Zero-field Spin Splitting Energy Research Articles

Large spin-orbit splitting in inversion layers on HgCdTe with an inverted band structure

This paper reports the study of the magneto-transport properties of a two-dimensional electron gas confined in inversion layers on HgCdTe with an inverted band structure. The magnetoresistance exhibits Shubnikov-de Hass oscillations, where beating patterns are observed at low magnetic field. This can be attributed to the zero-field spin splitting. By using the fast Fourier transformation of the observed beating patterns, the zero-field spin splitting energy is extracted. The extracted energy up to is obtained, which is far larger than that in inversion layers on HgCdTe with a normal band structure. This offers a route to realize a HgTe-based spintronic device that works at room temperature.

Spin-polarized Wide Electron Slabs in Functionally Graded Polar Oxide Heterostructures

We report on the high mobility wide electron slabs with enhanced correlation effects by tailoring the polarization effects in a functionally graded ZnMgO/ZnO heterostructures. The characteristics of three-dimensional (3D) spreading electrons are evidenced by the capacitance-voltage profiling and the quantization of 3D Fermi surface in magneto-transport measurements. Despite the weak spin-orbit interaction, such electron slabs are spin-polarized with a large zero-field spin splitting energy, which is induced by the carrier-mediated ferromagnetism. Our results suggest that the vast majority of electrons are localized at the surface magnetic moment which does not allow spin manipulations, and only in the region visited by the itinerant carriers that the ferromagnetic exchange interactions via coupling to the surface local moments contribute to the spin transport. The host ferromagnetism is likely due to the formation of Zn cation vacancies on the surface regime induced by the stabilization mechanism and strain-relaxation in ZnMgO polar ionic surface.

Spin-polarized two-dimensional electron gas in undoped MgxZn1−xO/ZnO heterostructures

Quantum transport properties of two-dimensional electron gas (2DEG) in undoped MgxZn1−xO/ZnO heterostructures grown by metal organic vapor phase epitaxy have been investigated. A large zero-field spin-splitting energy more than 15 meV in the 2DEG is determined at 1.6 K. Meanwhile, ferromagnetism is observed in the heterostructures. The findings reveal that the 2DEG is spin polarized at zero magnetic fields. It is believed that the exchange interaction between the itinerant electrons in the two-dimensional channel and the magnetic polarons in the MgxZn1−xO barrier around the interface results in the spin polarization of the 2DEG.

Zero-field spin splitting in a two-dimensional electron gas with the spin–orbit interaction revisited

We consider a two-dimensional electron gas (2DEG) with the Rashba spin–orbit interaction (SOI) in the presence of a perpendicular magnetic field. We derive analytical expressions of the density of states (DOS) of a 2DEG with the Rashba SOI in the presence of a magnetic field by using the Green’s function technique. The DOS allows us to obtain the analytical expressions of the magnetoconductivities for spin-up and spin-down electrons. The conductivities for spin-up and spin-down electrons oscillate with different frequencies and give rise to the beating patterns in the amplitude of the Shubnikov–de Haas (SdH) oscillations. We find a simple equation which determines the zero-field spin splitting energy if the magnetic field corresponding to any beat node is known from the experiment. Our analytical results reproduce well the experimentally observed non-periodic beating patterns, number of oscillations between two successive nodes and the measured zero-field spin splitting energy.

Anomalous shift of the beating nodes in illumination-controlledIn1−xGaxAs/In1−yAlyAstwo-dimensional electron gases with strong spin-orbit interaction

