Perpendicular Magnetic Anisotropy and High Spin Polarization in Tetragonal ${\mathrm{Fe}}_4\mathrm{N}/{\mathrm{BiFeO}}_3$ Heterostructures

The tetragonal ${\mathrm{Fe}}_4\mathrm{N}/{\mathrm{BiFeO}}_3(001)$ heterostructures aimed at simultaneously gaining the perpendicular magnetic anisotropy (PMA) and high spin polarization have been investigated by the first-principles method. It is found that ${\mathrm{Fe}}_4\mathrm{N}$ with ${\mathrm{Fe}}_A{\mathrm{Fe}}_B$ termination is better for achieving interfacial and inner PMA simultaneously than ${({\mathrm{Fe}}_B)}_2\mathrm{N}$ termination. When the positions of interfacial ${\mathrm{Fe}}_A$ and ${\mathrm{Fe}}_B$ relative to Fe in ${\mathrm{BiFeO}}_3$ are changed, the PMA in ${\mathrm{Fe}}_4\mathrm{N}$ transforms into the in-plane magnetic anisotropy. Especially, PMA in ${\mathrm{Fe}}_4\mathrm{N}$ near the heterointerfaces depends on the direction of ferroelectric polarization in ${\mathrm{BiFeO}}_3$. Finally, the interfacial and inner PMA of ${\mathrm{Fe}}_4\mathrm{N}$ along with high spin polarization appear in the stable ${\mathrm{Fe}}_A{\mathrm{Fe}}_B/\mathrm{Fe}{\text{−}\mathrm{O}}_2$ case owing to the $3d\text{−}3d$ orbital hybridization. These results provide the opportunities for developing multifunctional spintronic devices.

Figure 1

Structures and charge-density difference of ${\mathrm{Fe}}_4\mathrm{N}/\mathrm{BFO}$ heterostructures for (a),(b) ${\mathrm{Fe}}_A{\mathrm{Fe}}_B/\mathrm{Fe}{\text{−}\mathrm{O}}_2$, (c),(d) ${({\mathrm{Fe}}_B)}_2\mathrm{N}/\mathrm{Fe}{\text{−}\mathrm{O}}_2$, (e),(f) ${\mathrm{Fe}}_B{\mathrm{Fe}}_A/\mathrm{Fe}{\text{−}\mathrm{O}}_2$, (g),(h) ${\mathrm{Fe}}_A{\mathrm{Fe}}_B/{\mathrm{O}}_2\text{−}\mathrm{Fe}$ models (isosurface value $0.006e/{\AA }^3$). Side views of bulk ${\mathrm{Fe}}_4\mathrm{N}$ and BFO. ${\mathrm{Fe}}_A$, ${\mathrm{Fe}}_B$, and N of bulk ${\mathrm{Fe}}_4\mathrm{N}$ are located in the corner, face-centered, and body-centered sites, respectively. The ${\mathrm{Fe}}_A$ site (${\mathrm{Fe}}_B$ site, N site) indicates that ${\mathrm{Fe}}_A$ (${\mathrm{Fe}}_B$, N) atoms in the ${\mathrm{Fe}}_4\mathrm{N}\text{−}\mathrm{I}$ layer are at the top of Fe in the BFO-I layer. The gray arrows indicate the polarized direction of BFO. The yellow (blue) isosurfaces represent the charge accumulation (depletion). (i) Total and partial DOS for bulk ${\mathrm{Fe}}_4\mathrm{N}$ and BFO. $E_F=0\mathrm{eV}$.

Figure 2

Relaxed geometries of (a) ${\mathrm{Fe}}_A{\mathrm{Fe}}_B/\mathrm{Fe}{\text{−}\mathrm{O}}_2$, (b) ${({\mathrm{Fe}}_B)}_2\mathrm{N}/\mathrm{Fe}{\text{−}\mathrm{O}}_2$, (c) ${\mathrm{Fe}}_B{\mathrm{Fe}}_A/\mathrm{Fe}{\text{−}\mathrm{O}}_2$, and (d) ${\mathrm{Fe}}_A{\mathrm{Fe}}_B/{\mathrm{O}}_2\text{−}\mathrm{Fe}$ models. (e) The $z$-directional Fe(Bi)-O and ${\mathrm{Fe}}_B\text{−}{\mathrm{Fe}}_A(\mathrm{N})$ polar displacements in one layer. Distances between BFO-I and FN-I heterointerfaces ($d_{\text{inter}}$) are displayed.

Figure 3

Layer-resolved MAE of each model with $\mathrm{GGA}+U+\mathrm{SOC}$ calculations.

Figure 4

(a) DOS of Fe atoms and (b) its orbital-resolved MAE at FeAFeB/Fe-O2 (left panel) and ${\mathrm{Fe}}_B{\mathrm{Fe}}_A/\mathrm{Fe}{\text{−}\mathrm{O}}_2$ (right panel) heterointerfaces with $\mathrm{GGA}+U+\mathrm{SOC}$ calculations.

Figure 5

The magnetic order of (a) ${\mathrm{Fe}}_A{\mathrm{Fe}}_B/\mathrm{Fe}{\text{−}\mathrm{O}}_2$, (b) ${\mathrm{Fe}}_A{\mathrm{Fe}}_B/{\mathrm{O}}_2\text{−}\mathrm{Fe}$, (c) slab, and (d) bulk ${\mathrm{Fe}}_4\mathrm{N}$, based on the MAE and magnetic moment with $\mathrm{GGA}+U+\mathrm{SOC}$ calculations. The slab ${\mathrm{Fe}}_4\mathrm{N}$ is extracted from the ${\mathrm{Fe}}_A{\mathrm{Fe}}_B/\mathrm{Fe}{\text{−}\mathrm{O}}_2$ model. ${\mathrm{Fe}}_B$ in ${\mathrm{Fe}}_A{\mathrm{Fe}}_B(001)$ and ${({\mathrm{Fe}}_B)}_2\mathrm{N}(001)$ planes are defined as ${\mathrm{Fe}}_B(\mathrm{i})$ and ${\mathrm{Fe}}_B(\mathrm{ii})$, respectively. $M_{+}$ $(M_{-})$ indicates the magnetic moment with positive (negative) values.

Figure 6

(a) DOS of Fe atoms in the ${\mathrm{Fe}}_A{\mathrm{Fe}}_B/\mathrm{Fe}{\text{−}\mathrm{O}}_2$ interface with $\mathrm{GGA}+U$ and $\mathrm{GGA}+U+\mathrm{SOC}$ calculations, where positive (negative) values in the vertical axis represent spin-up and spin-down states. $E_F=0\mathrm{eV}$. SSP of the BFO-I and FN-I layer in the (001) plane are shown in (b), and SSP in the (100) plane with a location of $0.5a$ are depicted in (c), under $\mathrm{GGA}+U$ calculation. The energy intervals of [$E_F-0.4\mathrm{eV}$, $E_F$] and [$E_F$, $E_F+0.4\mathrm{eV}$] match with the below and above labels of (b) and (c), respectively. The relaxed ${\mathrm{Fe}}_A{\mathrm{Fe}}_B/\mathrm{Fe}{\text{−}\mathrm{O}}_2$ model is displayed in (c).