Magneto-chiral dichroism of ${\mathrm{CsCuCl}}_3$

In this Rapid Communication, we investigate the magneto-chiral dichroism (MChD) of right- and left-handed ${\mathrm{CsCuCl}}_3$ crystals in a strong magnetic field up to 14.5 T. We perform near-infrared optical measurements, and the results show a change in the absorption coefficient of an intra-atomic $d\text{−}d$ transition in a ${\mathrm{Cu}}^{2+}$ ion at approximately 1.5 eV. The magnitude of MChD was found to be proportional to the magnetization, which depends on the magnetic field and temperature. We verify this relation by developing a simple ${\mathrm{CuCl}}_6$ cluster model.

Figure 1

(a) Crystalline structure of right-handed (space group $P{6}_{1}22$) ${\mathrm{CsCuCl}}_3$. ${\mathrm{Cu}}^{2+}$ helical chains run along the $c$ axis. This figure was produced using vesta [25]. (b) Schematic of the measurement system. The directions of $\mathit{H}$ and $\mathit{k}$ are defined as shown. The direction of light was reversed by changing the fibers, as shown by the dotted lines.

Figure 2

$H$-odd component of absorption coefficient change, which is attributed to the magneto-chiral dichroism. (a), (b) Magnetic-field dependence of MChD spectrum, in (a) right-handed and (b) left-handed ${\mathrm{CsCuCl}}_3$ at 4.2 K. (c) Absorption spectrum of ${\mathrm{CsCuCl}}_3$ at 4.2 K. (d) Magnetic-field dependence of MChD at 1.5 eV and magnetization of ${\mathrm{CsCuCl}}_3$ at 3 K [17]. (e) Temperature dependence of MChD at 1.5 eV and magnetization of ${\mathrm{CsCuCl}}_3$ at 14 T [17] (green line). The blue line shows $M$ at 0.1 T.

Figure 3

(a) Energy levels of $d$ orbitals of ${\mathrm{Cu}}^{2+}$ ion in ${\mathrm{CsCuCl}}_3$. These energies are determined by a Gaussian fitting of the optical absorption spectrum. (b) Spin configuration of the initial state.

Figure 4

$H$-even component of absorption coefficient change $\mathrm{\Delta }{\alpha }_{\mathrm{even}}$, which is regarded as the Cotton-Mouton effect. (a) $\mathrm{\Delta }{\alpha }_{\mathrm{even}}$ spectrum with $H=1–14$ T (color lines) and absorption coefficient (black line). (b) The magnetic-field dependence of the $H$-even component at 1.55 eV (red circles). The green curve shows the square of the magnetization $M^2$. (c) Temperature dependence of the $H$-even component at 1.55 eV (red circles). The temperature dependence of $M^2$ is also drawn as a green line lower than 15 K. Blue lines show the temperature dependence of $M^2$ at 0.1 T to estimate the $M^2\text{−}T$ graph in the paramagnetic phase.