Excitation with a massive spin reversal of the individual skyrmion/antiskyrmion type is theoretically studied in a quantum Hall ferromagnet, where the zeroth and first Landau levels are completely occupied only by electrons with spins aligned strictly in the direction determined by the magnetic field. The Wigner-Seitz parameter is not necessarily considered to be small. The microscopic model in use is based on a reduced basic set of quantum states [the so-called "single-mode (single-exciton) approximation"], which allows proper account to be taken for mixing of Landau levels, and substantiating the equations of the classical O(3) nonlinear a model. The calculated "spin stiffness" determines the exchange gap for creating a pair of skyrmion and antiskyrmion. This gap is significantly smaller than the doubled cyclotron energy and the characteristic electron-electron correlation energy. Besides, the skyrmion-antiskyrmion creation gap is much smaller than the energy of creation of a separated electron-exchange-hole pair calculated in the limit case of a spin magnetoexciton corresponding to an infinitely large 2D momentum. At a certain magnetic field (related to the 2D electron density in the case of fixed filling factor v), the gap vanishes, which presumably points to a Stoner transition of the quantum Hall ferromagnet to a paramagnetic phase.

A macroscopic approach is applied to a system usually studied microscopically. The object of study is a two-dimensional electron gas in one of its quantum Hall states. The motion of a macroscopic object (its collective spin moment in a quantum Hall ferromagnet) can be studied phenomenologically as when using the Landau–Lifshitz equation to describe the motion of a magnetic moment in a conventional magnet.

In the present study we address the kinetics of long-lived excitations at zero temperature in an electronic quantum Hall system with filling factor $\nu=2$. The initial coherent state of spin-cyclotron magnetoexitons with two-dimensional wave vector ${\bf q}=0$ resulting from laser pumping is stochastized over time due to emission of acoustic phonons. The elementary emission process requires participation of two magnetoexitons, so the effective rate of phonon emission is proportional to the excitation density squared, and the stochastization process occurs nonexponentially with time. The final distribution of magnetoexitons over 2D momenta, established as a result of stochastization, is compared with equilibrium distribution at finite temperature.

We address damping of a Goldstone spin-rotation mode emerging in a quantum Hall ferromagnet due to laser pulse excitation. Recent experimental data show that the attenuation mechanism, dephasing of the observed Kerr precession, is apparently related not only to spatial fluctuations of the electron Landé factor in the quantum well, but to a hyperfine interaction with nuclei, because local magnetization of GaAs nuclei should also experience spatial fluctuations. The motion of the macroscopic spin-rotation state is studied microscopically by solving a non-stationary Schrödinger equation. Comparison with the previously studied channel of transverse spin relaxation (attenuation of Kerr oscillations) shows that relaxation via nuclei involves a longer quadratic stage of time-dependance of the transverse spin, and, accordingly, an elongated transition to a linear stage, so that a linear time-dependance may not be revealed.

Spin-flip excitations in a quantum Hall electron system at fixed filling factor nu=2 are modelled and studied under conditions of a strong Coulomb interaction when the `Landau level mixing' is a dominant factor determining the excitation energy. The `one-exciton' approach used for the purely electronic excitations in question allows us to describe the Stoner transition from the unpolarized/paramgnet state to the polarized/ferromagnet one. The theoretical results are compared with the available experimental data.

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 Schrödinger 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 stochastization mechanism (determined by spatial fluctuations of the Landé 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.

In connection with recent studies of extremely long-living spin-cyclotron excitations (actually magneto-excitons) in a quantum Hall electron gas, we discuss contribution to the light-absorption related to the presence of a magneto-exciton ensemble in this purely electronic system. Since the weakly interacting excitations have to obey the Bose-Einstein statistics, one can expect appearance of a coherent state in the ensemble. A comparative analysis of both incoherent and coherent cases is done. Conditions for a phase transition from the incoherent state to the coherent one are discussed.

In connection with recent studies of extremely long-living spin-cyclotron excitations (actually magneto-excitons) in a quantum Hall electron gas, we discuss contribution to the light-absorption related to the presence of a magneto-exciton ensemble in this purely electronic system. Since the weakly interacting excitations have to obey the Bose-Einstein statistics, one can expect appearance of a coherent state in the ensemble. A comparative analysis of both incoherent and coherent cases is done. Conditions for a phase transition from the incoherent state to the coherent one are discussed.

