Gate-Controllable Magneto-optic Kerr Effect in Layered Collinear Antiferromagnets

Using symmetry arguments and a tight-binding model, we show that for layered collinear antiferromagnets, magneto-optic effects can be generated and manipulated by controlling crystal symmetries through a gate voltage. This provides a promising route for electric field manipulation of the magneto-optic effects without modifying the underlying magnetic structure. We further demonstrate the gate control of the magneto-optic Kerr effect (MOKE) in bilayer ${\mathrm{MnPSe}}_3$ using first-principles calculations. The field-induced inversion symmetry breaking effect leads to gate-controllable MOKE, whose direction of rotation can be switched by the reversal of the gate voltage.

Figure 1

(a) Schematic of a honeycomb lattice with collinear Néel order. Up (down) spins are represented by filled (open) circles. The system possesses combined $\mathcal{T}\mathcal{I}$ symmetry although both $\mathcal{T}$ and $\mathcal{I}$ symmetries are individually broken. (b),(c) Energy bands of the tight-binding model with broken mirror symmetry (${\lambda }_R=0.05t$, ${\lambda }_V=0$) and broken in-plane inversion symmetry (${\lambda }_R=0$, ${\lambda }_V=0.05t$), respectively. In both cases, ${\lambda }_{\mathrm{SO}}=0.06t$ and ${\lambda }_M=0.7t$. The spin degeneracy of the bands is lifted in both cases. (d) The imaginary part of the optical Hall conductivity (${\sigma }_{xy}^{\prime \prime }$) computed for ${\lambda }_R=0.05t$ (black line), ${\lambda }_V=0.05t$ (red line), and ${\lambda }_V=-0.05t$ (blue line). ${\sigma }_{xy}^{\prime \prime }$ is zero when only ${\lambda }_R$ is turned on and becomes nonzero when ${\lambda }_V\ne 0$. As the sign of ${\lambda }_V$ is reversed, so is ${\sigma }_{xy}^{\prime \prime }$. The smearing parameter was set to $0.1t$.

Figure 2

(a) The crystal structure of monolayers of ${\mathrm{MnPSe}}_3$. The transition metal Mn atoms form a honeycomb structure with ${\mathrm{P}}_2{\mathrm{Se}}_6$ ligand occupying the center of the honeycomb. (b) The side view of the crystal structure of bilayer ${\mathrm{MnPSe}}_3$. The crystal structure is drawn using vesta [17]. (c) The band structure of the bilayer ${\mathrm{MnPSe}}_3$ in the absence of an electric field. The inset shows the Mn atoms in the bilayer. (d) The band structure of the bilayer ${\mathrm{MnPSe}}_3$ in the presence of an electric field ($0.4\mathrm{V}/\mathrm{nm}$) along the $z$ direction. The inset shows the lifting of the spin degeneracy of the bands due to the $\mathcal{T}\mathcal{I}$ symmetry breaking by the field.

Figure 3

(a) The real part of ${\sigma }_{xy}$, (b) the imaginary part of ${\sigma }_{xy}$, and (c) the real part of ${\sigma }_{xx}$ of bilayer ${\mathrm{MnPSe}}_3$ at zero field (black line) and a field with strength $0.4\mathrm{V}/\mathrm{nm}$ (red line). The smearing parameter was set to 0.1 eV. The corresponding (d) Kerr rotation angle and (e) ellipticity angle computed as a function of photon energy $\hslash \omega$ for bilayer ${\mathrm{MnPSe}}_3$ on a wedged ${\mathrm{SiO}}_2$ substrate. The zero point of the energy corresponds to the top of the valence band. (f) A schematic of a magneto-optic device made from layered antiferromagnets. $S$, $D$, and $G$ stand for source, drain, and gate, respectively. In the incident and the reflected light, an arrow shows the direction of the polarization direction. On reflection from the antiferromagnets, the plane of polarization of light can be rotated (from green to red arrow), and an ellipticity is induced, depending on the gate voltages.