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Register a new userCompeting Hyperfine and Spin-Orbit Couplings: Spin Relaxation in a Quantum Hall Ferromagnet
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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.
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We study spin wave relaxation in quantum Hall ferromagnet regimes. Spin-orbit coupling is considered as a factor determining spin nonconservation, and external random potential as a cause of energy dissipation making spin-flip processes irreversible. We compare this relaxation mechanism with other relaxation channels existing in a quantum Hall ferromagnet.
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.
Electron spin relaxation in a spin-polarized quantum Hall state is studied. Long spin relaxation times that are at least an order of magnitude longer than those measured in previous experiments were observed and explained within the spin-exciton relaxation formalism. Absence of any dependence of the spin relaxation time on the electron temperature and on the spin-exciton density, and specific dependence on the magnetic field indicate the definite relaxation mechanism -- spin-exciton annihilation mediated by spin-orbit coupling and smooth random potential.
A spin-rotation mode emerging in a quantum Hall ferromagnet due to laser pulse excitation is studied. This state, macroscopically representing a rotation of the entire electron spin-system to a certain angle, is not microscopically equivalent to a coherent turn of all spins as a single-whole and is presented in the form of a combination of eigen quantum states corresponding to all possible S_z spin numbers. The motion of the macroscopic quantum state is studied microscopically by solving a non-stationary Schroedinger equation and by means of a kinetic approach where damping of the spin-rotation mode is related to an elementary process, namely, transformation of a `Goldstone spin exciton to a `spin-wave exciton. The system exhibits a spin stochastizationa mechanism (determined by spatial fluctuations of the Lande g-factor) ensuring damping, transverse spin relaxation, but irrelevant to decay of spin-wave excitons and thus not involving longitudinal relaxation, i.e., recovery of the S_z number to its equilibrium value.
Cyclotron spin-flip excitation in a nu=2 quantum Hall system, being separated from the ground state by a slightly smaller gap than the cyclotron energy and from upper magnetoplasma excitation by the Coulomb gap [S. Dickmann and I.V. Kukushkin, Phys. Rev. B 71, 241310(R) (2005) ; L.V. Kulik, I.V. Kukushkin, S. Dickmann, V.E. Kirpichev, A.B. Vankov, A.L. Parakhonsky, J.H. Smet, K. von Klitzing, and W. Wegscheider, Phys. Rev. B 72, 073304 (2005)] cannot relax in a purely electronic way except only with the emission of a shortwave acoustic phonon (k~3*10^7/cm). As a result, relaxation in a modern wide-thickness quantum well occurs very slowly. We calculate the characteristic relaxation time to be ~1s. Extremely slow relaxation should allow the production of a considerable density of zero-momenta cyclotron spin-flip excitations in a very small phase volume, thus forming a highly coherent ensemble - the Bose-Einstein condensate. The condensate state can be controlled by short optical pulses (<1 mcs), switching it on and off.
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