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technical paper
First principles calculation of the 3m spin
Field-free switching of perpendicular magnetization has been observed in an epitaxial L11-ordered CuPt/CoPt bilayer 1 and attributed to spin-orbit torque (SOT) arising from the crystallographic 3m point group of the interface. Using a first-principles nonequilibrium Green’s function formalism 2 combined with the Andersen disorder model, we calculate the angular dependence of the SOT in a CuPt/CoPt bilayer and find that the magnitude of the 3m SOT is about 20% of the conventional dampinglike SOT. We study the magnetization dynamics in a perpendicularly magnetized circular nanodisk in the presence of the 3m SOT and Dzyaloshinskii-Moriya interaction using micromagnetic simulations and find that even a relatively small 3m torque can enable domain-wall-mediated field-free magnetization reversal. For further insight, we derive a collective-coordinate model describing the motion of a domain wall in a nanodisk. Numerical solutions and stability analysis of the equations of motion in this model are used to establish the roles of the dampinglike, fieldlike, and 3m SOT in the magnetization reversal process.
Wuzhang Fang and Edward Schwartz contribute equally to this work. This work was supported by NSF through Grant No. DMR-1916275, and by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award No. DE-SC0021019.
References 1 L. Liu et al., Nat. Nanotechnol. 16, 277 (2021).
2 K. D. Belashchenko, A. A. Kovalev, and M. van Schilfgaarde, Phys. Rev. Materials 3, 011401(R) (2019); Phys. Rev. B 101, 020407(R) (2020).