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

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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.