The beating patterns in the Shubnikov-de Haas oscillatory magnetoresistance originating from zero-field spin splitting of two-dimensional electron gases (2DEGs) in ${\text{In}}_{0.52}{\text{Al}}_{0.48}\text{As}/{\text{In}}_{\text{x}}{\text{Ga}}_{1\ensuremath{-}\text{x}}\text{As}/{\text{In}}_{0.52}{\text{Al}}_{0.48}\text{As}$ quantum wells with silicon $\ensuremath{\delta}$ doped on the upper barrier layer have been investigated by means of magnetotransport measurements before and after illumination. Contrary to the expectation, after each illumination, the beating nodes induced by the zero-field spin-splitting effect shift to lower and lower magnetic field due to the decrease in the zero-field spin-splitting energy of the 2DEGs. The anomalous phenomenon of the shift of the beating nodes and the decrease in spin-orbit coupling constants after illumination cannot be explained by utilizing the previous linear Rashba model. It is suggested that the decrease in the zero-field spin-splitting energy and the spin-orbit coupling constant arise from the nonlinear Rashba spin splitting.

Carrier density dependence of spin–orbit interaction in InAsSb quantum wells

We investigated the spin–orbit interaction (SOI) in Al 0.1In 0.9Sb/Sn-doped InAs 0.1Sb 0.9 quantum wells (QWs) with different doping levels using the weak anti-localization effect in the magneto-resistance. The inelastic scattering time is close to the T −1 law predicted theoretically for electron–electron interaction, and the spin–orbit scattering time is temperature independent as expected for the D'yakonov–Perel mechanism. The carrier-density dependence of zero-field spin-splitting energy extracted from the fits of magneto-resistance was examined by the theoretical calculation. The result confirms that the Dresselhaus SOI is much larger than the Rashba SOI in our QWs. The dominance of the Dresselhaus term in SOI originates in the large weight factor of InSb-based alloy.

Quantum transport and spin–orbit interaction in Al 0.1In 0.9Sb/InAs 0.1Sb 0.9 quantum wells

We have investigated the spin–orbit interaction in strain-free Al 0.1In 0.9Sb/InAs 0.1Sb 0.9 quantum wells with different widths. The weak anti-localization (WAL) effect was clearly observed in the magneto-resistance for all samples. The inelastic scattering time is close to the T −1 law predicted theoretically for electron–electron interaction in the diffusive regime, and the spin–orbit scattering time is temperature independent as expected for the D’yakonov–Perel mechanism. The zero-field spin-splitting energies extracted from these observations were around 1.0 meV. The WAL behavior becomes distinct in samples with wider well width, and the zero-field spin-splitting energy slightly increases with well width. This seems to reflect increase of the carrier concentration.

Zero-field spin splitting in AlxGa1−xN/GaN heterostructures with various Al compositions

The zero-field spin splitting in AlxGa1−xN/GaN heterostructures with various Al compositions has been investigated at low temperatures and high magnetic fields. The zero-field spin-splitting energy and the spin-orbit coupling parameter are obtained by means of beating pattern Shubnikov–de Haas measurements. It is found that the spin-orbit coupling parameter can be tuned by the polarization-induced electric field. The AlxGa1−xN/GaN heterostructure is one of the promising materials for the spin-polarized field effect transistor.

Influence of the illumination on the beating patterns in the oscillatory magnetoresistance inAlxGa1−xN∕GaNheterostructures

The beating patterns in the oscillatory magnetoresistance originating from zero-field spin-splitting and magnetointersubband scattering (MIS) effects of the two-dimensional electron gas (2DEG) in ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}∕\mathrm{Ga}\mathrm{N}$ heterostructures have been investigated by means of magnetotransport measurements under illumination. It is observed that the energy separation between the two subbands decreases due to the weakened electric field at the ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}∕\mathrm{Ga}\mathrm{N}$ heterointerfaces after the illumination. Meanwhile, the beating nodes induced by the MIS effect shift to higher magnetic field due to the increase of the 2DEG concentration at the second subband, and the beating nodes induced by the zero-field spin-splitting effect shift to lower magnetic field due to the decrease of the spin-splitting energy of the 2DEG. Since the weakened electric field decreases the zero-field spin-splitting energy, it is suggested that the zero-field spin splitting of the 2DEG in ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}∕\mathrm{Ga}\mathrm{N}$ heterostructures mainly arises from the Rashba effect.

