Hole Spin Relaxation In Semiconductors And Landau-Lifshitz-Gilbert Equation In Ferromagnetic Semiconductors

Semiconductor spintronics is an important branch in spintronics, which is based on the usage of the spin degree of freedom in solid state materials. Investigations on this field involve the generation, storage, manipulation and detection of spin polarization in semiconductors, where the spin dynamic properties are quite essential. This dissertation focuses on the dynamic properties in bulk III-V semiconductors and ferromagnetic semi-conductors, including the g-factor, spin relaxation time and the dynamic equation of the magnetization in semiconductors and/or ferromagnetic semiconductors.We first give a brief review on the background of the spintronics and the studies on the electron spin relaxation in III-V semiconductors in the literature. Then we explicitly intro-duce both experimetal and theoretical works on the hole spin relaxation in semiconductors. We also introduce the band-structure theory and ultrafast dynamics study in ferromag-netic semiconductors. Moreover, the development of the Landau-Lifshitz-Gilbert equation and the theoretical derivation on the Gilbert damping and non-adiabatic parameters are also introduced in the first chapter.In Chapter II, we discuss the spin-orbit coupling and g-factor in different valleys and different materials. We derive the spin-orbit coupling from the k-p theory and compare the coupling coefficients obtained from the k· p theory, tight-binding model and first principle calculation in the literature. Moreover, we also introduce the approach to calculate the g factor from the k· p theory, which we employ to study the L and X valleys in zincblende III-V semiconductors in Chapter III. The g factors of the L valley in GaAs and AlAs show significant anisotropy, while that of the X valley in GaN is almost isotropic. We find that the g factor of the X valley and the transverse component of the L valley are both close to the free electron g factor. In addition, we obtain the spin-orbit coupling coefficient of the X valley in GaN by calculating the spin splitting of the conduction band from the tight-binding models. The value from the sp3d5s*model is about0.29eVA, which is one order of magnitude larger than that from sp3s*.In Chapter IV, we first introduce the kinetic spin Bloch equations in semiconductor and explain the origin of the D’yakonov-Perel’and Elliott-Yafet mechanisms during the electron spin relaxation, by analyzing the coupling between the conduction and valence bands in the transformation between the collinear and helix representations. We also show the electron-hole exchange scattering term, which leads to the Bir-Aronov-Pikus spin relaxation mechanism, in the kinetic spin Bloch equations. By taking into account the large energy splitting between the light-and heavy-hole bands, we neglect all the interband coherence in the kinetic spin Bloch equations. Under this technique, the spin relaxation of hole gas solely due to the scatterings is attributed to the Elliott-Yafet mechanism, and that associated with the spin precession is referred as the D’yakonov-Perel’mechanism.From Chapter Ⅴ to Ⅷ, we study the spin dynamic properties in bulk GaAs and ferromagnetic GaMnAs. We first analyze the nonmonotonic doping-density dependence of the electron spin relaxation time observed in n-type GaAs at low temperature. By taking into account the laser-induced hot-electron effect, we confirm that the peak of the spin relaxation time is nothing but the consequence of the crossover between the degenerate and the non-degenerate limits.By employing the kinetic spin Bloch equations, we investigate the hole spin relaxation in both intrinsic and p-type bulk GaAs in Chapter Ⅵ. In our calculation, we include all the relevant scatterings, such as the hole-impurity, hole-phonon, hole-electron and hole-hole scatterings. We obtain the wave functions and spin splitting energies exactly from the Kane Hamiltonian, which allows us to determine the contributions from both the Elliott-Yafet and D’yakonov-Perel’mechanisms. We find that, due to the strong spin-orbit coupling, the Elliott-Yafet mechanism is always dominant during the hole spin relaxation. In the intrinsic case, the hole spin relaxation time is about110fs at room temperature, which agrees well with experiment. We show that the nonpolar hole-optical-phonon scattering and the spin coherence components between the two heavy-hole bands as well as light-hole bands, which were missed in the previous studies on the hole spin dynamics, both are very important. Further, we explicitly discuss the temperature and density dependences of the hole spin relaxation time. We find that the hole spin relaxation time can be extended by one order of magnitude as the temperature decreases. Moreover, we predict that the hole spin relaxation time decreases with increasing the density at high temperature, while a nonmonotonic density dependence appears. We show that the nonmonotonic density dependence of the hole spin relaxation time results from the different behaviors of the Coulomb scattering in the degenerate and non-degenerate limits. In the p-type case, we also predict rich nonmonotonic features in the temperature