We report on a study of the spin relaxation of a strongly correlated two-dimensional electron gas in the nu=2kappa+1 quantum Hall regime. As the initial state we consider a coherent deviation of the spin system from the B direction and investigate a breakdown of this Goldstone-mode (GM) state due to the spin-orbit coupling and smooth disorder. The relaxation is considered in terms of annihilation processes in the system of spin waves. The problem is solved at an arbitrary value of the deviation. We predict that the GM relaxation occurs nonexponentially with time.

An experimental technique for the indirect manipulation and detection of electron spins entangled in two-dimensional magnetoexcitons has been developed. The kinetics of the spin relaxation has been investigated. Photoexcited spin-magnetoexcitons were found to exhibit extremely slow relaxation in specific quantum Hall systems, fabricated in high mobility GaAs/AlGaAs structures; namely, the relaxation time reaches values over one hundred microseconds. A qualitative explanation of this spin-relaxation kinetics is presented. Its temperature and magnetic field dependencies are discussed within the available theoretical framework.

Experimental and theoretical studies of the coherent spin dynamics of two-dimensional GaAs/AlGaAs electron gas were performed. The system in the quantum Hall ferromagnet state exhibits a spin relaxation mechanism that is determined by many-particle Coulomb interactions. In addition to the spin exciton with changes in the spin quantum numbers of δS = δSz = −1, the quantum Hall ferromagnet supports a Goldstone spin exciton that changes the spin quantum numbers to δS = 0 and δSz = −1, which corresponds to a coherent spin rotation of the entire electron system to a certain angle. The Goldstone spin exciton decays through a specific relaxation mechanism that is unlike any other collective spin state. PACS numbers: 73.43. Lp,71.70.Di,75.30.Ds Introduction. Spin relaxation mechanisms in twodimensional (2D) electron systems have not yet been elucidated due to the large number of competing mechanisms and the complex effects of the manyparticle Coulomb interactions on relaxation. 2D confinement and the quantizing magnetic field ensure a cardinal rearrangement of the electron energy spectrum, effectively making it zero-dimensional. Standard single-particle relaxation channels (see, e.g., Ref.[1] and the references therein) are suppressed, which prolongs spin relaxation time. On the other hand, electron-electron correlations, very essential in the case, make the spectrum again two-dimensional. At integer filling factors and at some fractional ones the simplest electron excitations are magnetoexcitons [2] with well defined 2D momenta, specifically representing magnetoplasmons, spin waves, or spin-cyclotron excitons [3][4][5][6][7][8]. New spin relaxation mechanisms, e.g., related to the exciton-exciton scattering processes appear.

We report on a study of the zero-momentum cyclotron spin-flip excitation in the V = 2 quantum Hall regime. Using the excitonic representation the excitation energy is calculated up to the second-order Coulomb corrections. A considerable negative exchange shift relative to the cyclotron gap is established for cyclotron spin-flip excitations in the spin-unpolarized electronic system. Under these conditions this type of state presents the lowest-energy excitations. For a fixed filling factor ͑V =2͒ the energy shift is independent of the magnetic field, which is in agreement with recent experimental observations. It is well known that in a translationally invariant twodimensional ͑2D͒ electron system Kohn's theorem 1 prohibits coupling of a homogeneous external perturbation to collective excitations of the electrons. As a result, the energy of cyclotron excitations ͑CE͒ at zero momentum has no contribution from Coulomb interaction and the dispersion of CE starts from the cyclotron gap. In addition to inter-Landaulevel cyclotron excitations ͑magnetoplasma ͑MP͒ mode͒ there are two other branches of collective excitations in the system of 2D electrons: intra-Landau-level spin-flip ͑SF͒ excitations ͑spin waves͒ and inter-Landau-level combined cyclotron spin-flip excitations ͑CSFE's͒. In the case of SF excitations, there exists Larmor's theorem which forbids any contribution from Coulomb interaction to the excitation energy at zero momentum in spin rotationally invariant systems ͑see, e.g., Ref. 2͒. However, in contrast to the CE and SF excitations, there are no symmetry reasons for the absence of many-body corrections to the zero-momentum energy of CS-FE's. Moreover, it is well established now both theoretically and experimentally 3 that for the spin-polarized electron system ͑V =1͒ the energy of cyclotron spin-flip excitations is strongly shifted to higher values relative to the cyclotron gap due to the exchange interaction. Therefore, the energy of combined cyclotron spin-flip excitations is a very convenient tool to probe many-body effects, for example, in the inelastic light scattering measurements performed at zero momentum. [3][4][5] The sensitivity of CSFE energy at q = 0 to many-body effects strongly depends on the spin polarization of the electron system. For the spin-unpolarized electron system ͑V =2͒, theory 2 developed within the first-order perturbation approach in terms of the parameter r C = E C / ប c ͑E C is the characteristic Coulomb energy, c is the cyclotron frequency͒ predicts a zero many-body contribution to the zeromomentum energy of CSFE. We show below that calculation of the CSFE zero-momentum energy for the V = 2 system performed to within the second-order Coulomb corrections yields a considerable negative exchange shift relative to the cyclotron gap.The studied system is characterized by exact quantum numbers S, S z , and q and by a nonexact but "good" quantum number ␦n corresponding to the change of the singleelectron energy ប c ␦n with an excitation. The relevant excitations with q = 0 and ␦n ...

We measure the spin-resolved transport of dipolar excitons in a biased GaAs double quantum well structure. From these measurements we extract both spin lifetime and mobility of the excitons. We find that below a temperature of 4.8K, there is a sharp increase in the spin lifetime of the excitons, together with a sharp reduction in their mobility. At T = 1.5K, where the excitons have the lowest mobility, we observe an anomalous non-monotonous dependence of the exciton spin lifetime on the mobility. Below a critical power the spin lifetime increases with increasing mobility and density, while above the critical power the opposite trend is observed. We interpret this transition as an evidence of the interplay between two different spin dephasing mechanisms: at low mobility the dephasing is dominated by the hyperfine interaction with the lattice nuclei spins, while at higher mobility the spin-orbit interaction dominates, and a Dyakonov-Perel spin relaxation takes over. The excitation power and temperature regime where the hyperfine interaction induced spin dephasing is observed correlates with the regime where a dark dipolar quantum liquid was reported recently on a similar sample.