# Magnonic Hall Effect and Magnonic Holography of Hopfions

## TL;DR

This paper investigates how spin waves interact with magnetic hopfions, revealing emergent electromagnetic effects and proposing magnonic holography as a method to detect these topological structures.

## Contribution

It introduces a micromagnetic analysis of spin wave scattering by hopfions and demonstrates their potential for magnonic holography detection methods.

## Key findings

- Spin waves are deflected by hopfions acting as lenses.
- Skew scattering and Aharonov-Bohm effects occur for certain propagation directions.
- Magnonic holography can be used to detect hopfions.

## Abstract

Hopfions are localized and topologically non-trivial magnetic configurations that have received considerable attention in recent years. Through a micromagnetic approach, we analyze the scattering of spin waves by magnetic hopfions. We show that the spin waves experience an emergent electromagnetic field related to the topological properties of the hopfion. We find that spin waves propagating along the hopfion symmetry axis are deflected by the magnetic texture, which acts as a convergent or divergent lens, depending on the spin wave propagation direction. The effect differs for spin waves propagating along the plane perpendicular to the symmetry axis. In the last case, they respond with a skew scattering and a closely related Aharonov-Bohm effect. This allows probing the existence of a magnetic hopfion by magnonic holography.