Diffusive versus local spin currents in dynamic spin pumping systems

Abstract

Using microscopic theory, we investigate the properties of a spin current driven by magnetization dynamics. In the limit of smooth magnetization texture, the dominant spin current induced by the spin pumping effect is shown to be the diffusive spin current, i.e., the one arising from only a diffusion associated with spin accumulation. That is to say, there is no effective field that locally drives the spin current. We also investigate the conversion mechanism of the pumped spin current into a charge current by spin-orbit interactions, specifically the inverse spin Hall effect. We show that the spin-charge conversion does not always occur and that it depends strongly on the type of spin-orbit interaction. In a Rashba spin-orbit system, the local part of the charge current is proportional to the spin relaxation torque, and the local spin current, which does not arise from the spin accumulation, does not play any role in the conversion. In contrast, the diffusive spin current contributes to the diffusive charge current. Alternatively, for spin-orbit interactions arising from random impurities, the local charge current is proportional to the local spin current that constitutes only a small fraction of the total spin current. Clearly, the dominant spin current (diffusive spin current) is not converted into a charge current. Therefore, the nature of the spin current is fundamentally different depending on its origin and thus the spin transport and the spin-charge conversion behavior need to be discussed together along with spin current generation

Spin-charge conversion in a multiterminal Aharonov-Casher ring coupled to precessing ferromagnets: A charge-conserving Floquet nonequilibrium Green function approach

“…16 Here we analyze spin current generation by one or two precessing FM islands and the corresponding spin-charge conversion in two-and four-terminal mesoscopic rings, adjacent to those islands and patterned in the 2DEG with the Rashba SOC. Unlike the spin-charge conversion in experimental and theoretical studies discussed above, where electronic transport in semiclassical nature, 16 the device depicted in Fig. 1 involves spinsensitive quantum-interference effects caused by the difference in the Aharonov-Casher (AC) phase [19][20][21] gained by a spin traveling around the phase-coherent ring.…”

“…which can be deduced simply from the observations that M ≡ (E + iη) I −ȟ is a matrix of infinite size, and that (E + iη) I −ȟ n ph ,m ph +l ph and (E + l ph ω + iη) −ȟ n ph −l ph ,m ph evaluated according to (16) and (17) are at the same position of M, i.e., the same matrix element of M; therefore, the element at the same matrix position of M −1 implies Eq. (18), a manifestation of the reduced-zone scheme in which the energy E can be reduced to the zone of range ω.…”

“…Furthermore, the recent alternative description 16 of spin pumping in FM|NM multilayers, which encompasses both the earlier considered 17 nonlocal diffusion of the spin accumulation at the FM|NM interface generated by magnetization precession and the effective field described by the "standard model"…”

Charge pumping by magnetization dynamics in magnetic and semimagnetic tunnel junctions with interfacial Rashba or bulk extrinsic spin-orbit coupling

“…However, this framework 24 has treated SOCs only in the N layer away from the precessing F layer in order to analyze how each of these two pumped spin currents can be converted into charge current by the inverse spin Hall effect due to the extrinsic or intrinsic SOCs. That is, in this theory SOCs are not essential for the discussion of spin pumping effect itself.…”

“…1,16,18,23,24 The SOCs in the bulk or on the surface of ferromagnetic materials play crucial role in other phenomena, such as the anomalous Hall effect 25 or the tunneling anisotropic magnetoresistance [26][27][28][29][30][31] (TAMR). Moreover, the study of the interplay between SOC and STT has been recently initiated 9,32-34 through theoretical proposals 35 and experimental realizations 22,36 that exploit SOCs for STT-driven magnetization reversal of a single F layer with greatly reduced critical current required when compared to traditional spin valves or MTJs with two non-collinear magnetizations.…”