Spin pumping

Spin pumping is a method of generating a spin current, the spintronic analog of a battery in conventional electronics.

In order to make a spintronic device, the primary requirement is to have a system that can generate a current of spin-polarized electrons, as well as a system that is sensitive to the spin polarization. Most spintronic devices also have a unit in between these two that changes the current of electrons depending on the spin states. Candidates for such devices include injection schemes based on magnetic semiconductors and ferromagnetic metals, ferromagnetic resonance devices[1] , and a variety of spin-dependent pumps. Optical, microwave and electrical methods are also being explored[2] .These devices could be used for low-power data transmission in spintronic devices[3] or to transmit electrical signals through insulators.[4]

The spin pumped into an adjacent layer by a precessing magnetic moment is given by[1]

${\displaystyle {\vec {j}}_{s}={\hbar \over {4\pi }}g^{\uparrow \downarrow }{1 \over M_{S}^{2}}\langle {\vec {M}}(t)\times {{d{\vec {M}}(t))} \over {dt}}\rangle }$

where ${\displaystyle {\vec {j}}_{s}}$ is the spin current (the vector indicates the orientation of the spin, not the direction of the current), ${\displaystyle g^{\uparrow \downarrow }}$ is the spin-mixing conductance, ${\displaystyle M_{S}}$ is the saturation magnetization, and ${\displaystyle {\vec {M}}(t)}$ is the time-dependent orientation of the moment.