Mark D. Stiles

Spin transfer torques

This tutorial article introduces the physics of spin transfer torques in magnetic devices. Our intention is that it be accessible to beginning graduate students. We provide an elementary discussion of the mechanism of spin transfer torque and review the theoretical and experimental progress in this field. This article is meant to set the stage for the articles which follow in this volume of the Journal of Magnetism and Magnetic Materials, which focus in more depth on particularly interesting aspects of spin-torque physics and highlight unanswered questions that might be productive topics for future research.

Anatomy of Spin-Transfer Torque

Spin-transfer torques occur in magnetic heterostructures because the transverse component of a spin current that flows from a nonmagnet into a ferromagnet is absorbed at the interface. We demonstrate this fact explicitly using free-electron models and first-principles electronic structure calculations for real material interfaces. Three distinct processes contribute to the absorption: (1) spin-dependent reflection and transmission, (2) rotation of reflected and transmitted spins, and (3) spatial precession of spins in the ferromagnet. When summed over all Fermi surface electrons, these processes reduce the transverse component of the transmitted and reflected spin currents to nearly zero for most systems of interest. Therefore, to a good approximation, the torque on the magnetization is proportional to the transverse piece of the incoming spin current.

Oxygen as a surfactant in the growth of giant magnetoresistance spin valves

We have found a novel method for increasing the giant magnetoresistance (GMR) of Co/Cu spin valves with the use of oxygen. Surprisingly, spin valves with the largest GMR are not produced in the best vacuum. Introducing 5×10−9 Torr (7×10−7 Pa) into our ultrahigh vacuum deposition chamber during spin-valve growth increases the GMR, decreases the ferromagnetic coupling between magnetic layers, and decreases the sheet resistance of the spin valves. It appears that the oxygen may act as a surfactant during film growth to suppress defects and to create a surface which scatters electrons more specularly. Using this technique, bottom spin valves and symmetric spin valves with GMR values of 19.0% and 24.8%, respectively, have been produced. These are the largest values ever reported for such structures.

Current induced torques and interfacial spin-orbit coupling: semiclassical modeling

In bilayer nanowires consisting of a ferromagnetic layer and a nonmagnetic layer with strong spin-orbit coupling, currents create torques on the magnetization beyond those found in simple ferromagnetic nanowires. The resulting magnetic dynamics appear to require torques that can be separated into two terms, dampinglike and fieldlike. The dampinglike torque is typically derived from models describing the bulk spin Hall effect and the spin transfer torque, and the fieldlike torque is typically derived from a Rashba model describing interfacial spin-orbit coupling. We derive a model based on the Boltzmann equation that unifies these approaches. We also consider an approximation to the Boltzmann equation, the drift-diffusion model, that qualitatively reproduces the behavior, but quantitatively differs in some regimes. We show that the Boltzmann equation with physically reasonable parameters can match the torques for any particular sample, but in some cases, it fails to describe the experimentally observed thickness dependencies.

Magnetic normal modes of nanoelements

Micromagnetic calculations are used to determine the eigenfrequencies and precession patterns of some of the lowest-frequency magnetic normal modes of submicron patterned elements. Two examples are presented. For a Permalloy-like ellipse, 350nm×160nm×5nm thick in zero field, the lowest frequency normal mode at 4GHz corresponds to precession in the “ends” of the ellipse. Other resonant frequencies are compared with the frequencies of spinwaves with discrete wave vectors. For a normally magnetized 50nmdiameter×15nm thick cobalt disk, the calculated eigenfrequencies increase linearly with applied field, mimicking the behavior of the experimental critical current for spin transfer instabilities in an experimental realization of this disk.

Imaging the interface of epitaxial graphene with silicon carbide via scanning tunneling microscopy

Graphene grown epitaxially on SiC has been proposed as a material for carbon-based electronics. Understanding the interface between graphene and the SiC substrate will be important for future applications. We report the ability to image the interface structure beneath single-layer graphene using scanning tunneling microscopy. Such imaging is possible because the graphene appears transparent at energies of

Magnetoresistance values exceeding 21% in symmetric spin valves

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Macrospin models of spin transfer dynamics

above or below the Fermi energy

Identification of the Dominant Precession-Damping Mechanism in Fe, Co, and Ni by First-Principles Calculations

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Spin Transfer Torque for Continuously Variable Magnetization

. Our analysis of calculations based on density-functional theory shows how this transparency arises from the electronic structure of a graphene layer on a SiC substrate.