Session X10: Focus Session: Spin Transport/Novel Magnetic Semiconductors

Spin susceptibility of a 2D gas with Rashba spin-orbit in the HF approximation

The in plane and out of plane spin susceptibility $\chi_S^{ \parallel (\perp)} (r_s, \bar{\alpha})$ in a two dimensional electron gas with Rashba spin-orbit is studied within the Hartree-Fock approximation in both the static ($\omega \rightarrow 0$ first then $q \rightarrow 0$) and adiabatic ($q \rightarrow 0$ first then $\omega \rightarrow 0$) limits. The latter is related to what is commonly referred to as the spin-Hall conductivity. The behavior of $\chi_S^{ \parallel (\perp)} (r_s, \bar{\alpha})$ as a function of the density parameter $r_s$ and the spin-orbit coupling strength $\bar{\alpha}$ has been explored. At variance with a recent perturbative analysis, we find that, as one would expect, the exchange interaction tends to increase $\chi_S^{ \parallel (\perp)} (r_s, \bar{\alpha})$ over its non interacting value. The interplay between the differential instability of the paramagnetic chiral state as signaled by the divergence of $\chi_S^{ \parallel (\perp)} (r_s, \bar{\alpha})$ and the (first order) spin polarization transition to a spin-textured chiral state will be discussed.   

Mesoscopic spin Hall effect in two- and four-probe ballistic semiconductor nanostructures with Rashba spin-orbit coupling

Recent efforts in spintronics have ignited a quest for fundamental physical phenomena that make it possible to generate and manipulate spin currents in semiconductors by employing spin-orbit couplings. In particular, spin Hall effects, where pure transverse spin current is induced as a response to longitudinal charge current, have been the focus of intense theoretical and experimental investigation. While theoretical scrutiny finds that the intrinsic spin Hall current vanishes in the bulk of infinite homogeneous two-dimensional electron gases (2DEG) with Rashba spin-orbit coupling, we demonstrate that in inhomogeneous nanostructures consisting of a ballistic finite-size 2DEG attached to four leads pure spin Hall current will flow out of the sample through the transverse voltage probes where the magnitude of the spin current can be tuned by changing the Rashba coupling. In the two-probe structures such mesoscopic spin Hall effect leads to spin accumulation whose properties display the same phenomenology as recently observed in experiments. Thus, we establish the fundamental connection between the spin Hall accumulation in two-probe and spin Hall currents in the four-probe semiconductor nanostructures. REFERECES: B. K. Nikolic, L. P. Zarbo, and S. Souma, cond-mat/0408693. S. Souma and B. K. Nikolic, cond-mat/0410716.   

Hartree-Fock Instability Theorem for a Two Dimensional Electron Gas in the Presence of Rashba Spin-Orbit Coupling

With the idea of spin control in electronic devices in mind, great interest has recently developed on the physics of the two dimensional electron liquid in the presence of spin-orbit coupling of the Rashba type. In order to gain insight into the effects of the Coulomb interactions on the static and dynamic properties of this system we have carried out a systematic study of a number of possible solutions of the corresponding Hartree-Fock problem. In particular we have been able to prove that, similarly to the case of jellium in the absence of spin-orbit coupling, the homogeneous chiral Hartree-Fock states are unstable vis a vis the formation of certain classes of inhomogeneous spin-density-wave states. This result holds for all densities and constitutes the rigorous extension of the Overhauser Hartree-Fock instability theorem to the case of the spin-orbit coupled jellium. Basic properties of these inhomogeneous states have been analyzed and will be discussed.   

Stochastic Variational description of interacting few-electron quantum dots with Rashba spin-orbit interaction

We present a theoretical study of interacting electrons in a parabolically confined quantum dots in the presence of both magnetic field and Rashba spin-orbit interaction. The energy levels and wave functions are calculated by the stochastic variational method. The stochastic variational method, using a random trial and error search in the variational model space, provides a very accurate solution for these few-electron (N$<$10) systems. We will show how the competition between the electron- electron interaction, the magnetic field and the spin-orbit interaction effects the energy levels for different confining strengths. The presence of magnetic field enhances the possibility of spin polarization and the spin-orbit interaction leads to complicated dependence of the energy levels on the strength of the magnetic field. The effect of the electron- electron interaction on the spin transport properties will also be discussed.   

Shallow donor electron spins as qubits in silicon: detection and manipulation

Shallow donors such as P have been proposed as quibits to be used in Si and Si$_{x}$Ge$_{1-x}$. External gate control of the hyperfine interaction or of the g-factor have been envisaged for single qubit manipulation, while gate control exchange interaction will provide qubits coupling. We will report on the P shallow donor wave function manipulation via an external electric field. The experimental result, i.e. the electric field dependence of the hyperfine interaction, is compared with theoretical predictions. By means of the envelope function approximation we have computed the energy levels of the shallow P impurity in silicon as well as the hyperfine splitting of the ground state and investigated their dependence on the applied external electric field along the [001] direction. In our numerical calculation we use a Gaussian basis set and we have included valley-orbit interaction and central cell-corrections. Electrically detected spin resonance has been also used to explore the feasibility of the spin detection with enhanced sensitivity using metal/oxide/semiconductor structures.   

