Role of Ferroelectricity, Delocalization, and Occupancy of $d$ States in the Electrical Control of Interface-Induced Magnetization

In this study, the influence of generalized-gradient-approximation (GGA) deficiencies, $d$-band occupancy, and itinerancy in the magnetoelectric (ME) effect is investigated from first principles by changing the interface composition of the ${\mathrm{Fe}}_3\mathrm{Si/}M{/\mathrm{Ba}\mathrm{Ti}\mathrm{O}}_3$ heterostructure, where $M$ stands for an atomic layer of pure $3d$ or $4d$ metals (from Sc to $\mathrm{Cd}$). The lattice overestimation of the ferroelectric phase leads to the overestimation of the magnetoelectricity, which can be partially corrected by using the Perdew-Burke-Ernzerhof functional revised for solids. The inclusion of Hubbard-like corrections generally predicts larger changes of interface magnetization upon the reversal of polarization direction, although preserving the trends of plain GGA calculations. The itinerancy of $4d$ states does not favor the interface ME coupling due to the lower density of states near the Fermi level. Here, it is shown how the control of the $d$-state energy levels through their electronic occupancy has the potential to substantially enhance the interface ME effect induced by bonding effects. A substantial increase of magnetoelectricity in the ${\mathrm{Fe}}_3\mathrm{Si/}{\mathrm{Ba}\mathrm{Ti}\mathrm{O}}_3$ heterostructure can be achieved by replacing interface $\mathrm{Fe}$ atoms with V or $\mathrm{Mn}$.

Figure 1

(a) Bulk structures of ${\mathrm{Fe}}_3\mathrm{Si}$ ($Fm\overline{3}m$) and ${\mathrm{Ba}\mathrm{Ti}\mathrm{O}}_3$ ($P4mm$). The PBE local magnetic moment for each atomic site is shown for ${\mathrm{Fe}}_3\mathrm{Si}$, whereas the effective Bader charges are presented for ${\mathrm{Ba}\mathrm{Ti}\mathrm{O}}_3$. The top view with the in-plane lattice parameters obtained from PBE is shown, which correspond to a lattice mismatch of 0.97%. (b) The side view of the ${\mathrm{Fe}}_3\mathrm{Si/}M{/\mathrm{Ba}\mathrm{Ti}\mathrm{O}}_3(001)$ heterostructures having the ${\mathrm{Ti}\mathrm{O}}_2$ termination. The ferroelectric polarization reversal in the [$001$] direction is depicted.

Figure 2

PBEsol results for the interfacial separation work, $W_{\mathrm{sep}}$, and structural parameters used to characterize the interfacial region of the ${\mathrm{Fe}}_3\mathrm{Si/}M{/\mathrm{Ba}\mathrm{Ti}\mathrm{O}}_3$ heterostructures. The shortest distance between $M$ and $\mathrm{Ti}$, O, $\mathrm{Fe}$, and $\mathrm{Si}$ atoms, $d_{M-\mathrm{Ti}}$, $d_{M-\mathrm{O}}$, $d_{M-\mathrm{Fe}}$, and $d_{M-\mathrm{Si}}$, respectively.

Figure 3

The amplitude of the interfacial magnetic moment change, $\mathrm{\Delta }{m}_{\mathrm{int}}$, upon the polarization reversal in the ${\mathrm{Fe}}_3\mathrm{Si}/M/{\mathrm{Ba}\mathrm{Ti}\mathrm{O}}_3$ heterostructures. For the $\mathrm{GGA}+U$ calculations, the Hubbard-U corrections at the $\mathrm{Ti}$ sites of BTO are 4.31 eV (PBE) and 4.14 eV (PBEsol).

Figure 4

The PBEsol relative $\mathrm{Ti}—\mathrm{O}$ displacement along the ${\mathrm{Ba}\mathrm{Ti}\mathrm{O}}_3$ film for the ${\mathrm{Fe}}_3\mathrm{Si/}M{/\mathrm{Ba}\mathrm{Ti}\mathrm{O}}_3$ heterostructures in both $P_{\mathrm{up}}$ and $P_{\mathrm{down}}$ configurations [as illustrated in Fig. 1 (b)]. The dashed red and solid blue lines represent the values for the clean surface of ${\mathrm{Ba}\mathrm{Ti}\mathrm{O}}_3$. The respective interfacial magnetic moment change, $\mathrm{\Delta }{m}_{\mathrm{int}}$, is given for each system.

Figure 5

The PBEsol-averaged effective charges by species, $Q_{\mathrm{eff}}^X$, for the interfacial atoms $M$, $\mathrm{Ti}$, and $\mathrm{O}$, and includes the nearest neighbors $\mathrm{Fe}$ and $\mathrm{Si}$ atoms. Gray and orange regions indicate if the species are in a cationic or anionic state. Here, $Z_{\mathrm{val}}^X$ and $Q_{\mathrm{Bader}}^X$ represent the number of valence electrons and the Bader charge, respectively.

Figure 6

PBEsol results for (a) the electron density difference, $\mathrm{\Delta }\rho$, upon the ${\mathrm{Fe}}_3\mathrm{Si}/\mathrm{V}/{\mathrm{Ba}\mathrm{Ti}\mathrm{O}}_3$ formation from the FM and FE phases frozen in their interface relaxed configurations. (b) The local density of states for the $d_{xz}$ V and $d_{xz}$ Ti states in the heterostructure. The dashed red and solid blue lines correspond to the $P_{\mathrm{down}}$ and $P_{\mathrm{up}}$ configurations, respectively. The dashed vertical line indicates the Fermi energy, which is located at 0.00 eV.