Spin-transfer torques occur in magnetic heterostructures because the transverse component of a spin current that flows from a non-magnet 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.

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The evolution of the surface potential during homoepitaxial growth of Fe(001) is studied by scanning tunneling microscopy and reflection high energy electron diffraction. The observed morphology exhibits a non-self-affine collection of moundlike features that maintain their shape but coarsen as growth proceeds. The characteristic feature separation I. is set in the submonolayer regime and increases with thickness t as L(t) -to'"-o" . During the coarsening phase, the mounds are characterized by a magic slope and a lack of reflection symmetry. These observations are shown to be described by a continuum growth equation without capillarity. PACS numbers: 68.55.Jk, 05.70.Ln, 61.16.ChThe basic mechanisms of epitaxial growth onto Hat single crystal surfaces have been known for over fifty years [1]. In the absence of surface defects, growth occurs by the nucleation, growth, and coalescence of two-dimensional (single atom height) islands. Atoms from an external beam arrive at the surface, transfer the heat of condensation to the substrate, and begin activated surface diffusion. Pairs of migrating atoms collide randomly over the surface and may bind to form dimers. The dimers may or may not dissociate thermally before other atoms diffuse to join them. Eventually, stable nuclei form that grow in size as other atoms arrive and attach. Individual island growth continues until nearby islands begin to impinge upon one another and coalesce. Layer completion occurs as freshly deposited particles fill in the gaps between coalesced islands. In principle, this scenario repeats for each layer so that the surface roughness varies periodically in time. But in fact, shot noise in the deposition Aux randomly induces nucleation of new stable nuclei on top of existing islands before layer completion occurs. The progressive roughening of the growth front implied by this picture has been the subject of numerous experimental and theoretical studies in recent years [2,3]. Part of the impetus for many of these studies has been the theoretical expectation [4] that noise-induced roughening during crystal growth might lead to self-affine surfaces [5]. Very recently, however, experimental data obtained from GaAs(001) [6],Cu(001) [7],Ge(001) [8], and Pt (111) [9] have revealed that a completely different morphological scenario can occur for homoepitaxy onto high quality single crystal surfaces. The surface morphology here takes the form of a collection of fairly regular three-dimensional mounds characterized by a well-defined separation distance L(t). The mere existence of the single scale length L(r) implies that these surfaces are not self-affine. According to Villain [10], the origin of this behavior can be traced to an intrinsic instability of the Oat surface that occurs in the island nucleation and coalescence regime whenever energy barriers to the transport of diffusing atoms downward over step edges exceed the usual surface diffusion barrier on a Oat terrace. Since atoms on an incomplete layer that recoil from these barriers are more likely t...

We report quantum and semi-classical 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. Non-adiabatic 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 non-adiabatic contribution to the spin-transfer torque due to spin flip scattering.

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. (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. While many features of experiment appear in the simulations, there are two significant discrepancies: the current dependence of the precession frequency and the presence/absence of a microwave quiet magnetic phase with a distinct magnetoresistance signature. Comparison is made with micromagnetic simulations designed to model the same experiment.

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