uniform ac fields and remain distinguishable at realistic frequency resolution, providing a direct route to observing mesoscopic magnon multifractality.