Dislocation spin scattering: Opportunity for Spin-Interconnects by Heteroepitaxy

We develop a semi-classical theory of spin relaxation in direct-gap compound semiconductors due to Elliott-Yafet (EY) and Dyakanov-Perel (DP) scattering by edge dislocations from both charged cores, and the strain fields surrounding them. The results indicate a deleterious effect on spin transport in narrow bandgap III-V semiconductors. However, this form of scattering is found to be surprisingly benign for wide-bandgap semiconductors with small spin-orbit coupling (such as GaN). For room-temperature operation, the spin-lifetime is dominated by DP scattering from strain fields surrounding dislocations. The spin lifetime is found to be proportional to the areal density of dislocations, proportional to the third power of the bandgap, and inversely proportional to the square of the spin-orbit coupling energy. These facts point towards the fact that the spin lifetime can be considerably enhanced by using a wide bandgap semiconductor layer with small spin-orbit coupling, grown heteroepitaxially on a narrower gap layer such that there is an appreciable density of dislocations. The III-V nitride semiconductors, particularly GaN, is well suited for such spin-transport layers, and should be considered for spin-interconnects in the future. Thus, lattice-mismatched hybrid heterostructure devices can simultaneously take advantage of the long spin lifetimes of the wide-bandgap semiconductors and the wide tunability of spin in the narrow-bandgap semiconductors for spin logic-operations.   

Correlated Impurities in Diluted Magnetic Semiconductors: a disordered Heisenberg Model Monte Carlo study

We consider two types of correlated doping in ${\textrm Ga}_{1-x}{\textrm Mn}_{x}{\textrm As}$, patterned doping (in which Mn impurities are deposited as a cubic superlattice) and impurity clustering (in which dopants adhere, forming clusters); calculations are via classical Monte Carlo with impurity moments modeled as Heisenberg spins interacting through the damped RKKY range function with the damping scale given by the carrier mean free path. We calculate Curie Temperatures $T_{c}$, magnetization, and magnetic susceptibility. In both the patterned and clustered doping schemes, the deviation from the superlattice structure or the degree of impurity cluster formation is continuously tunable. In agreement with lattice Mean Field Theory (MFT), Curie Temperatures increase with increasing deviation from a perfect impurity superlattice. However, in the clustering scheme, $T_{c}$ is initially robust as clustering increases, ultimately decreasing slowly as impurities become strongly clumped; lattice MFT predicts instead that $T_{c}$ rises as clustering becomes more prevalent. When impurity clumping is very extensive, clusters of spins act as isolated moments; calculations reveal that the resulting paramagnetic state has a magnetic susceptibility which is distinct from that of the (ferromagnetic) states in which Mn dopants are more weakly clustered.   

Low frequency magnetic AC susceptibility and magnetization measurements of GaMnAs dilute semiconductors

We measured the magnetization and low frequency magnetic AC susceptibility of as-deposited and low temperature annealed (190 $^{\circ}$C for 100 hrs) GaMnAs samples. The annealed sample exhibits a higher Curie temperature (Tc=123.5 K) than the as-deposited sample (Tc=81.5 K) due to improved crystalline order which is reflected in higher Mn-core hole exchange constants derived from fits of the remnant magnetization curves to a mean filed model. Hysteresis loop measurements reveal an antiferromagnetically coupled soft and hard magnetic phase after annealing. Low frequency magnetic AC susceptibility measurements close to Tc show that both irreversible and magnetization reversible processes are present and are equally important.   

Rare Earth Doping of Semiconducting PtSb$_2$

We have measured the electronic transport, magnetic properties, and heat capacity of single crystals of semiconducting PtSb$_2$, doped with rare earth elements. The Hall voltage was measured in fields up to 9 T, and associated carrier concentrations ranged from 10$^{17}$ to 10$^{20}$ electrons per cm$^{3}$. Resistivity measurements from 1.8 K to 300 K showed metallic behavior for all the doped samples, and a superconducting transition near 2 K for some of the Yb and La doped samples. Subsequent heat capacity and Meissner effect measurements show that only a small fraction of the sample volume is superconducting. Magnetization measurements indicated ferromagnetism in some of the Gd and Ce doped crystals. Surface etching removed both the superconductivity and ferromagnetism, suggesting that both effects originate with surface phases, which we subsequently found and identified using electron microscopy. Despite the presence of these secondary phases, transport and heat capacity measurements indicate that rare earth doping introduces both magnetic moments and itinerant carriers into the semiconducting bulk. Work at the University of Michigan was performed under the auspices of the U.S. Department of Energy under grant DE-FG02- 94ER45526   

