Light-induced magnetization driven by interorbital charge motion in the spin-orbit assisted Mott insulator $\alpha \text{−}{\mathrm{RuCl}}_3$

In a honeycomb-lattice spin-orbit assisted Mott insulator $\alpha \text{−}{\mathrm{RuCl}}_3$, ultrafast magnetization is induced by circularly polarized excitation below the Mott gap. Photocarriers play an important role, which are generated by turning down the synergy of the onsite Coulomb interaction and the spin-orbit interaction realizing the insulator state. An ultrafast 6 fs measurement of photocarrier dynamics and a quantum mechanical analysis clarify the mechanism, according to which the magnetization emerges from a coherent charge motion between different $t_{2g}$ orbitals $\left(d_{yz}\text{−}{d}_{xz}\text{−}{d}_{xy}\right)$ of ${\mathrm{Ru}}^{3+}$ ions. This ultrafast magnetization is weakened in the antiferromagnetic (AFM) phase, which is opposite to the general tendency that the inverse Faraday effect is larger in AFM compounds than in paramagnetic ones. This temperature dependence indicates that the interorbital charge motion is affected by pseudospin rotational symmetry breaking in the AFM phase.

Figure 1

(a) Honeycomb lattice of $\alpha \text{−}{\mathrm{RuCl}}_3$ and hybridization between $t_{2g}$ orbitals of Ru and ligand $p_z$ orbital of Cl which causes hopping $t$ between different $t_{2g}$ orbitals (such as $d_{xz}\text{−}{d}_{yz}$). (b) Imaginary part of the permittivity spectrum in mid- and near-infrared regions [31]. The low-energy part $<0.9\mathrm{eV}$ (magnified 25 times) is attributed to spin-orbit coupling (SOC) in-gap states [31, 32, 33]. The experimental configuration of the optomagneto measurement (polarization rotation induced by a circularly polarized pump pulse) and the excitation from $J_{\mathrm{eff}}=\frac{3}{2}$ to $\frac{1}{2}$ states [32] are schematically shown.

Figure 2

(a) Time evolutions of $\mathrm{\Delta }\theta$ (upper panel) and transmittance ($\mathrm{\Delta }T/T$) (lower panel) of $\alpha \text{−}{\mathrm{RuCl}}_3$ ($E_{\mathrm{pu}}=0.89\mathrm{eV}$, $I_{\mathrm{ex}}=4\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$, $E_{\mathrm{pr}}=0.62\mathrm{eV}$, $\left|\right|ab$ plane, ${\sigma }^{+}$: red curves, ${\sigma }^{-}$: blue curves) at 4 K (dashed curves) and 17 K (solid curves). (b) Temperature dependences of $\mathrm{\Delta }\theta$ at $t_{\mathrm{d}}=0\mathrm{ps}$ (upper panel) and at $t_{\mathrm{d}}=10\mathrm{ps}$ (lower panel). Optomagneto spectra (17 K) of (c) $\mathrm{\Delta }\theta$ and (d) Δη for (i) $E_{\mathrm{pu}}=0.30\mathrm{eV}$, (ii) $E_{\mathrm{pu}}=0.62\mathrm{eV}$, and (iii) $E_{\mathrm{pu}}=0.89\mathrm{eV}$. The upper panel of (c) shows the imaginary permittivity spectrum [31] (×25 for $<0.9\mathrm{eV}$). The maximum values of $\mathrm{\Delta }\theta$ for $E_{\mathrm{pu}}=0.30–0.89\mathrm{eV}$ are shown by the red dots. A schematic illustration of the optomagneto two-step process is shown in the upper panel of (d).

Figure 3

(a) Imaginary part of the permittivity spectrum at 10 K [31] around the Mott gap. $\mathrm{\Delta }R/R$ spectra for (b) $E_{\mathrm{pu}}=0.62\mathrm{eV}$ and (c) $E_{\mathrm{pu}}=0.89\mathrm{eV}$. $I_{\mathrm{ex}}=1\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$, 17 K, $t_{\mathrm{d}}=0\mathrm{ps}$ (red dots), 0.5 ps (orange circles), 1 ps (green circles). The insets of (b) and (c) show the $I_{\mathrm{ex}}$ dependence of $\mathrm{\Delta }R/R$ at $E_{\mathrm{pr}}=1.2\mathrm{eV}$. The circles with the dashed curve in (c) show $\mathrm{\Delta }R/R$ for $E_{\mathrm{pu}}=1.55\mathrm{eV}$ ($4\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$, ×0.17, 4 K, $t_{\mathrm{d}}=0\mathrm{ps}$). (d) Time profiles of $\mathrm{\Delta }R/R$ ($E_{\mathrm{pr}}=1.2\mathrm{eV}$) for $E_{\mathrm{pu}}=0.62\mathrm{eV}$ (blue circles) and $E_{\mathrm{pu}}=0.89\mathrm{eV}$ (red circles ×0.6). (e) Time profile of $\mathrm{\Delta }R/R$ measured by using a 6 fs near-infrared pulse ($E_{\mathrm{pu}}=0.55–0.95\mathrm{eV}$, $E_{\mathrm{pr}}=0.60\mathrm{eV}$ (with polarization perpendicular to that of the pump pulse), $I_{\mathrm{ex}}=1.0\mathrm{mJ}/\mathrm{c}{\mathrm{m}}^2$, 17 K). The red curve shows exponential decay with a time constant of 0.17 ps. The oscillating component is shown in the inset [green circles: 17 K, blue circles 300 K, red curve: oscillation with a period of 36 fs (Supplementary 9 [21])].

Figure 4

(a) Honeycomb lattice structure of $\alpha \text{−}{\mathrm{RuCl}}_3$ used in the calculation. It has 3 u.c., each of which consists of two sites A and B. Periodic boundary conditions are used to maintain the threefold symmetry. $X_1$, $Y_1$, and $Z_1$ connect nearest-neighbor sites, and $X_2$, $Y_2$, and $Z_2$ connect next-nearest-neighbor sites. (b) Calculated optical conductivity spectra for the ground state (red and blue curves are used for $\left|\right|a$, $\left|\right|b$). The spectra $<0.9\mathrm{eV}$ are magnified by 15 times. (c) Calculated time profiles of photoinduced magnetization in the direction of $\perp ab$. An electric field amplitude times intersite distance $F$ (V) of 0.2 (an electric field amplitude of 5.8 MV/cm), frequencies $\hslash \omega$ (eV) of 0.3, 0.6, and a pulse width of 96 fs are used.