Spin relaxation in a quantum Hall ferromagnet, where filling is $ u=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 $Bsimeq 18,$T in the $ u=1$ Quantum Hall system and at $Bsimeq 12,$T for that of $ u=1/3,$. We estimate these times as $sim10,-,30,mu$s and $sim2,-,5,mu$s, respectively.
تحميل البحث