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

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

Magnetic anisotropy of vicinal (001) fcc Co films: role of crystal splitting and structure relaxation in step-decoration effect

The uniaxial in-plane magnetic anisotropy (UIP-MA) constant is calculated for a single step on the (001) surface of fcc Co($N$) films. The calculations are done for both an undecorated step and the step decorated with one or more, up to 7, Cu wires. Our objective is to explain the mechanisms by which the decoration decreases the UIP-MA constant, which is the effect observed experimentally for ultrathin Co films deposited on vicinal (001) Cu surfaces and can lead to reorientation of magnetization within the film plane. Theoretical calculations performed with a realistic tight-binding model show that the step decoration changes the UIP-MA constant significantly only if the splitting between the on-site energies of various $d$-orbitals is included for atoms located near the step edge. The local relaxation of atomic structure around the step is also shown to have a significant effect on the shift of the UIP-MA constant. The influence of these two relevant factors is analyzed further by examining individual contributions to the UIP-MA constant from atoms around the step. The magnitude of the obtained UIP-MA shift agrees well with experimental data. It is also found that an additional shift due to possible charge transfer between Cu and Co atoms is very small.Comment: 12 pages,9 figures, RevTeX, submitted to Physical Review B version 3: additions to content version 2: minor correction

Reflection mechanism for generating spin transfer torque without charge current

A reflection mechanism for generating spin-transfer torque is proposed. It is due to interference of bias-driven nonequilibrium electrons incident on a switching junction, with the electrons reflected from an insulating barrier inserted in the junction after the switching magnet. It is shown, using the rigorous Keldysh formalism, that this out-of-plane torque T ? is proportional to an applied bias and is as large as the torque in a conventional junction generated by a strong charge current. However, the charge current and the in-plane torque T k are almost completely suppressed by the insulating barrier. This junction thus offers the highly applicable possibility of bias-induced switching of magnetization without charge current. V C 2012 American Institute of Physics. [http://d

Reflection mechanism for generating spin transfer torque without charge current

A reflection mechanism for generating spin-transfer torque is proposed. It is due to interference of bias-driven nonequilibrium electrons incident on a switching junction, with the electrons reflected from an insulating barrier inserted in the junction after the switching magnet. It is shown, using the rigorous Keldysh formalism, that this out-of-plane torque T⊥ is proportional to an applied bias and is as large as the torque in a conventional junction generated by a strong charge current. However, the charge current and the in-plane torque T∥ are almost completely suppressed by the insulating barrier. This junction thus offers the highly applicable possibility of bias-induced switching of magnetization without charge current

Strong enhancement of the tunneling magnetoresistance by electron filtering in an Fe/MgO/Fe/GaAs(001) junction

Calculations of the tunneling magnetoresistance (TMR) of an epitaxial Fe/MgO/Fe tunneling junction attached to an n-type GaAs lead, under positive gate voltage, are presented. It is shown that for realistic GaAs carrier densities the TMR of this composite system can be more than 2 orders of magnitude higher than that of a conventional Fe/MgO/Fe junction. Furthermore, the high TMR is achieved with modest MgO thicknesses and is very robust to disorder at the Fe/GaAs interface and within the GaAs layer itself. The significant practical advantage of this system is that huge TMRs should be attainable for junctions with modest resistances. For a GaAs carrier density of 1019??cm-3 the system is calculated to have a TMR in excess of 10?000% but its resistance is equivalent to that of a conventional Fe/MgO/Fe junction with only 6–7 at. planes of MgO

Synthetic route to low damping in ferromagnetic thin-films

Previous theory indicated that the individual monolayers within transition metal ferromagnet thin-films contribute different magnitudes to the total ferromagnetic damping. Here, the aim was to investigate if the thin-film damping could be reduced by electronic engineering of the higher damping regions via localized doping. We present new theoretical analysis and experimental results for sputtered Co thin-films in which the upper and lower surface regions were locally doped with Cr. Theory indicates that local doping does reduce the damping and the experiments show a comparable reduction of the damping with increasing local doping up to 30% Cr, while the measured damping falls further with higher local doping, which may be attributed to changes in the film structure. This work opens a route to create low-damping magnetic thin-films

Interference effects in electronic transport through metallic single-wall carbon nanotubes

In a recent paper Liang {\it et al.} [Nature {\bf 411}, 665 (2001)] showed experimentally, that metallic nanotubes, strongly coupled to external electrodes, may act as coherent molecular waveguides for electronic transport. The experimental results were supported by theoretical analysis based on the scattering matrix approach. In this paper we analyze theoretically this problem using a real-space approach, which makes it possible to control quality of interface contacts. Electronic structure of the nanotube is taken into account within the tight-binding model. External electrodes and the central part (sample) are assumed to be made of carbon nanotubes, while the contacts between electrodes and the sample are modeled by appropriate on-site (diagonal) and hopping (off-diagonal) parameters. Conductance is calculated by the Green function technique combined with the Landauer formalism. In the plots displaying conductance {\it vs.} bias and gate voltages, we have found typical diamond structure patterns, similar to those observed experimentally. In certain cases, however, we have found new features in the patterns, like a double-diamond sub-structure.Comment: 15 pages, 4 figures. To apear in Phys. Rev.

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