Dirty quantum Hall ferromagnets and quantum Hall spin glasses

TL;DR

This paper investigates the effects of disorder on quantum Hall ferromagnets, revealing a phase transition from ferromagnetic to spin glass states driven by impurity strength and filling factor deviations, using a combination of theoretical modeling and numerical simulations.

Contribution

It introduces a phase diagram for disordered quantum Hall ferromagnets and characterizes the spin glass phase through magnetic, charge, and conductivity responses.

Findings

Disorder induces a transition from ferromagnetic to spin glass phase.

Screening of impurities distorts spin configurations significantly.

The phase diagram maps disorder strength and filling factor deviations to phases.

Abstract

We study quantum Hall ferromagnets in the presence of a random electrostatic impurity potential, within the framework of a classical non-linear sigma model. We discuss the behaviour of the system using a heuristic picture for the competition between exchange and screening, and test our conclusions with extensive numerical simulations. We obtain a phase diagram for the system as a function of disorder strength and deviation of the average Landau level filling factor from unity. Screening of an impurity potential requires distortions of the spin configuration. In the absence of Zeeman coupling there is a disorder-driven, zero-temperature phase transition from a ferromagnet at weak disorder and small deviation from integer filling to a spin glass at stronger disorder or large charge deviation. We characterise the spin glass phase in terms of its magnetic and charge response, as well as its ac conductivity.