The alphabet of spin in nanostructures

Abstract

In a ferromagnetic nanostructure, a domain wall is a transition region that separates two different but uniformly magnetized regions. Moving a domain wall with an electrical current instead of a magnetic field is of great appeal to researchers; it could lead to spin-based devices in which information is stored and processed in domain walls. Such storage, memory, and logic devices could potentially be more flexible, efficient, and scalable. The mechanism underlying this motion is called the spin-transfer torque, in which conduction electrons transfer a spin angular momentum to the local magnetization. The torque comes in an adiabatic and a so-called nonadiabatic part. There is much debate regarding the magnitude [1–5], microscopic origin [6–8], and even the existence [9] of the nonadiabatic term. In a paper in Physical Review Letters, Lutz Heyne and co-workers at the Universitat Konstanz in Germany, along with collaborators in Switzerland, the US, and Germany [10], tell us how they measure the torque with a scheme [11] that involves displacing a single magnetic vortex by electrical current. They find a surprisingly large nonadiabaticity—favorable for spintronic devices based on domain walls—that not only dictates how quickly a domain wall moves but allows it to do so in the absence of applied magnetic fields, even for very small currents. An intuitive phenomenological theory addresses the underlying physics. The Landau-Lifshitz-Gilbert (LLG) equation describes the evolution of magnetization in time: the magnetization vector precesses around any magnetic field that is present, eventually aligning with it as energy dissipates through dampening of the precession. In addition to the magnetization and the magnetic field, two quantities come into play: γ, the gyromagnetic ratio that determines the frequency of precession, and α, the parameter that describes the damping efficiency. As a spin-polarized current flows through a ferromagnet, the traveling spins tend to align with the magnetization. If the local magnetization direction changes, such as in a domain wall, angular momentum conservation requires the spins to exert a torque on the magnetization. This may result in domain-wall motion. This interaction is intricate, and two spin-transfer torque terms had to be incorporated into the LLG equation to describe it [6, 12]. The first term is adiabatic: it describes the effect of spins as they move and adapt to locally varying magnetization. It is an “antidamping” term that is, like standard damping, proportional to α, and contains no free spin-torque parameters. As noted in the paragraph above, the origin of the second term is unfortunately less clear. It has, for instance, been attributed to spin-flip scattering, which prevents the conduction electron spins from fully aligning with the magnetization [6] (hence dubbed “nonadiabatic”). This term introduces β [12], the nonadiabaticity parameter, which is expected to be large for large magnetization gradients or narrow domain walls. The spintronics community is intrigued by both the absolute sizes as well as the ratio of these two terms, as illustrated by the large number of ongoing theoretical and experimental studies. These two terms determine the ease with which domain walls can be pushed along by current pulses.