Direct and indirect spin current generation and spin-orbit torques in ferromagnet/nonmagnet/ferromagnet trilayers

Amin, V. P.; Baez Flores, G. G.; Kovalev, A. A.; Belashchenko, K. D.

doi:10.1103/PhysRevB.110.214427

Direct and indirect spin current generation and spin-orbit torques in ferromagnet/nonmagnet/ferromagnet trilayers

Journal Article · Wed Dec 18 00:00:00 EST 2024 · Physical Review. B

DOI:https://doi.org/10.1103/PhysRevB.110.214427· OSTI ID:2568303

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Indiana University, Indianapolis, IN (United States)
University of Nebraska–Lincoln, NE (United States)

Spin-orbit torques in ferromagnet/nonmagnet/ferromagnet trilayers are studied using a combination of symmetry analysis, circuit theory, semiclassical simulations, and first-principles calculations using the nonequilibrium Green's function method with supercell disorder averaging. Here, we focus on unconventional processes involving the interplay between the two ferromagnetic layers, which are classified into direct and indirect mechanisms. The direct mechanism involves spin current generation by one ferromagnetic layer and its subsequent absorption by the other. In the indirect mechanism, the in-plane spin-polarized current from one ferromagnetic layer “leaks” into the other layer, where it is converted into an out-of-plane spin current and reabsorbed by the original layer. The direct mechanism results in a predominantly dampinglike torque, which damps the magnetization towards a certain direction 𝐬_𝑑. The indirect mechanism results in a predominantly fieldlike torque with respect to a generally different direction 𝐬_𝑓. Similarly to the current-in-plane giant magnetoresistance, the indirect mechanism is only active if the thickness of the nonmagnetic spacer is smaller than or comparable to the mean free path. Numerical calculations for a semiclassical model based on the Boltzmann equation confirm the presence of both direct and indirect mechanisms of spin current generation. First-principles calculations reveal sizable unconventional spin-orbit torques in Co/Cu/Co, Py/Cu/Py, and Co/Pt/Co trilayers and provide strong evidence of indirect spin current generation.

View Accepted Manuscript (DOE)

Research Organization:: University of Nebraska–Lincoln, NE (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0021019

OSTI ID:: 2568303

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 21 Vol. 110; ISSN 2469-9950; ISSN 2469-9969

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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