**Artificial magnetic field in spin-orbit coupled semiconductors and new devices for spin electronics**

By: Victor Galitski

Conventional electronic devices are based on the transport of charged carriers (electrons or holes) in metals and semiconductors. Now, condensed matter physicists are trying to use another route to create a new generation of spintronic devices by using the quantum degree of freedom of the electron – spin – rather than its charge. Much of the recent work in this direction has concentrated on the theoretical understanding and experimental development of mechanisms to electrically manipulate the spin degree of freedom in non-magnetic systems. An important recent experimental discovery is that by applying an electric field, one can achieve electron-spin polarization near the edges of semiconductor structures with spin-orbit interactions (see Fig. 1). This remarkable phenomenon, dubbed the spin Hall effect, has a great potential for technological applications (sensing technologies, novel memory devices, quantum computing, etc.), primarily because it is compatible with existing semiconductor technologies. Apart from the purely technological interest, understanding spin transport is a very interesting problem from the theoretical point of view.

Figure 1: Electrically induced electron-spin polarization near the edges of a semiconductor channel (Kato *et al.*, Science **306**, 1910, 2004)

The key to understanding electric-field-induced spin accumulation in semiconductors is spin-orbit interaction, which couples the electron’s momentum and spin. It turns out that non-trivial spin transport in clean spin-orbit coupled systems is due to so-called Berry’s phase, which is a beautiful and unusual quantum-mechanical effect. To understand the latter effect, one has to recall that the properties of a quantum particle (such as the electron) are described in terms of a wave-function, which has an absolute value and a phase. In 1984, Michael Berry showed that if one very slowly (adiabatically) changes the properties of a quantum system so that in the end of the adiabatic evolution all parameters return to their initial values, the wave-function does not necessarily returns to its original value, but may acquire an additional phase (now known as the Berry’s phase). This phase has a very elegant mathematical interpretation: If we imagine that the relevant parameters describing the system form a vector space (just like the coordinates x, y, and z form a three-dimensional space in which we live), the adiabatic evolution of the system would be described as a loop in this space. Remarkably, the Berry’s phase can be interpreted as a flux of a fictitious magnetic field in this parameter space through the area enclosed by the loop. This strange “magnetic field” occurs due to “magnetic charges” or monopoles, which are located in the points where the spectrum is degenerate (energy of the quantum particle has special degenerate values). What does it have to do with the electron in a semiconductor? If there were no spin-orbit interactions, the electron spectrum would be the familiar parabolic dispersion, which will be the same for the electrons with up and down spins. However, once spin-orbit interaction appears, it splits the dispersion into two curves (see Fig. 2), which originate from the electrons with different projections of spin. These two bands cross at a degeneracy point, which serves a source of an artificial magnetic field in momentum space. The latter affects the motion of electrons with opposite spin projections differently. In the presence of an external electric field, electrons with opposite spin projections flow in the opposite directions and eventually lead to measurable spin polarizations near the edges of the sample.

Figure 2: Electron spectrum in the presence of spin-orbit interactions. The coupling between the momentum and spin splits the conventional parabolic dispersion into two bands, which cross at a degeneracy point. This degeneracy point serves as a source of an artificial magnetic field in momentum space.

We, at the University of Maryland, have been trying to understand spin transport and electric-field-induced spin accumulation in realistic disordered spin-orbit coupled systems. All real materials contain impurities and other defects, which strongly affect the above-mentioned picture of spin transport based on the Berry’s phase. Electrons scatter off of the impurities and each scattering sharply changes the momentum. Due to the spin-orbit interaction, this also leads to a sharp and random change in the spin precession axis. Thus, in the presence of disorder, the electron spin precesses in a random fashion. This spin dynamics can be visualized as diffusion or random walk of the spin on a sphere. For example, if we start with the state in which the electron’s spin points in the up direction (toward the North pole of the sphere), after a few scatterings, the spin will deviate from its original direction. Eventually, spin diffusion will lead to complete spin relaxation. In our research, we have been studying different mechanisms of spin relaxation and in particular looking for ways to minimize its negative effects. It has been shown that by considering different types of spin-orbit interactions and boundary structures, one can find optimal conditions, which would enhance the desired effect of spin accumulation. This opens a new exciting opportunity for engineering of new spintronic devices.

*Dr. Galitski is an Assistant Professor of Physics at the University of Maryland. He is a member of the Condensed Matter Theory group. If you would like to contact him, please send any questions or comments to the Editor . *