Continuum quantum ferromagnets at finite temperature and the Quantum Hall effect

TL;DR

This paper analyzes the finite temperature behavior of continuum quantum ferromagnets and their relation to the Quantum Hall effect, providing a scaling theory and predictions for experimental signatures.

Contribution

It develops a scaling theory for finite temperature quantum ferromagnets and predicts a ferromagnetic coherence peak in NMR relaxation rates in quantum Hall systems.

Findings

Scaling theory describes crossovers in different dimensions.

Predicted a finite T ferromagnetic coherence peak in NMR relaxation.

Compared theoretical results with recent experimental data.

Abstract

We study finite temperature ($T$) properties of the continuum quantum field theory of systems with a ferromagnetic ground state. A scaling theory of the $T=0$ system is discussed carefully, and its consequences for crossovers between different finite $T$ regimes in dimensions 1, 2, and 3 are described. The results are compared with recent NMR measurements of the magnetization of a quantum Hall system with filling factor $\nu=1$; we predict that the relaxation rate $1/T_1$ of this system may have a finite $T$ ``ferromagnetic coherence peak''.