We compute the magnetocrystalline anisotropy energy within two-dimensional Rashba models. For a ferromagnetic free-electron Rashba model, the magnetic anisotropy is exactly zero regardless of the strength of the Rashba coupling, unless only the lowest band is occupied. For this latter case, the model predicts in-plane anisotropy. For a more realistic Rashba model with finite band width, the magnetic anisotropy evolves from in-plane to perpendicular and back to in-plane as bands are progressively filled. This evolution agrees with first-principles calculations on the interfacial anisotropy, suggesting that the Rashba model captures energetics leading to anisotropy originating from the interface provided that the model takes account of the finite Brillouin zone. The results show that the electron density modulation by doping or an external voltage is more important for voltage-controlled magnetic anisotropy than the modulation of the Rashba parameter.
Bibliographical noteFunding Information:
The authors acknowledge R. D. McMichael, C.-Y. You, P. M. Haney, and J. McClelland for critical reading of the manuscript. K.W.K. acknowledges support under the Cooperative Research Agreement between the University of Maryland and the National Institute of Standards and Technology, Center for Nanoscale Science and Technology, Grant No. 70NANB10H193, through the University of Maryland. K.W.K. was also supported by Center for Nanoscale Science and Technology, National Institute of Standards and Technology, based on a Collaborative Research Agreement with Basic Science Research Institute, Pohang University of Science and Technology. K.J.L was supported by the National Research Foundation of Korea (Grant No. 2011-028163, 2015M3D1A1070465). H.W.L. was supported by the National Research Foundation of Korea (Grant No. 2013R1A2A2A05006237) and the Ministry of Trade, Industry and Energy of Korea (Grant No. 10044723).
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ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics