Goldstone Mode Relaxation in a Quantum Hall Ferromagnet due to Hyperfine Interaction with Nuclei

TL;DR

This paper investigates how hyperfine interactions with nuclei cause non-exponential relaxation of Goldstone modes in quantum Hall ferromagnets, highlighting a dominant relaxation mechanism at high magnetic fields.

Contribution

It provides an analytical study of Goldstone mode relaxation due to hyperfine coupling, revealing a non-exponential decay process that competes with spin-orbit mechanisms.

Findings

Relaxation occurs non-exponentially over time.

Hyperfine interaction dominates at strong magnetic fields.

Analytical expressions for relaxation rate are derived.

Abstract

Spin relaxation in quantum Hall ferromagnet regimes is studied. As the initial non-equilibrium state, a coherent deviation of the spin system from the ${\vec B}$ direction is considered and the breakdown of this Goldstone-mode state due to hyperfine coupling to nuclei is analyzed. The relaxation occurring non-exponentially with time is studied in terms of annihilation processes in the "Goldstone condensate" formed by "zero spin excitons". The relaxation rate is calculated analytically even if the initial deviation is not small. This relaxation channel competes with the relaxation mechanisms due to spin-orbit coupling, and at strong magnetic fields it becomes dominating.