Spin and charge pumping

We are focusing on the spin and charge pumping in magnetic nanostructures, like spin valves or magnetic tunnel junctions. This type of pumping is a special case of parametric pumping following Landauer-Büttiker and Brouwer using scattering formalism. [1-4]

In general, a structure can pump particles from reservoirs if there are two potential parameters changing periodically (with frequency ω) but with a phase difference, such that the trajectory encircles a finite area in the phase space spanned by these two parameters. The oscillating potentials provide quanta ħω, which can cause quantum transitions. If the relative phase between the two parameters are controlled correctly, the quantum transitions can lead to pumping of particles such that particles flows in a definite direction. These process can be simply described by the time-dependent scattering matrices. [4] The pumping effect can also be understood using the Berry phase.

For a ferromagnet (FM) that is connected with non-magnet (NM) leads/reservoirs. If the magnetization m is precessing around some axis (z-axis for example), there are two parameters that oscillates periodically: m_x and m_y. But these two parameters has no effect on electron charge, thus the scattering matrices (in real space) have no time dependence, and so no electron charge will be pumped by the precessing magnetization. However, the scattering matrices in spin space are indeed time dependent due to the interaction between itinerant electron spin and the magnetization m: σ·m. This time dependent scattering matrices then lead to a pumping of spins, i.e. pumping spin-down to spin-up by absorbing quanta from the precessing magnetization. More specifically, for an NM|FM|NM structure (see above), the precessing magnetization can pump a pure spin current (that carries no charge current) from FM to NM. The pumped current has the following form:

${\bf I}_{sp} = {\hbar\over 4\pi}\left(g_r{\bf m}\times{d{\bf m}\over dt} + g_i {d{\bf m}\over dt} \right)$

where g_r and g_i are the real and imaginary part of the spin-mixing conductance. These two parts of the mixing conductance also governs the in-plane and out-of-plane component of the spin-transfer torque in magnetic multilayers. The g_r term in the spin pumping current has the same form as the magnetic damping, therefore the FM in contact with NM leads has larger magnetic damping than the standalone FM because of the spin pumping.

This pure spin pumping current can be filtered into a charge current by a spin dependent filter, such as an additional FM layer. Therefore in a spin valve structure (FM|NM|FM, see above), when the magnetization in one of the FM layer is under precession, a charge pumping voltage can be observed, and is directly related to the torkance in the structure:

$V_{cp} = R(\theta)\left[\tau_{ip}(\theta) {\bf m\times\dot{m}} + \tau_{op}(\theta)\dot{\bf m} \right]\cdot{\bf m}_0$

where R is the resistance of the structure.

References:

[1]. Büttiker, M. Scattering theory of current and intensity noise correlations in conductors and wave guides. Phys. Rev. B 46, 12485 (1992).
[2]. Büttiker, M., Prêtre, A. & Thomas, H. Dynamic conductance and the scattering matrix of small conductors. Phys. Rev. Lett. 70, 4114 (1993).
[3]. Büttiker, M., Thomas, H. & Prêtre, A. Current partition in multiprobe conductors in the presence of slowly oscillating external potentials. Zeitschrift für Physik B Condensed Matter 94, 133-137 (1994).
[4]. Brouwer, P.W. Scattering approach to parametric pumping. Phys. Rev. B 58, R10135 (1998).
[5]. Tserkovnyak, Y., Brataas, A. & Bauer, G.E.W. Enhanced Gilbert Damping in Thin Ferromagnetic Films. Phys. Rev. Lett. 88, 117601 (2002).
[6]. Xiao, J., Bauer, G.E.W. & Brataas, A. Charge pumping in magnetic tunnel junctions: Scattering theory. Phys. Rev. B 77, 180407-4 (2008).
[7]. Xiao, J., Bauer, G.E.W., Maekawa, S. & Brataas, A. Charge pumping and the colored thermal voltage noise in spin valves. Phys. Rev. B 79, 174415-9 (2009).