Spin-current vortices in current-perpendicular-to-plane nanoconstricted spin valves

The charge and spin diffusion equations, taking into account spin-flip and spin-transfer torque, were numerically solved using a finite element method in complex noncollinear geometry with strongly inhomogeneous current flow. As an illustration, spin-dependent transport through a nonmagnetic nanoconstriction, separating two magnetic layers was investigated. Unexpected results such as vortices of spin-currents in the vicinity of the nanoconstriction were obtained. The angular variations of magnetoresistance and spin-transfer torque are strongly influenced by the structure geometry.

Figure 1

Model system used for the finite element calculation of CPP spin transport through a nanoconstricted spin valve. The metallic pinhole (PH) connecting the two ferromagnetic layers is 2 nm thick and of variable diameter. Note that in the case of the 2D model, all quantities are calculated per 1 nm depth. Thus, the cross-section surface of the stack with a continuous Cu spacer is 100 nm × 1 nm, and the volume of the free magnetic layer is 3 nm × 100 nm × 1 nm.

Figure 2

Zoom around the nanoconstriction showing the charge current flow (arrows) through the constriction and electrostatic potential (color mapping) corresponding to the antiparallel state.

Figure 3

Zoom around the nanoconstriction: $y$-component of spin current (black arrows) and $y$-component of spin accumulation (color mapping) for three magnetic configurations: (a) parallel, (b) 90°, and (c) antiparallel. In Fig. 3c, the white arrows show the charge flow, and the grey closed arrows indicate the formation of spin current vortices, which are better evidenced in the inset.

Figure 4

Angular variation of the CPP-reduced resistance for the constriction of the 5-nm diameter and continuous spacer. The dots are the calculated values, and the lines are fits according to Slonczewski's expression (see text).

Figure 5

(a) In-plane and (b) perpendicular components of averaged spin-transfer torque over the whole volume of the “free” (right) magnetic layer as a function of the angle between the magnetizations. (c) Mapping of the amplitude of the in-plane torque for 90° magnetic configuration in the presence of nanoconstriction with 10-nm diameter.