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Results of calculations of MAE. (a) Unit cell of a monolayer Fe film on used in the calculation. The vacuum layer between each slice is thick. (b) MAE as a function of a polarization scaling factor (b). Here, and correspond to the spontaneous polarization up and down, respectively. Circles: MAE obtained using ab initio calculations. Triangles: MAE obtained by a model calculation based on Eq. (2). In the latter, the effective spin-orbit coupling parameter for Fe is taken to be .
Calculated magnetocrystalline anisotropy constant for a monolayer Fe film on . is presented for two opposite polarization orientations and is given in units of (or ). The result for a freestanding Fe monolayer is given for comparison.
Calculated spin and orbital magnetic moments (, , in units of ) of Fe and interfacial Ti atoms at the interface. Results are listed for different magnetization orientations and ferroelectric polarization orientations . is the anisotropy of the orbital moment. The results of monolayer Fe on the same square lattice are also listed for comparison.
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