VCMA effect describes the fact that in a capacitor, in which one of electrodes is made of a thin ferromagnetic metal, the magnetic properties of the ferromagnetic metal changes, when a voltage is applied to the capacitor1. Inside a metal the electrical field is screened by free electrons and cannot penetrate deep inside the metal. As a result, the voltage, which is applied to the capacitor dielectric (gate), may penetrate into and affect only the few uppermost atomic layers of the metal near the gate. However, the change of magnetic properties of the uppermost layer by the gate voltage affects the magnetic properties of the whole film. This can be only the case if the interfacial perpendicular magnetic anisotropy (PMA) is affected by the gate voltage 2. The strength of PMA is characterized by the anisotropy field Hani and proportional to the strength of spin-orbit interaction, demagnetization field and magnetization of nanomagnet. Fig.1 shows the measured Hani and coefficient of spin-orbit interaction kso in FeCoB nanomagnet under a different gate voltage. kso defies the strength of the spin-orbit interaction3. Hani decreases and kso increases under an increase of gate voltage. It is unexpected because Hani is linearly proportional to kso 3 and should increase when kso increases. It means that even though the strength of the spin-orbit interaction is affected by the gate voltage, but additionally to kso there is another voltage- dependent parameter, which defines the voltage dependence of Hani. The intrinsic field in nanomagnet or demagnetization field might be such a parameter. Fig.2 shows measured Hani and kso of different nanomagnet of different wafers. The same tendency exists in all measured nanomagnets.

References 1 Y. Shiota, T. Nozaki, F. Bonell, S. Murakami, T. Shinjo, Y. Suzuki, Nat. Mater. 11 (2012) 39–43. 2 V. Zayets, T. Nozaki, H.Saito, A. Fukushima, S.Yuasa, arXiv:1812.07077 ( 2018). 3 V.Zayets, IOA-07, MMM 2021.