Ferroelectric control of the Néel vector in $L10\text{-type}$ antiferromagnetic films

How to efficiently manipulate the Néel vector of antiferromagnets by electric methods is one of the major focuses in current antiferromagnetic spintronics. In this work, we investigated the ferroelectric control of magnetism in antiferromagnetic $L10\text{−}\mathrm{Mn}\mathrm{Pt}/\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ bilayer structures by using first-principles calculation. We studied the effect of ferroelectric polarization reversal on magnetic crystalline anisotropy (MCA) of $L10$-MnPt films with different interface structures. Our results predict a large perpendicular MCA in $L10$-MnPt films with Pt-O interface, and an in-plane MCA with Mn-O interface when they are interfaced with ferroelectric $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$. In addition, the magnitude of MCA for both interfaces can be modulated efficiently by the polarization reversal of $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$. The ferroelectric control of MCA has been analyzed based on second order perturbation theory, and it can be mainly attributed to the ferroelectric polarization driven redistribution of Pt-$5d$ orbital occupation around Fermi energy. Especially, for the Mn-O interface, the Néel vector can be switched between in-plane [100] and [110] directions, or even from in plane to out of plane at certain film thickness by reversing ferroelectric polarization. Our results may provide a nonvolatile concept for ferroelectric control of Néel vector in $L10$ antiferromagnets, which could stimulate experimental investigations on magnetoelectric effect of antiferromagnets and promote its applications in low-power consumption spintronic memory devices.

Figure 1

The side view of MnPt $\left(4\mathrm{u}.\mathrm{c}.\right)/\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ (4 u.c.)/vacuum structures with Pt-O (a) and Mn-O (b) interfaces for $P_{\uparrow }$ and $P_{\downarrow }$ ferroelectric polarization states. The light blue squares highlight the interfacial layers of $L10$-MnPt films. Yellow arrows indicate the directions of ferroelectric polarization. The crystal coordinate axes are also indicated in the bottom right corner. (c) The planar averaged electrostatic potential energy distribution in MnPt $\left(4\mathrm{u}.\mathrm{c}.\right)/\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ (4 u.c.)/vacuum structure for $P_{\uparrow }$ (black line) and $P_{\downarrow }$ (red line) polarization states.

Figure 2

Thickness dependence of MCA $\left(=E_{\mathrm{band}}\left[100\right]\text{−}{E}_{\mathrm{band}}\left[001\right]\right)$ in $\mathrm{Mn}\mathrm{Pt}/\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ bilayers for $P_{\uparrow }$ (blue) and $P_{\downarrow }$ (orange) states for the cases of (a) Pt-O and (c) Mn-O interfaces. The layer-resolved MCA for the cases of (b) Pt-O and (d) Mn-O interfaces. Panels (b) and (d) have the same tick labels for MCA, and for simplicity, only tick labels for 3 u.c. MnPt films have been shown.

Figure 3

The $d$-orbital resolved MCA on interfacial Pt atomic layer for $P_{\downarrow }$ (a) and $P_{\uparrow }$ (b) ferroelectric polarization states for the case of Pt-O interface in MnPt $\left(4\mathrm{u}.\mathrm{c}.\right)/\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ bilayer. The orbital-resolved DOS on interfacial Pt and O atoms in MnPt $\left(4\mathrm{u}.\mathrm{c}.\right)/\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ bilayers for $P_{\downarrow }$ and $P_{\uparrow }$; (c),(d) for Pt-$5d$ orbitals; (e),(f) for O-$2p$ orbitals. The Fermi level is set to zero.

Figure 4

The $d$-orbital (upper panels for spin up; lower panels for spin down) projected band structures on interfacial Pt atomic layer for $P_{\downarrow }$ (a) and $P_{\uparrow }$ (b) ferroelectric polarization states in MnPt $\left(4\mathrm{u}.\mathrm{c}.\right)/\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ bilayers. The size of symbols represents the projected weight of different $d$ orbitals. The Fermi level is set to zero.

Figure 5

The $d$-orbital resolved MCA on Pt atomic layer nearest to Mn-O interface for $P_{\downarrow }$ (a) and $P_{\uparrow }$ (b) ferroelectric polarization states for the case of Mn-O interface in MnPt $\left(4\mathrm{u}.\mathrm{c}.\right)/\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ bilayer. And the corresponding $d$-orbital resolved density of states for $P_{\downarrow }$ (c) and $P_{\uparrow }$ (d) polarization states. The Fermi level is set to zero.

Figure 6

(a) The calculated MAE ($=E\left[abc\right]-E\left[001\right]$, where $\left[abc\right]=\left[100\right]$ or [110]; the solid and dashed lines indicate MAE[100] and MAE[110], respectively) and (b) ΔMAE $\left(=\mathrm{MAE}\left[100\right]\text{−}\mathrm{MAE}\left[110\right]\right)$ as a function of MnPt films thickness in $\mathrm{Mn}\mathrm{Pt}/\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ bilayer for Mn-O interface. The red and blue lines represent the MAE for $P_{\downarrow }$ and $P_{\uparrow }$ polarization states. (c)The illustration of ferroelectric control of Néel vector in MnPt films. The black arrows indicate the polarization direction of $\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ (BTO), and the blue, red, and green arrows represent Néel vector along in-plane [100], [110], or out-of-plane [001] directions, respectively.

Figure 7

MnPt thickness dependence of MCA, magnetic dipole-dipole anisotropy energy $M_{dd}$ and the total MAE of $\mathrm{Mn}\mathrm{Pt}/\mathrm{Ba}\mathrm{Ti}{\mathrm{O}}_3$ bilayers with Pt-O interface.