Magnetochiral Dichroism in a Collinear Antiferromagnet with No Magnetization

We show the directional dichroism in a collinear antiferromagnet ${\mathrm{MnTiO}}_3$. The dichroism between two distinctive antiferromagnetic states with opposite signs of staggered magnetic moments can be regarded as magnetochiral dichroism in the absence of external fields. Electric-field reversal of antiferromagnetic domain causes a change in the absorption intensity of unpolarized light around 2.15 eV. The difference in optical absorption between two antiferromagnetic states is reversed for the light propagating in the opposite direction. The absorption coefficient displays a hysteretic behavior for a cycle of sweeping the external electric or magnetic field.

Figure 1

(a) Antiferromagnetic structures of ${\mathrm{MnTiO}}_3$ (left) and ${\mathrm{Cr}}_2{\mathrm{O}}_3$ (right) projected along the $a$ axis. Arrows denote magnetic moments. Purple, light-purple and green spheres denote ${\mathrm{Mn}}^{2+}$, ${\mathrm{Ti}}^{4+}$, and ${\mathrm{Cr}}^{3+}$ ions, respectively. Oxygen atoms are omitted. On the right panel, twofold rotation axes along the $a$ axis are denoted by blue symbols. (b) A honeycomb network of ${\mathrm{Mn}}^{2+}$ in ${\mathrm{MnTiO}}_3$. White circles denote inversion centers located at bond centers.

Figure 2

(a) Magnetically induced electric polarization $P$ in ${\mathrm{MnTiO}}_3$ in the absence of electric field in a temperature $T$-increasing run. (b) Magnetic-field dependence of $P$ in ${\mathrm{MnTiO}}_3$. Before each measurement, an electric field $E_{\text{poling}}$ of $\pm 1.1\mathrm{MV}/\mathrm{m}$ and a magnetic field of 6 T were applied along the $c$ axis at 55 K and then the electric field was switched off. (c) Electric-field dependence of magnetically induced component of $P$ in ${\mathrm{MnTiO}}_3$ in a magnetic field of 6 T along the $c$ axis. Component in $P$ induced by the external electric field is subtracted.

Figure 3

(a) Optical absorption spectra of ${\mathrm{MnTiO}}_3$ at 55 and 80 K in a magnetic field of ${\mu }_0{H}_c=6\mathrm{T}$ and an electric field of $E_c=2.2\mathrm{MV}/\mathrm{m}$. (b) Experimental configuration of the measurements of the differential spectrum for the light propagating along the $c$ axis. External electric and magnetic fields are simultaneously applied along the $c$ axis. The electric field is isothermally switched between $E_c=2.2$ and $-2.2\mathrm{MV}/\mathrm{m}$ to reverse the direction of $\mathit{L}$. (c) Differential spectra $\mathrm{\Delta }\alpha d(\omega )$ of ${\mathrm{MnTiO}}_3$ between an electric field $E_c=2.2$ and $-2.2\mathrm{MV}/\mathrm{m}$. The contribution of the scattering by the gold electrodes to the observed electrochromic effect is also excluded. (d),(e) The variation of $\mathrm{\Delta }\alpha d(\omega )$ with the reversal of magnetic field and/or the direction of light propagation. (f),(g) Experimental configurations corresponding to (d) and (e), respectively. Compared with (b), the magnetic field $\mathit{H}$ is reversed in (f) and the propagation vector $\mathit{k}$ is reversed in (g).

Figure 4

(a) Control of absorbance in ${\mathrm{MnTiO}}_3$ by sweeping (a) electric and (b) magnetic fields. The integrated absorption intensities $I={\int }_{2.0\mathrm{eV}}^{2.3\mathrm{eV}}\alpha dd(\hslash \omega )$ for a photon-energy range between 2.0 and 2.3 eV are plotted. (c) Differential spectra of ${\mathrm{MnTiO}}_3$ in the absence of external fields between two different antiferromagnetic states. (d) Relation among the coordination environment, local magnetization, and the sign of MCHD of each ${\mathrm{MnO}}_6$ cluster. Pairs of two ${\mathrm{MnO}}_6$ clusters with the same sign of $T^c$ and MCHD are shaded with the same color, red or blue according to the chirality (left or right handed) and local magnetization ($+$) or ($-$). Purple and blue spheres are ${\mathrm{Mn}}^{2+}$ and ${\mathrm{O}}^{2-}$ ions, respectively. Arrows on ${\mathrm{Mn}}^{2+}$ ions denote magnetic moments. Schematic top view of each ${\mathrm{MnO}}_6$ cluster is shown in the left column.