The interplay between magnetoelectricity and magnetoelasticity (MEL) is studied in the context of voltage-controlled magnetic anisotropy (VCMA). Strain plays more than the role of changing lattice constants—that of the internal electric field in the heterostructure. As a prototype, FePt/MgO(001) is visited, where the behavior of two interfaces are drastically different: one exhibits switching, the other does not. Whether an external electric field ($E_{\text{ext}}$) is present or not, we found the VCMA coefficient larger than $1\mathrm{pJ}/\left(\mathrm{V}\mathrm{m}\right)$ as a consequence of the rearrangement of $d$ orbitals with $m=\pm 1$ and $\pm 2$ in response to an external electric field. In addition, magnetocrystalline anisotropy is analyzed with strain taken into account, where a nonlinear feature is presented, only accountable by invoking second-order MEL.

• Received 5 January 2020
• Revised 22 May 2020
• Accepted 27 May 2020

DOI:https://doi.org/10.1103/PhysRevB.101.214436