Spin-orbit coupling is a first order correction to the Hamiltonian due to relativity. You can think of it as the electric fields being "seen" as magnetic fields by moving electrons. In this sense, it allows the control of spins without using real magnetic fields. In this section, we show that strain can largely modify such an effect, and that it can be used to efficiently manipulate spin states within epitaxial layers of GaAs and InGaAs.
The sample structure is shown above. We have made a window by removing the GaAs substrate in that region. The AlGaAs layer pops up, possibly due to its larger lattice constant or its oxidation. The GaAs channel which sits on top is therefore strained.
The right figure shows the spatiotemporal evolution of optically injected spins in the absence of magnetic fields in such a device. The applied electric field drags the electrons, faster with increasing electric fields as seen before. At the same time, the signal changes sign for large electric fields, implying spin precession. Indeed, the linecuts shown in panel e demonstrate spin precession at zero magnetic field.
In order to characterize the effective magnetic field, field sweeps at a fixed delay are taken. Panel a shows the field sweeps for various geometries. The top curve is when the electric field is zero, and the sharp peaks are due to RSA. The data is symmetric around zero magnetic field, but upon application of electric field, a shift occurs (middle curve) or the center peak is suppressed (bottom curve). These changes are due to the effective magnetic field being parallel (middle curve) or perpendicular (bottom curve) to the external magnetic field. The bottom geometry is used to determine the strength of the effective magnetic field. In panels b and c, field scans at various pump-probe separation and the results of the fits are shown, respectively. The effective magnetic field varies along the position within the spin packet due to spin diffusion. We repeat such measurements for various electric fields (panels d and e), and characterize the effect using the average spin splitting (panel f).
In the figure below, field scans for various electric fields are shown to demonstrate the equivalence of the two fields. In the upper panel, the electric field and the magnetic field are parallel, so that the equal phase contour becomes an ellipse. In the lower panel the electric field and the magnetic field are perpendicular, so the equal phase lines are straight and diagonal. In this measurement, pump-probe distance is adjusted at each electric field so that the probe is always at the center of the spin packet.
Surprisingly, the origin of this effect turns out to be strain. The samples without the windows barely show spin splittings (figure below).
Strain can also be introduced into a heterostructure by using materials with a lattice mismatch. We prepared InGaAs grown on top of GaAs, and results from two representative samples (200 nm InGaAs and 2000 nm InGaAs with In concentration of 7%) are shown below. Here, we also notice that the effects differ along the two crystal directions that the electric fields are applied. On the right side, x-ray diffraction data is shown. The vertical axis is the growth direction, and the horizontal axis is the [1 -1 0] direction in reciprocal space. The position of the InGaAs peak is different, indicating different strain in each epilayer due to different degrees of strain relaxation. The vertical line indicates the coherently strained case (thus having the same in-plane lattice constant as the substrate,) and the diagonal line shows where the peaks for a cubic lattice should appear (completely strain-relaxed case).
The observed effective magnetic field can also be used to electrically drive spin resonance. In the geometry of panel a inset, we observe sharp peaks in Faraday rotation at a negative delay of -50 ps. The position of the peak shifts with microwave frequency (panel b), and the slope gives a g-factor of -0.441. At higher powers, the Faraday rotation changes sign, indicating a nutation angle of more than 90 degrees (panel c and d).
To learn more about our studies, please refer to "Coherent spin manipulation without magnetic fields in strained semiconductors", Y. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, Nature 427, 50 (2004). Previous Research Index Related Publications Next