Transport, Magnetic and Thermodynamic Properties of Doped and Undoped Yb$_{14}$MnSb$_{11}$ Crystals

Hall, Seebeck, magnetization and heat capacity data are reported for La doped (Yb$_{13.3}$La$_{0.7}$MnSb$_{11}$, T$_{c} \quad \approx $39 K) and undoped crystals of the nearly half-metallic ferromagnet Yb$_{14}$MnSb$_{11}$ (T$_{c} \quad \approx $ 53 K). Since only about 4 {\%} of the atoms are magnetic (only the Mn atoms are magnetic), these materials represent ideal dilute magnetic semiconductors because there is no possibility of forming magnetic clusters. Hall and Seebeck data from the undoped crystals indicate a carrier concentration of about 1.9 x 10$^{21}$ hole/cm$^{3}$ near room temperature increasing to about 2.5 x 10$^{21}$ holes/cm$^{3}$ at 5 K. The carrier concentration in the doped crystals is typically 4 x 10$^{20}$ holes/cm$^{3}$ consistent with the filling of holes in the Sb bands by the extra electron donated when La$^{+3}$ replaces Yb$^{+2}$. The T$_{c}$ decreases with fewer holes but the saturation moment increases from 4.2 to 4.5 $\mu _{B}$ per Mn. The characteristics of the anomalous Hall effect, and the unusual magnetism in these materials will be discussed. Oak Ridge National Laboratory is managed by UT-Battelle, LLC for the Department of Energy.   

Recent Neutron and Transport Measurements on Yb$_{14}$MnSb$_{11}$ and La$_2$Yb$_{12}$MnSb$_{11}$ Single Crystals

Yb$_{14}$MnSb$_{11}$ and Yb$_{13.3}$La$_{0.7}$MnSb$_{11 }$are ferromagnetic Zintl compounds where the magnetic Mn atoms are well-defined crystallographic sites about 10{\AA} apart. Since only about 4{\%} of the atoms are magnetic (only the Mn atoms are magnetic), these materials represent ideal dilute magnetic semiconductors because there is no possibility of forming clusters of magnetic impurity phases. The measured carrier concentration of about 1 x 10$^{21}$ holes/cm$^{3}$ in several Yb$_{14}$MnSb$_{11}$ crystals (T$_{c}$=53K) is characteristic of a heavily doped semiconductor. La doped crystals (T$_{c}$=39K) were grown in an attempt to lower the carrier concentration and to study the change in the magnetic coupling between the Mn atoms via the holes. In this structure, each Mn atom is tetrahedrally coordinated by 4 Sb atoms. Preliminary unpolarized neutron diffraction experiments showed no clear evidence of a magnetic moment on the Sb in contrast to the previously reported results. Recent magnetization and Hall data on these crystals will be presented along with existing neutron diffraction data.   

Effects of electron-electron interactions on the rate of spin-relaxation

Spin-relaxation, in the presence of a uniform intrinsic spin- orbit interaction, is studied in a disordered two-dimensional electron gas when the temperature corrections to the conductivity arising as a result of the combined action of the electron-electron interaction and disorder are important. We find that the rate of spin-relaxation $\tau_{so}$ follows the temperature dependence of the conductivity $\sigma$, i.e., $\tau_{so}^{-1}(T)\propto \sigma(T)$.   

Spin Relaxation due to Dyakonov-Perel's Mechanism in N-type Quantum Wells under an Externally Applied Stress

We derived and calculated the spin relaxation time in n-type quantum wells grown along an arbitrary orientation. Unlike the early theory [1] for quantum wells, we include spin relaxation due to polar longitudinal-phonon and impurity scattering mechanisms by treating the corresponding Fourier components of the interaction matrix elements and the occupation number in the phase space exactly. Without using an extracted momentum relaxation time from the experimental data as an input parameter [2], our direct theoretical result of the spin relaxation time as a function of temperature agrees well with the experimental data for quantum wells grown along the [100] direction [3]. We further derived the strain-dependent effective magnetic field for the DP interaction Hamiltonian in the momentum space for quantum wells grown along an arbitrary direction. The influences of the magnitude and direction of the external stress on spin relaxation in n-type quantum wells will also be discussed. [1] M. I. D'yakonov and V. Yu. Kachorovskii, Sov. Phys. Semicond. 20, 110-112 (1986). [2] W. H. Lau, J. T. Olesberg, and M. E. Flatte, Phys. Rev. B 64, 161301(R) (2001). [3] T. Adachi, Y. Ohno, F. Matsukura, and H. Ohno, Physica E 10, 36-39 (2001).