Tuning of the spin-orbit interaction in two-dimensional GaAs holes via strain

Abstract

We report direct measurements of the spin-orbit interaction induced spin-splitting in a modulation-doped GaAs two-dimensional hole system as a function of anisotropic, in-plane strain. The change in spin-subband densities reveals a remarkably strong dependence of the spin-splitting on strain, with up to about 20% enhancement of the splitting upon the application of only about 2 × 10 −4 strain. The results are in very good agreement with our numerical calculations of the strain-induced spin-splitting.

Strain-modulated anomalous circular photogalvanic effect in p-type GaAs

“…When a uniform strain of 10 −4 order is applied, the variation in the SOC coefficient was approximately 55%, which is obtained by dividing the uniform-strain-induced ACPGE currents by the ACPGE currents without strain. The strain-enhanced SOC coefficients of previous studies show an approximately 20% enhancement in splitting upon the application of approximately 2 × 10 −4 strain in two-dimensional GaAs [19] and up to 55% with a shear strain of 2.7 × 10 −4 in GaN [20]. The variation in SOC splitting measured in our experiment is similar to that reported in previous studies.…”

Strain-modulated anomalous circular photogalvanic effect in p-type GaAs

“…When a uniform strain of 10 −4 order is applied, the variation in the SOC coefficient was approximately 55%, which is obtained by dividing the uniform-strain-induced ACPGE currents by the ACPGE currents without strain. The strain-enhanced SOC coefficients of previous studies show an approximately 20% enhancement in splitting upon the application of approximately 2 × 10 −4 strain in two-dimensional GaAs [19] and up to 55% with a shear strain of 2.7 × 10 −4 in GaN [20]. The variation in SOC splitting measured in our experiment is similar to that reported in previous studies.…”

Spin–orbit interaction and transport in GaAs two-dimensional holes

“…Second, we emphasize that despite the uncertainty in the absolute value of the strain (see footnote 5), the overall agreement of the experimental and calculated spin-splitting, including its strain dependence, is remarkable. Furthermore, our measurements on a different sample with the piezo-stack's poling direction aligned to the [ 2 3 3] crystal direction showed similar results and matched well with the corresponding calculations [11].…”

“…Most importantly, the strain enhancement of the spin-splitting for the 2D holes is about 100 times larger than for 2D electrons [54] and, moreover, is essentially independent of the strain direction. Combined, our results establish the extreme sensitivity of the SO coupling in 2DHSs to strain and demonstrate the potential use of the 2D holes for spintronic and related applications [11]. In addition, in this section we report a large piezoresistance effect in 2DHSs.…”

“…The results show a significant (about 20%) enhancement of spin-splitting with strain. SdH oscillations measured in the [ 2 3 3] direction show the same amount of spin-splitting, consistent with the fact that f is related to the areas of the Fermi contours of the two spin subbands[11].We adapted our theoretical model to the (3 1 1) orientation of our sample by a suitable coordinate transformation and incorporated the strain Hamiltonian of Bir and Pikus[29] into our calculations of the magneto-oscillations of the DOS at E F . Figure6presents our calculated f (solid curves) as a function of strain for three different 2DHS densities.…”

Hole spin helix: Anomalous spin diffusion in anisotropic strained hole quantum wells

“…However recent experiments performed by attaching a piezo to hole-doped GaAs samples have revealed that strain can be used to cause large changes in the spin orbit interaction [18][19][20][21]. The experimental results largely confirm the standard Kane and Luttinger k · p Hamiltonian which predicts that strain and anisotropy substantially deform the two heavy hole Fermi surfaces [18,19,21,22].…”

Strain-modulated anomalous circular photogalvanic effect in p-type GaAs

“…When a uniform strain of 10 −4 order is applied, the variation in the SOC coefficient was approximately 55%, which is obtained by dividing the uniform-strain-induced ACPGE currents by the ACPGE currents without strain. The strain-enhanced SOC coefficients of previous studies show an approximately 20% enhancement in splitting upon the application of approximately 2 × 10 −4 strain in two-dimensional GaAs [19] and up to 55% with a shear strain of 2.7 × 10 −4 in GaN [20]. The variation in SOC splitting measured in our experiment is similar to that reported in previous studies.…”

