Competing Hyperfine and Spin-Orbit Couplings: Spin Relaxation in a Quantum Hall Ferromagnet

TL;DR

This paper investigates spin relaxation mechanisms in quantum Hall ferromagnets, highlighting the competition between hyperfine and spin-orbit couplings, and predicts non-monotonic relaxation times with magnetic field variations.

Contribution

It introduces a detailed analysis of competing hyperfine and spin-orbit interactions affecting spin relaxation, including non-exponential behavior and specific magnetic field-dependent relaxation maxima.

Findings

Relaxation times peak at specific magnetic fields (~18 T for ν=1 and ~12 T for ν=1/3).

Estimated relaxation times are approximately 10-30 microseconds for ν=1 and 2-5 microseconds for ν=1/3.

Spin relaxation can occur non-exponentially and independently of temperature at low temperatures.

Abstract

Spin relaxation in a quantum Hall ferromagnet, where filling is $\nu=1, 1/3, 1/5,...$, can be considered in terms of spin wave annihilation/creation processes. Hyperfine coupling with the nuclei of the GaAs matrix provides spin non-conservation in the two-dimensional electron gas and determines spin relaxation in the quantum Hall system. This mechanism competes with spin-orbit coupling channels of spin-wave decay and can even dominate in a low-temperature regime where $T$ is much smaller than the Zeeman gap. In this case the spin-wave relaxation process occurs non-exponentially with time and does not depend on the temperature. The competition of different relaxation channels results in crossovers in the dominant mechanism, leading to non-monotonic behavior of the characteristic relaxation time with the magnetic field. We predict that the relaxation times should reach maxima at $B\simeq 18\,$T in the $\nu=1$ Quantum Hall system and at $B\simeq 12\,$T for that of $\nu=1/3\,$. We estimate these times as $\sim10\,-\,30\,\mu$s and $\sim2\,-\,5\,\mu$s, respectively.