Spin Relaxation Mechanisms in the Organic Semiconductor Alq3

1. Introduction

The field of “spintronics” has always been driven by the motivation to use the spin degree of freedom of a single electron, or a collection of electrons, to store, process, sense and communicate information. Information is encoded in the spin polarization of the electron(s), then “processed” using spin-spin or spin-orbit interactions, subsequently communicated over long distances using spin waves or spin chains, and finally sensed using techniques that are able to measure spin polarizations or single or multiple electrons. A well known embodiment of this idea is the Single Spin Logic (SSL) paradigm (Bandyopadhyay et al., 1994) where a single electron’s spin polarization is rendered “bistable” by placing it in a static magnetic field. The polarization can point either parallel to the direction of the magnetic field, or anti-parallel to it, since only these two polarizations are allowed eigenstates. By engineering the interactions between nearest neighbor spins, it is possible to implement (classical) digital Boolean logic gates and combinational logic circuits for universal computation (Bandyopadhyay et al., 1994; Bandyopadhyay, 2005; Agarwal & Bandyopadhyay, 2007). These circuits have the advantage of being extremely energy efficient and amenable to high levels of integration, which results in much enhanced computational prowess (Cahay & Bandyopadhyay, 2009).

The most important concern in all such approaches is preserving the fidelity of the data that is being processed. The processed information must remain intact during the entire computational cycle, which can happen only if spin does not flip spontaneously while computation takes place. Coupling of an electron’s spin with the environment can randomly flip the spin, leading to errors in the computation. The probability of such an error occurring during one computational cycle is, (1) where T is the duration of a computational cycle (typically the period of the clock that drives the computation) and T_s is the spin relaxation time. In order to make the error probability as low as possible, we will have to make T_s as long as possible and/or T as short as possible.

There are two distinct types of spin relaxation time T_s that matter. To understand them, consider the fact that an electron’s spin is a quantum mechanical entity and can exist in a state that is a coherent superposition of two mutually anti-parallel polarizations, which we will label as “up” and “down”. An arbitrary spin can therefore be written as, (2) wheredenotes the “up” polarization and denotes the “down” polarization. The coefficients a and b are complex quantities. Because of this property, an electron’s spin is able to represent a quantum bit (or “qubit”) which is a coherent superposition of the classical binary bits 0 and 1. If we encode the classical bit 0 in the up-polarization and the classical bit 1 in the down-polarization, then a spin can represent the qubit