Detecting Magnetoelectric Effect in a Metallic Antiferromagnet via Nonreciprocal Rotation of Reflected Light

Certain types of media breaking both space-inversion (P) and time-reversal (T) symmetries but preserving their combination PT exhibit the polarization rotation of reflected light even when that of transmitted light is prohibited. Such an effect is termed nonreciprocal rotation of reflected light (NRR). Although NRR shows nearly the same phenomenon as the magnetooptical Kerr effect or, equivalently, the Hall effect at optical frequencies, its origin is distinct and ascribed to a magnetoelectric (ME) effect at optical frequencies, i.e., the optical ME effect. Here we show the observation of NRR in a metallic antiferromagnet ${\mathrm{TbB}}_4$. The result demonstrates that the ME effect in a metallic system, which is considered to be ill defined, can be detected using reflected light. Furthermore, we spatially resolve antiferromagnetic domains in ${\mathrm{TbB}}_4$ by microscope observations of NRR. Our work offers a unique way to probe the ME effect in metallic systems.

Figure 1

(a) Crystal and magnetic structures in the AFM1 phase $[T_{\mathrm{N}2}\le T\le T_{\mathrm{N}1}]$ of ${\mathrm{TbB}}_4$. Red and blue arrows denote Tb moments. Two distinct domain states ($\mathrm{A}+$ and $\mathrm{A}-$) related by either space-inversion operation ($\overline{1}$) or time-reversal operation ($1^{\prime }$) are depicted. (b) Temperature profiles of $M/H$ along the $a$ axis and resistivity normal to the $c$ axis. (c) A schematic image of nonreciprocal rotation of reflected light (NRR). The polarization plane (green arrows) of light reflected from the $ab$ face of ${\mathrm{TbB}}_4$ is rotated in opposite directions for the two distinct domains.

Figure 2

Spatial distributions of NRR in ${\mathrm{TbB}}_4$. (a)–(c) Two-dimensional maps of $\mathrm{\Delta }I/I$, which approximately correspond to the polarization rotation of reflected light, at 50 (a) and 35 K (b),(c). These maps were obtained in the same area of the specimen. The map of (b) was obtained during the first cooling. Then, that of (c) was obtained during the second cooling after the sample was heated above $T_{\mathrm{N}1}$. Schematic illustrations in (b) depict the expected domain states in the respective contrast regions. (d) Temperature dependence of the difference between $\mathrm{\Delta }I/I$ at the light and dark areas, i.e., $\mathrm{A}+$ and $\mathrm{A}-$ domains, $|{(\mathrm{\Delta }I/I)}_{\mathrm{A}+}-{(\mathrm{\Delta }I/I)}_{\mathrm{A}-}|$, which is proportional to the magnitude of NRR. The insets of (d) display $\mathrm{\Delta }I/I$ maps used to obtain the difference at the respective temperatures. The red curve is a guide to the eye.

Figure 3

Antiferromagnetic domains in the two AFM phases. $\mathrm{\Delta }I/I$ maps at 35 K in the AFM1 phase (a),(c) and at 14 K in the AFM2 phase (b),(d). The incident linearly polarization light ($E_{\mathrm{LP}}^{\omega }$) was set along $[1\overline{1}0]$ for (a),(b) and along [110] for (c),(d). Schematic illustrations depict the expected domain states in the respective contrast regions.

Figure 4

NRR spectra in the AFM1 phase. (a)–(f) Two-dimensional maps of the rotation angle $\theta$ (a)–(c) and the ellipticity $\eta$ (d)–(f) at 34 K with monochromatic light whose photon energy is 2.10 (left), 2.25 (middle), and 2.73 eV (right). (g) Spectra of $\theta$ and $\eta$. $\theta$ crosses the zero line at approximately 2.3 eV (green-colored area) while $\eta$ shows a peak. The red and blue curves are guides to the eye.