and density dependences of the hole spin relaxation time, which result from the variation of the hole-impurity and hole-phonon scattering strength. The screening is found to play an important role in the hole-impurity scattering.In Chapter Ⅶ, we derive the Landau-Lifshitz-Gilbert equation based on the s-d ex-change model in ferromagnetic semiconductors, where we define the spin operators under the local and instantaneous magnetization orientation hence introduce the spin couplings through the gauge field. By employing the non-equilibrium Green’s-function approach, we derive the kinetic spin Bloch equations of the itinerant carriers from the Hamiltonian with the gauge field. Under the relaxation time approximation, we solve the kinetic spin Bloch equations and calculate the spin torque of the magnetization due to the itinerant electron spin polarization. In the spatially homogeneous system, we show that the spin-conserving scattering as well as the spin-flip scattering can contribute to the electron spin relaxation time through the D’yakonov-Perel’ mechanism, hence correct the Gilbert damping torque. Moreover, the spatially homogeneous spin current is also found to contribute to the Gilbert damping coefficient in the presence of spin-orbit coupling. In the inhomogeneous case, the first-order gradient of the magnetization leads to two spin transfer torques, the transverse mode of which is proportional to the non-adiabatic parameter. At the second-order gra-dient, we obtain two effective magnetic fields. One is the conventional spin stiffness term, while the other, the vertical spin stiffness, is perpendicular to both the spin stiffness and magnetization. We show that the vertical spin stiffness makes the domain wall violate the ideal Neel wall structure, resulting in a spiral feature. Since the non-adiabatic parameter is large in ferromagnetic semiconductors, the vertical spin stiffness can be important.Further, we calculate the coefficients in the Landau-Lifshitz-Gilbert equation by us-ing the parameters in GaMnAs samples in experiments. Since these coefficients are all dependent on the carrier spin lifetime, we first calculate the hole spin relaxation time by numerically solving the kinetic equations under the Zener model. In the calculation, we neglect the Coulomb scattering due to the strong degenerate condition of the hole gas in all cases. The temperature effect is introduced through the temperature dependence of the magnetization following the Brillouin function. We show that, as the temperature increases, the hole spin relaxation time monotonically decreases for a small p-d exchange coefficient, while it first increases then decreases for the strong p-d exchange case. We analyze the nonmonotonic phenomenon and conclude that it originates from the variation of the inter-band spin mixing while the Zeeman splitting changes. We then substitute the hole spin relaxation time into the analytical expressions of the Landau-Lifshitz-Gilbert coefficients. We find that the non-adiabatic parameter β is around0.3, which shows good agreement with the experiment. As the temperature approaches to the Curie temperature, the non-adiabatic parameter increases and can even exceed one. In the regime with β<1, the Gilbert damping coefficient gradually increases with increasing temperature, which is consistent with the experiments. In the regime with β>1, we predict a decrease of the Gilbert damping coefficient with increasing temperature. Moreover, we also calculate the temperature dependence of the spin stiffness and vertical spin stiffness coefficients, where the latter also shows a nonmonotonic feature.Furthermore, we explicitly analyze the influence of a serried7r-pulse spin rephasing sequence on the electron spin relaxation in (001) GaAs quantum wells. We find that the spin relaxation time is only slightly affected by the pulses, both in the strong and weak scattering limits, when the inter-pulse spacing is larger than40ps. As the inter-pulse spacing decreases, the electron spin relaxation time can be significantly extended. We show that the temperature and density dependences of the spin relaxation time are consistent with those of the momentum scattering time. The reason lies in the fact that, under the serried π-pulse sequence, the inhomogeneous broadening is mainly suppressed by the pulses, and the scattering mainly performs as the source of the spin relaxation channel. According to our results, the efficient manipulation of the spin lifetime through the π-pulse rephasing sequence requires high mobility samples with very low (or high) electron densities and low temperature.Finally, we propose a spin transistor model at the mesoscopic level, which is based on a T-shaped waveguide with local Rashba spin-orbit coupling. By combining the Fano-Rashba effect and the structure antiresonance due to the geometry of the waveguide, we show that there would be a wide energy gap on the transmission curve when the Fano an-tiresonance and structure antiresonance points are tuned to be close to each other. Hence, the leakage current in the gap is rather small. We show that our spin transistor is of better robustness than those based on a single Fano antiresonance or structure antiresonance.