Peculiar corner states in magnetic fractals

TL;DR

This paper explores the emergence of topologically protected corner states in magnetic fractal structures, specifically a Sierpiński carpet, revealing novel higher-order topological phases absent in regular lattices.

Contribution

It introduces the concept of topological corner states in magnetic fractals and demonstrates their robustness and unique properties through theoretical analysis and micromagnetic simulations.

Findings

Identification of three higher-order topological states in magnetic fractals

Demonstration of topological protection and robustness against disorder

Verification of theoretical predictions with micromagnetic simulations

Abstract

Topological excitations in periodic magnetic crystals have received significant recent attention. However, it is an open question on their fate once the lattice periodicity is broken. In this work, we theoretically study the topological properties embedded in the collective dynamics of magnetic texture array arranged into a Sierpi\'nski carpet structure with effective Hausdorff dimensionality $d_{f}=1.893$. By evaluating the quantized real-space quadrupole moment, we obtain the phase diagram supporting peculiar corner states that are absent in conventional square lattices. We identify three different higher-order topological states, i.e., outer corner state, type I and type II inner corner states. We further show that all these corner states are topologically protected and are robust against moderate disorder. Full micromagnetic simulations are performed to verify theoretical predictions with good agreement. Our results pave the way to investigating topological phases of magnetic texture based fractals and bridging the gap between magnetic topology and fractality.