# Self-Organized Criticality of Domain Walls and Magnetization Curve

## TL;DR

This paper introduces a Ginzburg--Landau model with quenched randomness that exhibits self-organized criticality in domain wall dynamics and magnetization, revealing power-law behavior and hysteresis in magnetic systems.

## Contribution

It presents a novel model capturing self-organized criticality in magnetic domain walls and magnetization curves, linking pinning-depinning transitions with hysteresis phenomena.

## Key findings

- Magnetization increases stepwise with power-law distribution of jumps.
- Hysteresis loop observed under cyclic magnetic field changes.
- Coercivity corresponds to the critical pinning-depinning transition.

## Abstract

We propose a kind of Ginzburg--Landau equation with quenched randomness. There is a pinning--depinning transition in the system when the external magnetic force is changed. The transition is self-organized when the external magnetic field is slowly changed under the demagnetizing effect. The total magnetization increases stepwise and the probability distribution of the increase in the total magnetization approximately obeys a power law. A hysteresis loop is obtained when the external magnetic field is changed reciprocally. In our model, the coercivity in the magnetization curve is expressed as the critical value for the pinning-depinning transition.