# Dynamics of domain walls in weak ferromagnets

## TL;DR

This paper derives equations describing domain wall dynamics in weak ferromagnets, revealing a velocity-field relationship with a maximum velocity and negative differential mobility, similar to ferromagnets.

## Contribution

It extends the Walker solution framework to weak ferromagnets and calculates the velocity dependence on magnetic field.

## Key findings

- Maximum domain wall velocity ~2 x 10^6 cm/sec in YFeO3
- Velocity peaks at magnetic field ~4000 Oe
- Negative differential mobility observed in the velocity-field curve

## Abstract

It is shown that the total set of equations, which determines the dynamics of the domain bounds (DB) in a weak ferromagnet, has the same type of specific solution as the well-known Walker's solution for ferromagnets. We calculated the functional dependence of the velocity of the DB on the magnetic field, which is described by the obtained solution. This function has a maximum at a finite field and a section of the negative differential mobility of the DB. According to the calculation, the maximum velocity $ c \approx 2 \times 10^6$ cm/sec in YFeO$_3$ is reached at $H_m \approx 4 \times 10^3$ Oe.