Theory of current induced domain wall motion
When a current is passed to a ferromagnetic wire that contains domain walls, the flowing electrons exert a pressure on the domain wall that tends to drive the domain wall in the direction of the electron flow. This current control of domain wall motion is proposed as a basis for a memory device in which the information is stored in magnetic domains. The domain walls between the domains can be moved past a read out device by a current flowing through the wire. Such a device could potentially have a high storage density, fast read out, and non-volatility. Such current induced domain wall motion is currently studied in the Electron Physics Group using Scanning Electron Microscopy with Polarization Analysis (SEMPA).
Experimentally, current induced domain wall motion is typically studied in lithographically defined, narrow magnetic wires. The wires are frequently curved or the ends are designed to make it possible to controllably introduce a domain wall into the wire using an applied field. The position of the domain walls can be imaged using techniques such as Magnetic Force Microscopy (MFM) or Scanning Electron Microscopy with Polarization Analysis (SEMPA). Measuring the position before and after a current pulse with a technique like Scanning Electron Microscopy allows an estimate of the wall velocity. Alternatively, the location of the wall could be determined in real time using the Magneto-Optic Kerr Effect (MOKE) or electrically using GMR sandwich structures or through the extra resistance due to anisotropic magnetoresistance (AMR) in a domain wall. Using these various techniques, experimentalists typically determine the wall velocity as a function of current and applied magnetic field and compare with theoretical predictions.
To a first approximation, current induced domain wall motion is quite simple. The flowing electron spins adiabatically follow the magnetization direction because the magnetization exerts a torque on them. There is a reaction torque on the magnetization that is proportional to the current. If the current is uniform, this torque density simply translates the domain wall in the direction of electron flow with a speed that is proportional to the current. There are several factors that complicate this simple description, including damping, non-adiabatic torques, and extrinsic effects like pinning.
A schematic view of the magnetization direction in a domain
wall (red) in a narrow wire. As electrons flow through the domain
wall, their spins (blue) remain aligned with the magnetization due to
a torque exerted by the magnetization. The reaction torque on the
magnetization tends to translate it.
We have computed the degree to which the spin adiabatically follow the magnetization. The deviations are small except for rather narrow domain walls. When they are non-negligible, the adiabatic torque becomes non-local and there is a additional non-local torque perpendicular to the adiabatic torque. This torque is referred to as a non-adiabatic torque because it derives from the inability of the electron spins to adiabatically follow the magnetization direction. For realistic walls, this correction is not important.
The theoretical description of current induced domain wall motion has lead to significant debate associated with how to describe the damping and whether there is an additional torque in the direction of the non-adiabatic torque that arises from the same processes that lead to damping. Even though this torque is physically distinct from the non-adiabatic torque discussed above, it is in the same direction and is frequently called a non-adiabatic torque and less frequently the beta term. It is closely tied to the description of the magnetization damping. The two most commonly used descriptions of the damping are due to Landau and Lifshitz and to Gilbert. In the absence of current induced torques, these can be shown to be equivalent. They remain equivalent in the presence of spin transfer torques, but with different values of this non-adiabatic torque. We argue that the Landau-Lifshitz form of the damping gives a more physical description of current induced domain wall motion. This description emphasizes the importance of the adiabatic torque, which is much larger than its non-adiabatic counterpart.
Adiabatic Domain Wall Motion and Landau-Lifshitz Damping
Spin Transfer Torque for Continuously Variable Magnetization
Mark D. Stiles
Andy Zangwill - Georgia Institute of Technology
Jiang Xiao - Delft University of Technology
Wayne Saslow - Texas A&M University
Michael Donahue - NIST
Online: October 2007
Last Updated: February 2008
Website comments: epgwebmaster@nist.gov