Theory of Spin-Transfer Torque in the Current-in-Plane Geometries

Two alternative current-induced switching geometries, in which the current flows parallel to the magnet/nonmagnet interface, are investigated theoretically using the nonequilibrium Keldysh theory. In the first geometry, the current is perpendicular to the polarizing magnet/nonmagnet interface but parallel to the nonmagnet/switching magnet interface (CPIP). In the second geometry, the current is parallel to both the polarizing magnet/nonmagnet and nonmagnet/switching magnet interfaces (CIP). Calculations for a single-orbital tight binding model indicate that the spin current flowing parallel to the switching magnet/nonmagnet interface can be absorbed by a lateral switching magnet as efficiently as in the traditional current-perpendicular-to-plane (CPP) geometry. The results of the model calculations are shown to be valid also for experimentally relevant Co/Cu CPIP system described by fully realistic tight binding bands fitted to an ab initio band structure. It is shown that almost complete absorption of the incident spin current by a lateral switching magnet occurs when the lateral dimensions of the switching magnet are of the order of 50-100 interatomic distances, i.e., about 20nm and its height as small as a few atomic planes. It is also demonstratedthat strong spin current absorption in the CPIP/CIP geometry is not spoilt by the presence of a rough interface between the switching magnet and nonmagnetic spacer. Polarization achieved using a lateral magnet in the CIP geometry is found to be about 25% of that in the traditional CPP geometry. The present CPIP calculations of the spin transfer torque are also relevant to the so called pure-spin-current-induced magnetization switching that had been recently observed.Comment: 9 pages 8 figure

Quantum oscillation of magnetoresistance in tunneling junctions with a nonmagnetic spacer

We make a theoretical study of the quantum oscillations of the tunneling magnetoresistance (TMR) as a function of the spacer layer thickness. Such oscillations were recently observed in tunneling junctions with a nonmagnetic metallic spacer at the barrier-electrode interface. It is shown that momentum selection due to the insulating barrier and conduction via quantum well states in the spacer, mediated by diffusive scattering caused by disorder, are essential features required to explain the observed period of oscillation in the TMR ratio and its asymptotic value for thick nonmagnetic spacer.Comment: 4 pages, 5 figures, two column, REVTex4 styl

Fundamental Oscillation Periods of the Interlayer Exchange Coupling beyond the RKKY Approximation

A general method for obtaining the oscillation periods of the interlayer exchange coupling is presented. It is shown that it is possible for the coupling to oscillate with additional periods beyond the ones predicted by the RKKY theory. The relation between the oscillation periods and the spacer Fermi surface is clarified, showing that non-RKKY periods do not bear a direct correspondence with the Fermi surface. The interesting case of a FCC(110) structure is investigated, unmistakably proving the existence and relevance of non-RKKY oscillations. The general conditions for the occurrence of non-RKKY oscillations are also presented.Comment: 34 pages, 10 figures ; to appear in J. Phys.: Condens. Mat

A selfconsistent theory of current-induced switching of magnetization

A selfconsistent theory of the current-induced switching of magnetization using nonequilibrium Keldysh formalism is developed for a junction of two ferromagnets separated by a nonmagnetic spacer. It is shown that the spin-transfer torques responsible for current-induced switching of magnetization can be calculated from first principles in a steady state when the magnetization of the switching magnet is stationary. The spin-transfer torque is expressed in terms of one-electron surface Green functions for the junction cut into two independent parts by a cleavage plane immediately to the left and right of the switching magnet. The surface Green functions are calculated using a tight-binding Hamiltonian with parameters determined from a fit to an {\it ab initio} band structure.This treatment yields the spin transfer torques taking into account rigorously contributions from all the parts of the junction. To calculate the hysteresis loops of resistance versus current, and hence to determine the critical current for switching, the microscopically calculated spin-transfer torques are used as an input into the phenomenological Landau-Lifshitz equation with Gilbert damping. The present calculations for Co/Cu/Co(111) show that the critical current for switching is $\approx 10^7A/cm^2$, which is in good agreement with experiment.Comment: 23 pages, 16 figure

Influence of disorder on the perpendicular magnetoresistance of magnetic multilayers

The effect of disorder on the perpendicular magnetoresistance of magnetic multilayers is investigated theoretically. Various kinds of disorder are considered: (i) interface substitutional disorder and (ii) bulk disorder in the various layers and in the leads. The calculations are based upon the non-equilibrium Green's function formalism, together with the recursion method for calculating the real-space Green's function.Comment: RevTeX, 3 pages, 3 eps figures included; minor changes in v

The Nature and Validity of the RKKY limit of exchange coupling in magnetic trilayers

The effects on the exchange coupling in magnetic trilayers due to the presence of a spin-independent potential well are investigated. It is shown that within the RKKY theory no bias nor extra periods of oscillation associated with the depth of the well are found, contrary to what has been claimed in recent works. The range of validity of the RKKY theory is also discussed.Comment: 10, RevTe

Theory of tunneling magnetoresistance in a disordered Fe/MgO/Fe(001) junction

Calculation of the tunneling magnetoresistance (TMR) of an Fe/MgO/Fe(001) junction with a disordered Fe/MgO interface is reported. It is shown that intermixing of Fe and Mg atoms at the interface decreases the TMR ratio rapidly and when about 16% of interfacial Fe atoms are substituted by Mg the calculated TMR saturates with increasing MgO thickness in good agreement with experiment. It is demonstrated that the saturation of TMR occurs because interfacial scattering leads to a redistribution of conductance channels, which opens up the perpendicular tunneling channel in the antiferromagnetic configuration that is forbidden for a perfect epitaxial junction