Spin–orbit interaction and transport in GaAs two-dimensional holes

“…Second, we emphasize that despite the uncertainty in the absolute value of the strain (see footnote 5), the overall agreement of the experimental and calculated spin-splitting, including its strain dependence, is remarkable. Furthermore, our measurements on a different sample with the piezo-stack's poling direction aligned to the [ 2 3 3] crystal direction showed similar results and matched well with the corresponding calculations [11].…”

“…Most importantly, the strain enhancement of the spin-splitting for the 2D holes is about 100 times larger than for 2D electrons [54] and, moreover, is essentially independent of the strain direction. Combined, our results establish the extreme sensitivity of the SO coupling in 2DHSs to strain and demonstrate the potential use of the 2D holes for spintronic and related applications [11]. In addition, in this section we report a large piezoresistance effect in 2DHSs.…”

“…The results show a significant (about 20%) enhancement of spin-splitting with strain. SdH oscillations measured in the [ 2 3 3] direction show the same amount of spin-splitting, consistent with the fact that f is related to the areas of the Fermi contours of the two spin subbands[11].We adapted our theoretical model to the (3 1 1) orientation of our sample by a suitable coordinate transformation and incorporated the strain Hamiltonian of Bir and Pikus[29] into our calculations of the magneto-oscillations of the DOS at E F . Figure6presents our calculated f (solid curves) as a function of strain for three different 2DHS densities.…”

Hole spin helix: Anomalous spin diffusion in anisotropic strained hole quantum wells

“…However recent experiments performed by attaching a piezo to hole-doped GaAs samples have revealed that strain can be used to cause large changes in the spin orbit interaction [18][19][20][21]. The experimental results largely confirm the standard Kane and Luttinger k · p Hamiltonian which predicts that strain and anisotropy substantially deform the two heavy hole Fermi surfaces [18,19,21,22].…”

Strain-modulated anomalous circular photogalvanic effect in p-type GaAs

“…When a uniform strain of 10 −4 order is applied, the variation in the SOC coefficient was approximately 55%, which is obtained by dividing the uniform-strain-induced ACPGE currents by the ACPGE currents without strain. The strain-enhanced SOC coefficients of previous studies show an approximately 20% enhancement in splitting upon the application of approximately 2 × 10 −4 strain in two-dimensional GaAs [19] and up to 55% with a shear strain of 2.7 × 10 −4 in GaN [20]. The variation in SOC splitting measured in our experiment is similar to that reported in previous studies.…”

Spin–orbit interaction and transport in GaAs two-dimensional holes

“…Second, we emphasize that despite the uncertainty in the absolute value of the strain (see footnote 5), the overall agreement of the experimental and calculated spin-splitting, including its strain dependence, is remarkable. Furthermore, our measurements on a different sample with the piezo-stack's poling direction aligned to the [ 2 3 3] crystal direction showed similar results and matched well with the corresponding calculations [11].…”

“…Most importantly, the strain enhancement of the spin-splitting for the 2D holes is about 100 times larger than for 2D electrons [54] and, moreover, is essentially independent of the strain direction. Combined, our results establish the extreme sensitivity of the SO coupling in 2DHSs to strain and demonstrate the potential use of the 2D holes for spintronic and related applications [11]. In addition, in this section we report a large piezoresistance effect in 2DHSs.…”

“…The results show a significant (about 20%) enhancement of spin-splitting with strain. SdH oscillations measured in the [ 2 3 3] direction show the same amount of spin-splitting, consistent with the fact that f is related to the areas of the Fermi contours of the two spin subbands[11].We adapted our theoretical model to the (3 1 1) orientation of our sample by a suitable coordinate transformation and incorporated the strain Hamiltonian of Bir and Pikus[29] into our calculations of the magneto-oscillations of the DOS at E F . Figure6presents our calculated f (solid curves) as a function of strain for three different 2DHS densities.…”

Hole spin helix: Anomalous spin diffusion in anisotropic strained hole quantum wells

“…However recent experiments performed by attaching a piezo to hole-doped GaAs samples have revealed that strain can be used to cause large changes in the spin orbit interaction [18][19][20][21]. The experimental results largely confirm the standard Kane and Luttinger k · p Hamiltonian which predicts that strain and anisotropy substantially deform the two heavy hole Fermi surfaces [18,19,21,22].…”