SPINTRONICS

Spintronics (slide) is a new branch of electronics in which electron spin, in addition to charge, is manipulated to yield a desired outcome. All spintronic devices act according to the simple scheme: (1) information is stored (written) into spins as a particular spin orientation (up or down), (2) the spins, being attached to mobile electrons, carry the information along a wire, and (3) the information is read at a terminal. Spin orientation of conduction electrons survives for a relatively long time (nanoseconds, compared to tens of femtoseconds during which electron momentum decays), which makes spintronic devices particularly attractive for memory storage and magnetic sensors applications, and, potentially for quantum computing where electron spin would represent a bit (called qubit) of information. |
We reviewed the mechanisms of spin relaxation, and efforts (both experimental and theoretical) to enhance the spin memory of conduction electrons in metals and semiconductors, in J. Fabian and S. Das Sarma, J. Vac. Sc. Technol. B 17, 1708 (1999).

My own spintronics research concentrates on theoretical understanding of the ways the electron spins decay in metals and semiconductors (slide1,slide2). As was shown in the 50's and 60's by Overhauser, Elliott, and Yafet, there are two ways for spins to decay, and both include spin-orbit coupling of some kind. First, impurities can induce a spin-orbit interaction that can flip an electron spin. Second, a spin-orbit interaction can be induced by host-lattice ions. The second mechanism is the only important at high temperatures where electrons scatter off phonons, and also at low temperatures, if the impurities are light--have a small spin-orbit coupling. This second mechanism is somewhat tricky. One has to realize (as Elliott did first) that in the presence of a spin-orbit coupling, spin up and spin down states are no longer valid quantum numbers. Instead, new Bloch eigenstates are mixtures of spin up and down species, although almost always one of the species dominates and electrons can still be nicknamed "up" and "down." Now even scalar (spin-independent) interactions due to impurities or phonons can cause spins to flip (slide). First CESR (conduction electron spin resonance) experiments seemed to be consistent with the above--now called Elliott-Yafet-- picture, although no real calculation based on this mechanism had been done. One interesting observation of Yafet was that spin relaxation rate should be proportional to resistivity (or, momentum relaxation rate). The coefficient of proportionality is b2, which is the probability of finding a Bloch state with spin down, if the large amplitude is spin up (that is, the Bloch state is in state "up"). Monod and Beuneu set out to check this relation and thus also the whole Elliott-Yafet theory. They took b2 from atomic physics, collected then known data of spin relaxation rates of different metals, and tried to reproduce the Gruneisen behavior, as explained in the following Figures. The result was surprising: |
| Vertically this figure plots spin relaxation rate (Gs) divided by spin-orbit-coupling strength (b2) and resistivity at Debye temperature TD. Horizontal scale is given by the reduced temperature, T/TD. Monod and Beuneu expected that data for all metals will fall onto a single, Gruneisen-like curve. Only alkali and noble metals followed the expected behavior.
| This is what Monod and Beuneue expected to find: a nice Gruneisen scaling valid for all (simple) metals. Reduced resistivity R/RD (RD is the resistivity at TD) is plotted as a function of reduced temperature T/TD and is found to be a single, universal function of T/TD, as first noticed by Gruneisen.
