# Scattering theory of transport through disordered magnets

## TL;DR

This paper develops a scattering theory for transport in disordered magnetic insulators, comparing models of spin disorder, and finds that localization lengths follow universal power laws in weak disorder regimes.

## Contribution

It introduces a scattering framework for disordered magnetic systems and characterizes localization lengths, revealing universal behavior and critical exponents.

## Key findings

- Both models exhibit Anderson localization with exponential decay of conductance.
- Localization lengths follow power laws with respect to disorder strength.
- Results are expressed via a universal exchange length, indicating general applicability.

## Abstract

We present a scattering theory of transport through noncollinear disordered magnetic insulators. For concreteness, we study and compare the random field model (RFM) and the random anisotropy model (RAM). The RFM and RAM are used to model random spin disorder systems and amorphous materials, respectively. We utilize the Landauer-Buttiker formalism to compute the transmission probability and spin conductance of one-dimensional disordered spin chains. The RFM and the RAM both exhibit Anderson localization, which means that the transmission probability and spin conductance decay exponentially with the system length. We define two localization lengths based on the transmission probability and the spin conductance, respectively. Next, we numerically determine the relationship between the localization lengths and the strength of the disorder. In the limit of weak disorder, we find that the localization lengths obey power laws and determine the critical exponents. Our results are expressed via the universal exchange length and are therefore expected to be general.