The recent experimental studies of extremely long-lived macroscopic ensembles of spin-cyclotron excitons (magnetoexcitons) which have to obey the Bose-Einstein statistics signal the emergence of an excitonic coherent phase. In the present paper the theory of a weakly interacting Bose gas of spin-cyclotron excitations is developed in terms of a virial correction to the single-magnetoexciton energy. The condition for coherent-incoherent phase transition is discussed. It is expected to be strongly related to the studied long-distance interexcitonic correlations. The results obtained theoretically are discussed in terms of their agreement with specific experimental data.

Experimental results on the properties of a recently discovered new collective state, the magnetofermionic condensate, are summarized herein. Condensation occurs in a fermionic system, a quantum Hall insulator (filling factor nu = 2), as a result of the formation of a dense ensemble of long-lived spin cyclotron magnetoexcitons, composite bosons. At temperatures below 1 K, the exciton ensemble exhibits a sharp enhancement in its response to an external electromagnetic field due to the formation of a super-absorbing state that interacts coherently with the electromagnetic field. Simultaneously, the electrons below the Fermi level rearrange to form a new non-equilibrium radiative recombination channel. The condensate shows a sharp decrease in viscosity and the ability to spread over macroscopically large distances, on the order of a millimeter, at a speed of approximate to 103cms-1. Due to this rapid long-distance spin transfer, new opportunities in the field of spintronics have been opened up.

Coherent condensate states of particles obeying either Bose or Fermi statistics are in the focus of interest in modern physics. Here we report on condensation of collective excitations with Bose statistics, cyclotron magnetoexcitons, in a high-mobility two-dimensional electron system in a magnetic field. At low temperatures, the dense non-equilibrium ensemble of long-lived triplet magnetoexcitons exhibits both a drastic reduction in the viscosity and a steep enhancement in the response to the external electromagnetic field. The observed effects are related to formation of a super-absorbing state interacting coherently with the electromagnetic field. Simultaneously, the electrons below the Fermi level form a super-emitting state. The effects are explicable from the viewpoint of a coherent condensate phase in a non-equilibrium system of two-dimensional fermions with a fully quantized energy spectrum. The condensation occurs in the space of vectors of magnetic translations, a property providing a completely new landscape for future physical investigations.

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 delta S = delta S-z = 1, the quantum Hall ferromagnet supports a Goldstone spin exciton that changes the spin quantum numbers to delta S = 0 and delta S-z = 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.

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.

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. The absence of any dependence of the spin-relaxation time on the electron temperature and on the spin-exciton density, and a specific dependence on the magnetic field indicate a definite relaxation mechanism-spin-exciton annihilation mediated by spin-orbit coupling and a smooth random potential.

Cyclotron spin-flip excitation in a ν=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. Van'kov, 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 ~1 s. 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 μs), switching it on and off.

Spin relaxation in a quantum Hall ferromagnet, where filling is � = 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 nonexponentially 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 ≃18T in the �=1 Quantum Hall system and at B ≃12T for that of �=1/3. We estimate these times as ∼10 − 30µs and ∼2 − 5µs, respectively. PACS numbers 73.43.Lp, 78.67.De, 73.21.Fg

Cyclotron spin-flip excitation in an even-integer quantum Hall system is the lowest-energy excitation separated from the ground state by the gap slightly smaller than the cyclotron energy, and from the upper magnetoplasma excitation by the Coulomb gap [1, 2]. At the filling factor ν = 2 in a real system these gaps are in the vicinity of 10 meV and 0.5 meV and thus are much larger than the Zeeman gap (∼ 0.1 meV) and temperature (< 0.01 meV) respectively. Under these conditions the cyclotron spin flip excitation can not relax in a purely electronic way but only with emission of a short-wave phonon (k ∼ 3 107 /cm). As a result the relaxation in a modern wide-thickness quantum well occurs very slowly, the characteristic relaxation time being ∼ 1 s. The cyclotron spin-flip excitation in the narrow vicinity of filling factors ν = 2, 4, ... should therefore be considered as a collective metastable excitation in the quantum Hall system.

Spin relaxation in quantum Hall ferromagnet regimes is studied. As the initial non-equilibrium state, a coherent deviation of the spin system from the 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.

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.