Spin-orbit torques induced by spin Hall and spin swapping currents of a separate ferromagnet in a magnetic trilayer

• Published in: Current applied physics Vol. 29; pp. 54 - 58
• Main Authors: Park, Eun-Sang, Min, Byoung-Chul, Koo, Hyun Cheol, Kim, Kyoung-Whan, Lee, Kyung-Jin
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.09.2021; 한국물리학회
• Subjects: Spin Hall effect; Spin swapping effect; Spin-orbit torque; 물리학; Spin Hall effect; Spin-orbit torque; Spin swapping effect
• ISSN: 1567-1739; 1878-1675; 1567-1739
• DOI: 10.1016/j.cap.2021.05.015

Spin-orbit torques (SOTs) have been investigated most widely in normal metal/ferromagnet bilayers where the spin Hall effect of normal metal is a main source of spin currents. Recently, ferromagnets are found to also serve as spin-current sources through spin-orbit coupling. In this work, we theoretically investigate SOT acting on ferromagnet2 in ferromagnet1/normal metal/ferromagnet2 trilayers, which is caused by the spin Hall and spin swapping effects of ferromagnet1. Our result provides an analytical expression of SOT in the trilayers, which may be useful for quantifying the spin Hall and spin swapping effects of ferromagnets and also for designing and interpreting SOT experiments where a ferromagnet is used as a spin-current source instead of a normal metal. •Spin-orbit torque theory for magnetic trilayers.•Analytical equation of spin-orbit torque due to spin-orbit coupling of ferromagnet.•Distinct contributions from spin Hall and spin swapping effects.