Fig. 2

Origin of voltage-controlled magnetic anisotropy (VCMA) and VCMA coefficient. a First-principle calculation result shows the induced charge density at ferromagnet (FM)/oxide interface at bias electric field \(E = + 0.2{\mathrm{Vnm}}^{{\mathrm{ - 1}}}\) with respect to \(E = - 0.2{\mathrm{V}}\,{\mathrm{nm}}^{{\mathrm{ - 1}}}\). The blue and red color scale represents the accumulation and depletion of holes, respectively³⁸. Reproduced with the permission from https://doi.org/10.1103/PhysRevB.96.220412. b Areal density of interfacial perpendicular magnetic anisotropy (iPMA) as a function of E for different annealing temperatures. Nonlinear behavior of VCMA and local minima of iPMA are observed⁴² at \(E = + 100{\mathrm{mV}}\,{\mathrm{nm}}^{{\mathrm{ - 1}}}\). Reproduced with permission from Xiang, Q., Wen, Z., Sukegawa, H., Kasai, S., Seki, T., Kubota, T., Takanashi, K., Mitani, S. Nonlinear electric field effect on perpendicular magnetic anisotropy (PMA) in Fe/MgO interfaces, J. Phys. D: Appl. Phys. 50, 40, 40LT04 (2017). https://doi.org/10.1088/1361-6463/aa87ab© IOP Publishing. Reproduced with permission. All rights reserved. c Variation of first- and second-order perpendicular magnetic anisotropy fields are shown as a function of bias voltage⁴³. Reprinted from Kanai, S., Gajek, M., Worledge, D. C., Matsukura, F. & Ohno, H. Electric field-induced ferromagnetic resonance in a CoFeB/MgO magnetic tunnel junction under dc bias voltages. Appl. Phys. Lett. 105, 242409 (2014), with the permission of AIP Publishing. d Variation of Gilbert damping constant with E⁴⁴. Reprinted from Okada, A., Kanai, S., Yamanouchi, M., Ikeda, S., Matsukura, F., Ohno, H. Electric-field effects on magnetic anisotropy and damping constant in Ta/CoFeB/MgO investigated by ferromagnetic resonance, Appl. Phys. Lett. 105, 052415 (2014), with the permission of AIP Publishing