Andrew Zangwill

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.

Equilibrium theory of the Stranski-Krastanov epitaxial morphology

Abstract We present a theory of the equilibrium morphology adopted by N atoms of one material when they crystallize epitaxially onto the surface of a dissimilar material. The discussion is limited to the case of the so-called Stranski-Krastanov morphology where a strongly bound but elastically strained wetting layer coats the substrate. The arrangement of atoms atop this layer is determined by minimizing an approximate total energy expression derived for a set of vertically coupled Frenkel-Kontorova chains of finite yet variable length. In this way, both elastic and plastic strain accommodation are treated with a common formalism. Our semi-analytic treatment permits us to compare very rapidly the energy of essentially all configurations of N atoms (up to about N = 5000) including uniform films, coherent islands and dislocated islands. The results are presented in the form of a morphological phase diagram as a function of misfit, surface energy and total particle number for the case of diamond structure materials. Coherent islands are found to be stable in a non-negligible portion of the phase diagram and the relevant phase boundaries are well predicted by simple analytic expressions. A kinetic interpretation of the results is possible when the variable N is redefined appropriately.

Macrospin models of spin transfer dynamics

The current-induced magnetization dynamics of a spin valve are studied using a macrospin (single-domain) approximation and numerical solutions of a generalized Landau-Lifshitz-Gilbert equation. For the purpose of quantitative comparison to experiment [S. I. Kiselev, J. C. Sankey, I. N. Krivortov, N. C. Emley, R. J. Schoelkopf, R. A. Buhrman, and D. C. Ralph, Nature 425, 380 (2003)], we calculate the resistance and microwave power as a function of current and external field, including the effects of anisotropies, damping, spin-transfer torque, thermal fluctuations, spin-pumping, and incomplete absorption of transverse spin current. Although many features of experiment appear in the simulations, there are two significant discrepancies: the current dependence of the precession frequency and the presence and/or absence of a microwave quiet magnetic phase with a distinct magnetoresistance signature. Comparison is made to micromagnetic simulations designed to model the same experiment.

Growth and Erosion of Thin Solid Films

Thin films that are grown by the process of sputtering are, by and large, quite unlike the smooth, featureless structures that one might expect. In general, these films have a complicated surface morphology and an extended network of grooves and voids in their interiors. Such features can have a profound effect on the physical properties of a thin film. The surface irregularities and the bulk defects are the result of a growth instability due to competitive shadowing, an effect that also plays a role in geological processes such as erosion. For amorphous thin films, the shadow instability can be described by a remarkably simple model, which can be shown to reproduce many important observed characteristics of thin film morphology.

Spin Transfer Torque for Continuously Variable Magnetization

We report quantum and semiclassical calculations of spin current and spin-transfer torque in a free-electron Stoner model for systems where the magnetization varies continuously in one dimension. Analytic results are obtained for an infinite spin spiral and numerical results are obtained for realistic domain wall profiles. The adiabatic limit describes conduction electron spins that follow the sum of the exchange field and an effective, velocity-dependent field produced by the gradient of the magnetization in the wall. Nonadiabatic effects arise for short domain walls but their magnitude decreases exponentially as the wall width increases. Our results cast doubt on the existence of a recently proposed nonadiabatic contribution to the spin-transfer torque due to spin-flip scattering.

Noncollinear spin transfer in Co/Cu/Co multilayers (invited)

This article has two parts. The first part uses a single point of view to discuss the reflection and averaging mechanisms of spin transfer between current-carrying electrons and the ferromagnetic layers of magnetic/nonmagnetic heterostructures. The second part incorporates both effects into a matrix Boltzmann equation and reports numerical results for current polarization, spin accumulation, magnetoresistance, and spin-transfer torques for Co/Cu/Co multilayers. When possible, the results are compared quantitatively with relevant experiments.

Phenomenological theory of current-induced magnetization precession

We solve appropriate drift-diffusion and Landau-Lifshitz-Gilbert equations to demonstrate that unpolarized current flow from a nonmagnet into a ferromagnet can produce a precession-type instability of the magnetization. The fundamental origin of the instability is the difference in conductivity between majority spins and minority spins in the ferromagnet. This leads to spin accumulation and spin currents that carry angular momentum across the interface. The component of this angular momentum perpendicular to the magnetization drives precessional motion that is opposed by Gilbert damping. Neglecting magnetic anisotropy and magnetostatics, our approximate analytic and exact numerical solutions using realistic values for the material parameters show (for both semi-infinite and thin-film geometries) that a linear instability occurs when both the current density and the excitation wave vector parallel to the interface are neither too small nor too large. For many aspects of the problem, the variation of the magnetization in the direction of the current flows makes an important contribution.

Novel growth mechanism of epitaxial graphene on metals.

Graphene, a hexagonal sheet of sp(2)-bonded carbon atoms, has extraordinary properties which hold immense promise for nanoelectronic applications. Unfortunately, the popular preparation methods of micromechanical cleavage and chemical exfoliation of graphite do not easily scale up for application purposes. Epitaxial graphene provides an attractive alternative, though there are many challenges, not least of which is the absence of any understanding of the complex atomistic assembly kinetics of graphene layers. Here, we present a simple rate theory of epitaxial graphene growth on close-packed metal surfaces. On the basis of recent low-energy electron-diffraction microscopy experiments, our theory supposes that graphene islands grow predominantly by the attachment of five-atom clusters. With optimized kinetic parameters, our theory produces a quantitative account of the measured time-dependent carbon adatom density. The temperature dependence of this density at the onset of nucleation leads us to predict that the smallest stable precursor to graphene growth is an immobile island composed of six five-atom clusters. This conclusion is supported by a recent study based on temperature-programmed growth of epitaxial graphene, which provides direct evidence of nanoclusters whose coarsening leads to the formation of graphene layers. Our findings should motivate additional high-resolution imaging experiments and more detailed simulations which will yield important input to developing strategies for the large-scale production of epitaxial graphene.

Submonolayer epitaxy without a critical nucleus

Abstract The nucleation and growth of two-dimensional islands is studied with Monte Carlo simulations of a pair-bond solid-on-solid model of epitaxial growth. The conventional description of this problem in terms of a well-defined critical island size fails because no islands are absolutely stable against single atom detachment by thermal bond breaking. When two-bond scission is negligible, we find that the ratio of the dimer dissociation rate to the rate of adatom capture by dimers uniquely indexes both the island size distribution scaling function and the dependence of the island density on the flux and the substrate temperature. Effective pair-bond model parameters are found that yield excellent quantitative agreement with scaling functions measured for Fe Fe (001) .

Some causes and a consequence of epitaxial roughening

This article consists of two related parts. In the first part, a review is presented of the theory of surface roughening during homoepitaxial growth or lattice-matched heteroepitaxial growth. Emphasis is placed on qualitative concepts and general mechanisms. Rate equations, Monte Carlo simulations, and continuum equations of motion are used to illustrate roughening due to asymmetric diffusion barriers to interlayer mass transport and from statistical fluctuations in the incident deposition flux. In the second part, we report new results regarding one consequence of such roughening that is pertinent to the growth of semiconductor alloys that exhibit long-range order induced by local thermodynamics at the free surface. The qualitative ingredients for a kinetic mean field theory are described along with preliminary results that indicate that surface roughness induces the injection of anti-phase domains that progressively destroy the lateral coherence of order in a growing film.