Spin pumping

The spin current pumped into an adjacent layer by a precessing magnetic moment is given by[2]

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

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 characterizing the spin transparency of the interface, ${\displaystyle M_{S}}$ is the saturation magnetization, and ${\displaystyle {\vec {M}}(t)}$ is the time-dependent orientation of the moment.

Optical, microwave and electrical methods are also being explored.[3] These devices could be used for low-power data transmission in spintronic devices[4] or to transmit electrical signals through insulators.[5]

Spin pumping in antiferromagnetic materials does not vanish because the antiparallel magnetic moments contribute constructively rather than destructively to spin current, which was theoretically predicted in 2014.[6] Since the frequency of antiferromagnetic resonance[7] is much higher than that of ferromagnetic resonance, spin pumping in antiferromagnets can be utilized to study electromagnetic signals in the sub-terahertz and terahertz regime, which had been demonstrated by two independent experiments in 2020.[8][9]

Besides higher frequency, spin pumping in antiferromagnets features the chirality degree of freedom of magnetic dynamics that does not exist in ferromagnets. For example, the spin currents pumped by the left-handed and the right-handed resonance modes are opposite in direction.

• Spintronics
• Spin wave
• Spin Hall effect