Publication: Direct and inverse spin Hall effects: Zeeman energy
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2020-04-15
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Elsevier
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Abstract
It is shown that magnetic forces as the force -/+ mu(V) over barB, exerted on electron spins at rest, account for both the transverse spin imbalance typical of spin Hall effect and the transverse charge imbalance associated with pure spin currents (inverse spin Hall effect). Considering that for stationary currents the laboratory reference frame, and those for which the spin up and spin down carriers are at rest, are inertial systems one can easily find the forces exerted by the lattice on both spin sub-bands, as well as the force between sub-bands.
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©2020 Elsevier B.V.
The authors are indebted to P. Echenique, J. Hirsch, V. Golovach, A. Arnau and J. M. Rojo for many fruitful discussions. This work has been supported by the Spanish Ministry of Innovation, Science and Technology and Spanish Ministry of Economy and Competitiveness through Research Projects MAT2015-67557-C2-1-P, MAT2017-86450-C4-1-R S2013/MIT-2850 NANOFRONTMAG, RTI2018-095856-B-C21, by the European Commission AMPHIBIAN (H2020-NMBP-2016-720853) and by the Comunidad de Madrid S2018/NMT-4321 NANOMAGCOST-CM.