Identification of Transverse Spin Currents in Noncollinear Magnetic Structures

Abstract

We show that the transverse components of spin current in a ferromagnet is linked to an off diagonal spin component of the transmission matrix at interfaces;it has little to do with the mismatch of band structures between dissimilar metals. When we take account of this component,not considered in prior analyses, we find spin torque comes from a region of at lease 3 nm around an interface. It occurs when one drives an electric current across a multilayered structure in which the magnetic layers are noncollinear. The central idea behind the switching is that when the spin polarized current that develops in a fixed ferromagnetic layer of a multilayered structure impinges on a second noncollinear free magnetic layer the component of the spin current transverse to the magnetization is absorbed. As one assumes the conservation of spin angular momentum this creates the torque on the background magnetization to switch it. One of the unresolved issues is the length scale over which the transverse component of the spin current is absorbed and what material parameters controls it. Here, we point out, that the detail of the transverse spin near the interface does matter in determining the spin transfer torque. The reason is that transport is inherently non-local so that the incident spin polarization at an interface does depend on the detail of the transverse spin accumulation even if this length scale is small, i.e., one must include transverse pin accumulation. Mathematically, the boundary condition solely from the vanishing transverse spin density in ferromagnets is not sufficient to determine the spin torque. If we write the boundary condition to the distribution function on the two sides of an interface, we have found that the truncation of the transmission matrix to a diagonal matrix in spin space misses key relations between the spinor distribution functions on the two sides of an interface, and thus the transport across the entire structure is unable to be self-consistently determined.We recently found a possible mechanism by which one can inject off diagonal spin distributions into each sheet of the spin split Fermi surface of a magnetic layer, i.e., in the presence a current a spin flip potential can exist at interfaces in noncollinear magnetic multilayers. [3] This additional scattering excites the transverse components of spin currents in magnetic layers that are found by adopting the Boltzmann equation's definition of spin current and then we find there is no discontinuity in the spin current at an interface between two dissimilar layers. This transverse current is different from that evaluated from equilibrium states; [4,5] they complement one another but the existence of the latter does not negate the former. We evaluate the relevant parameters over which this component is absorbed by using ab-initio band structure calculations and find the characteristic length scale in a typical 3d transition-metal ferromagnet(Co) is 3 nm. This is an order of magnitude greater than that found in prior analysis which evaluat...

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