Together with S. Das Sarma, I explained the Monod-Beuneu surprising result by pointing out that the two groups of metals (one that follows the scaling and one with spin relaxation rates off by orders of magnitude) have different valence: monovalent metals (Na, Cu, ...) follow the Gruneisen behavior, while polyvalent metals (Al, Pd, Be, and Mg) do not. What is so peculiar about polyvalent metals? Band structure. Because of complicated character of Bloch bands in polyvalent metals one cannot use b2 from atomic physics. Instead, b2 is band-renormalized by the presence of band-structure anomalies--spin hot spots. Spin hot spots are points on the Fermi surface where the surface cuts through a Brillouin zone boundary, special symmetry point, or a line of accidental degeneracy. If an electron jumps from (or, into) a spin hot spot, the electron's spin flips with much larger probability than usual. Since the resulting spin-flip probability is an average over the whole Fermi surface, on has to know how big the spin hot spots are. We showed that they are big enough to completely monopolize spin relaxation: to calculate the average it suffices to count contributions from the spin hot spots only. |
| The spin-hot-spot model was introduced to explain the Monod-Beuneu scaling. For alkali and nobel metals, which are monovalent, an electron performing a random walk on the Fermi surface has a small chance of flipping its spin everywhere on the surface. All Fermi states are equivalent. By contrast, polyvalent metals (like Al, Be, Mg, and Pd from the Monod-Beuneu graph) have the so called spin hot spots (red) where a chance of a spin flip is much greater, by several orders of magnitude
The following Figures illustrate the occurence of spin hot spots on the Fermi surface of Aluminum. |
| The stereograph of the almost spherical Fermi surface of Aluminum. The center of the stereograph is the north pole, the circumference is the equator. The Fermi surface cuts through Brillouin zone boundaries at white areas (here the Bragg scattering makes some spherical angles unaccessible for electrons). The blue part is the second band, the red is third (the first band is completely occupied--aluminum has 3 valence electrons).
| A quarter of the above stereograph with only spin hot spots (points with the largest spin-flip probabilities) shown. Violet points are at Brillouin zone boundaries, blue, green,and yellow are around accidental degeneracy points which are red.
Spin-hot-spot model is a general concept that explains the details of spin relaxation in metals within the framework of the Elliott-Yafet mechanism. A real calculation that would clearly show, without any fitting or adjusting, that the mechanism works, was still lacking. We therefore decided to do such a calculation and chose aluminum, for it is both simple to calculate and complicated enough (polyvalent) to exhibit the spin-hot-spot model attributes. We used realistic pseudopotentials to model electron-ion interaction (which included the spin-orbit interaction) and electronic band structure, realistic empirical force constants between aluminum ions to get a good phonon structure, some techniques to calculate Fermi surface averages (the tetrahedron summation with an adaptive mesh), and got a wonderful curve which is in excellent agreement with experiment. In addition, our curve predicts what spin relaxation time T1 should be at room temperature, since no experiments there exist. Below I also show our calculated spin-flip Eliashberg function, which we used to get the final curve for T1. |
| Here I plot spin relaxation time T1 of aluminum in nanoseconds (on a logarithmic scale) versus temperature in Kelvins. The solid curve is our first-principles calculation. Symbols come from two measurements: spin injection (Johnson and Silsbee) and CESR (Lubzens and Schultz). The agreement between theory and experiment is very good, showing, for the first time, that the Elliott-Yafet mechanism and the spin-hot-spot model work.
| Spin-flip Eliashberg function is a somewhat advanced concept. It essentially measures how effective phonons with given frequency (Omega--horizontal scale) are in scattering electrons in such a way that the electrons' spins flip. Here I plot it for aluminum (solid line). The long-dashed curve is phonon density of states (F) and short-dashed curve is ordinary (non-spin-flip) Eliashberg function which plays important role in superconductivity.
Currently, we explore methods of generating spin-polarized currents in electronic materials. We try to figure out ways in which such currents would last "forever," and do not decay within T1 times as in current methods. We already found that this is possible and prepare our findings for publication. |
The spin-hot-spot model was introduced in J. Fabian and S. Das Sarma, Phys. Rev. Lett. 81,5624 (1998). The first realistic calculation of the spin relaxation time in a metal (aluminum) was reported in J. Fabian and S. Das Sarma, Phys. Rev. Lett. 83, 1211 (1999). A semi-popular account of how band-structure affects spin relaxation is in J. Fabian and S. Das Sarma, J. Appl. Phys. 85, 5075 (1999). Our theory is reviewed in J. Fabian and S. Das Sarma, J. Vac. Sc. Technol. B 17, 1708 (1999).