Spintronics without Magnetism ?

J. Hugo Dil, Physik-Institut, Universität Zürich, 8057 Zürich, and Swiss Light Source, Paul Scherrer Institute, 5232 Villigen PSI

Introduction

Spintronics is the vision of using the spin of the electron rather than its charge to control information flows, which can be exploited in a future quantum computer. In the field of data storage, spintronics has already become reality; the giant magnetoresistance effect, for the discovery of which Fert and Grünberg received the 2008 Nobel prize, is used in modern memory devices. Currently many researchers are working on systems where small magnetic structures are used to design a complete spintronics ensemble. The magnetic moments of the electrons, i.e. the spin, lead to a net magnetization in these structures. As we know from our basic physics lectures the spin of an electron can in the simplest approach be manipulated by magnetic fields. Here we will discuss a possible alternative which is fully based on non-magnetic materials and utilizes the spin-orbit interaction in low-dimensional structures to control the electron spin. The advantage of this approach is that it can lead to reduced information processing time at even lower energy consumption and is as such highly interesting and promising for future applications.

For any useful spin computer one needs at least the following components:

1. The manipulation of the electron spin in a controlled way.
2. The creation of a spin-polarized current from a non-polarized source of electrons; i.e. a spin filter.
3. The coherent transport of spin-polarized electrons over macroscopic distances without the loss of information.
4. The storage of information on macroscopic time scales.

Because spin-orbit interaction is a dynamic process it is diffcult to envisage spin-storage based on such an effect, as data storage requires a steady state solution and thus will most likely remain based on magnetic structures. The possible realization of the other three components without magnetic materials is discussed in the next sections.

Spin manipulation; the Rashba effect

Spin manipulation without magnetic fields relies on spin-orbit coupling. A promising candidate to achieve a controlled manipulation is the Rashba effect, which relies on the breaking of space inversion symmetrie, as will be explained below.
In many cases the surface of a metal (or semiconductor) crystal is not just a truncation of the bulk. For instance at semiconductor surfaces the dangling bonds which are formed due to the sudden truncation of the crystal, induce a rearrangement of the atoms to lift these free bonds. Furthermore due to the confinement between a projected band gap and the image potential, surface states can form, which have totally different properties as the electronic states in the bulk material. In both cases the main cause of the differences is that at the surface the translational symmetry is broken along the surface normal, or, more general, that the space inversion symmetry is broken.
For an electron with a given momentum and spin space inversion symmetry means that it is equivalent whether the electron moves in one direction or the other; i.e. . In the absence of a magnetic field, time inversion symmetry holds; i.e. . In the bulk of a non-magnetic, centrosymmetric metal both time and space inversion symmetry are observed, resulting in the formation of spin-degenerate states For states located at a surface or interface (e.g surface states or quantum well states) the space inversion symmetry is actually broken, which means that the spin degeneracy does not necessarily hold for these states.

The use of this Rashba-type spin-splitting to manipulate the spin of an ensemble of electrons is based on basic quantum mechanical arguments and follows the lines of a proposal from 1990 [2]. An electron with its spin along the positive z axis can be decomposed into electrons with spins along the y axis, reading .

Similarly, a spin along x can be written as

A phase difference between thus causes a rotation in the xz plane. This phase difference is exactly what is accumulated along an electrons path through a solid due to the different vectors at a given energy (typically Fermi energy) of the bands with opposite spin. As a result, the spin of an electron travelling through this Rashba medium will rotate as a function of distance travelled, where the amount of rotation depends on the momentum difference between the two parabolae; i.e. 2k₀. The goal is now to manipulate this momentum splitting by an external parameter so that one can directly control the spin of an electron at the end of this medium. While this can be done by a gate voltage for some structures, we will here discuss the influence of structural changes. In our group we have shown by spin and angle-resolved photoemission that the Rashba splitting can be tuned by mixing different amounts of Pb and Bi on a Ag(111) surface [3]. Furthermore we have found that the spin-splitting of quantum well states in thin Pb films on Si(111) shows a strong dependence on the interface barrier [4] and may thus be tuned through the charge density in the substrate.

Spin injection and transport

A spin injector or spin filter can be defined as a medium which creates a current with a certain degree of spin-polarization from an initially unpolarized current. In a magnetic material this is achieved through the difference in density-of-states (DOS) of the majority and minority spin states at the Fermi level. As a result of the Rashba effect the density-of-states of the nearly two-dimensional electron gas is no longer constant, but shows a strong energy dependence as depicted in Fig. 1(b). Between the crossing point of the two parabolae and the band apex the DOS shows a Van Hove type singularity, which is predicted to have substantial influence on the electronic properties through the enhanced electron-phonon coupling. An other interesting situation arises exactly at the crossing point , here the DOS of one spin orientation vanishes whereas the other spin direction has a large DOS. At the interface between a Rashba medium and a normal metal the spin polarization of a current accross this interface can be as large as 80% [3]. Depending on the polarity of a voltage accross the interface, a Rashba-spin-degenerate metal interface can either be used as a spin injector or acceptor.

This mechanism functions even better if the DOS of one spin direction would not only go to zero, but if the band would not be present around the Fermi level at all. This is exactly what happens for the novel class of materials called topological insulators [5]. In a simple picture a topological insulator is a band insulator with a metallic surface which supports an odd number of spin polarized states for any momentum direction. Although some of these spin channels will ”cancel“ with channels with opposite spin, there will always be at least one spin polarized channel left over. Because time-inversion symmetry still hold this state forms a pair (Kramers pair) with a state with opposite momentum and spin. If an electron encounters an impurity it is typically forced to partly reverse its direction of motion, which causes an decrease in conductance. For an electron travelling in one of the channels of a topological insulator a reversal of direction means that it would also have to flip its spin, which is extremely unlikely in the absence of magnetic impurities. As a result, the conductance is hardly influenced by non-magnetic impurities and one could expect a very efficient spin transport, without the loss of information.
In our group we have studied several topological insulators or their parent compounds using spin and angle resolved photoemission. The advantage of this technique is that one can directly identify the number of Fermi level crossings including their spin polarization. First conclusive results were obtained for pure Sb and a BiSb alloy [6], where the correct topology could be identified but which has only a bulk band gap of 50 meV and as much as five Fermi crossings. The next generation of topological insulators is formed by BiSe and related compounds with only one spin polarized state at the Fermi level and a bulk band gap of 350 meV [7]. The advantage of the latter compounds is that through bulk and surface doping the bands can be aligned such as to achieve the required conditions.