# A dynamical magnetic field accompanying the motion of ferroelectric domain walls

## TL;DR

This paper predicts a measurable magnetic field generated by moving ferroelectric domain walls due to a dynamical multiferroic effect, combining theoretical modeling and proposing experimental detection methods.

## Contribution

It introduces a theoretical framework for the dynamical magnetic field at ferroelectric domain walls and calculates its magnitude for BaTiO₃, linking ferroelectric motion to magnetic effects.

## Key findings

- Magnetic field of several microteslas at domain walls predicted.
- Derived an expression for the dynamical magnetic field.
- Proposed nitrogen-vacancy magnetometry experiments for detection.

## Abstract

The recently proposed dynamical multiferroic effect describes the generation of magnetization from temporally varying electric polarization. Here, we show that the effect can lead to a magnetic field at moving ferroelectric domain walls, where the rearrangement of ions corresponds to a rotation of ferroelectric polarization in time. We develop an expression for the dynamical magnetic field, and calculate the relevant parameters for the example of 90$^\circ$ and 180$^\circ$ domain walls in BaTiO$_3$ using a combination of density functional theory and phenomenological modeling. We find that the magnetic field reaches the order of several $\mu$T at the center of the wall, and we propose two experiments to measure the effect with nitrogen-vacancy center magnetometry.