Beating patterns in the oscillatory magnetoresistance originatedfrom zero-field spin splitting in AlxGa1−xN∕GaN heterostructures

Beating patterns in the oscillatory magnetoresistance in Al0.11Ga0.89N∕GaN heterostructures with one subband occupation have been investigated by means of temperature dependent Shubnikov–de Haas measurements at low temperatures and high magnetic fields. The zero-field spin splitting effect is observed by excluding the magnetointersubband scattering effect. The obtained zero-field spin splitting energy is 2.5meV, and the obtained spin-orbit coupling parameter is 2.2×10−12eVm. Despite the strong polarization-induced electric field in the heterostructures, the spin-orbit coupling parameter in AlxGa1−xN∕GaN heterostructures is smaller than that in other heterostructures, such as InxGa1−xAs∕InyAl1−yAs ones. This is due to the large effective mass of the two-dimensional electron gas and the large GaN energy band gap in AlxGa1−xN∕GaN heterostructures. With an increase in magnetic field, the spin splitting energy becomes smaller. The zero-field effect is still the dominant mechanism in AlxGa1−xN∕GaN heterostructures at a magnetic field as high as 4.4T.

Microwave induced Shubnikov–de Hass-type oscillation in InGaAs/InAlAs heterostructures

Microwave photoconductivity measurements of InGaAs/InAlAs and GaAs/AlGaAs heterostructures were carried out to investigate electronic spin states. In far-infrared magneto-optical absorption measurement, we confirmed a zero-field spin-splitting energy of the InGaAs/InAlAs heterostructure is 9 meV. In microwave modulated photoconductivity measurements, Shubnikov–de Haas oscillation was observed with quite high sensitivity. The energy of the sample was also determined from the oscillation. A dip structure was observed near cyclotron resonance field. By comparing with the result in GaAs/AlGaAs heterostructures and considering the heating effect by microwave irradiation, the origin of the Shubnikov–de Haas-type oscillation and the appearing dip structure are discussed.

Classical in-plane negative magnetoresistance and quantum positive magnetoresistance in undoped InSb thin films on GaAs (1 0 0) substrates

Magnetoresistance (MR) effects have been investigated in perpendicular and parallel magnetic fields at 300, 80 K and liquid He temperatures for undoped InSb thin films 0.1– 2.3 μm thick grown on GaAs(1 0 0) substrates by MBE. At high temperatures, the intrinsic carriers show the parabolic negative MR observable only in magnetic fields parallel to the film. The skipping-orbit effect due to surface boundary scattering in the classical orbits in the plane vertical to the film has been argued to be responsible for the negative MR. At low temperatures (T=80 K) , the transport is dominated by the two-dimensional (2D) electrons in the accumulation layers at the InSb/GaAs(1 0 0) hetero interface; MR is positive and shows a logarithmic increase with anisotropy between parallel and perpendicular field orientation, arising from the 2D weak anti-localization (WAL) that reflects the interplay between the spin-Zeeman effect and strong spin–orbit interaction caused by the asymmetric potential at the interface (Rashba term). The zero-field spin splitting energy of Δ 0∼13 meV , the electron effective mass of m ∗∼0.10m 0 seven times of the band edge mass in bulk InSb and the effective g-factor of |g ∗|∼15 in the accumulation layer have been inferred from fits of MR for the 0.1 μm thick film to the 2D WL theory.

Rashba spin-splitting energies probed by anti-weak-localization analysis in symmetric and asymmetric InGaAs/InAlAs quantum wells

The values of the zero-field spin-splitting energy Δ 0 in InAlAs/InGaAs/InAlAs heterostructures are investigated using anti-weak-localization analysis. The obtained values for Δ 0 are compared with values that were theoretically predicted assuming Rashba spin–orbit coupling (denoted by Δ R). The good agreement between Δ 0 and Δ R and their dependence on quantum well asymmetry suggest that our approach provides a useful tool for designing future spintronics devices using Rashba spin–orbit coupling.