Magnetic order in $\alpha -{\text{RuCl}}_3$: A honeycomb-lattice quantum magnet with strong spin-orbit coupling

We report magnetic and thermodynamic properties of single crystal $\alpha -{\text{RuCl}}_3$, in which the ${\text{Ru}}^{3+}\left(4d^5\right)$ ion is in its low spin state and forms a honeycomb lattice. Two features are observed in both magnetic susceptibility and specific heat data; a sharp peak at 7 K and a broad hump near 10–15 K. In addition, we observe a metamagnetic transition between 5 and 10 T. Our neutron diffraction study of single crystal samples confirms that the low temperature peak in the specific heat is associated with a magnetic order with unit cell doubling along the honeycomb (100) direction, which is consistent with zigzag order, one of the types of magnetic order predicted within the framework of the Kitaev-Heisenberg model.

Figure 1

(a) Temperature dependence of magnetic susceptibilities with a field of 0.5 T applied parallel to the $c$ axis and within the $ab$ plane. Inset shows a photograph of a typical single crystal sample used in our studies. (b) Inverse susceptibility in both directions. Also plotted is the inverse of powder average susceptibility ${\chi }_{\text{ave}}\equiv (2{\chi }_{ab}+{\chi }_c)/3$.

Figure 2

(a) Detailed view of low temperature region of the parallel and perpendicular susceptibilities shown in Fig. 1. ${\chi }_c$ values are multiplied by 10 to fit on the same scale. Also shown is the temperature dependence of heat capacity. (b) The nonmonotonic part of the heat capacity, obtained by subtracting a smooth polynomial background [i.e., the solid line in (a)] from the raw data. The entropy change $\Delta S_m$ was obtained by integration: $\Delta S_m={\int }_0^T(\Delta C_p/T)dT$.

Figure 3

(a) Scans across the ($-0.5$, 0, 1) peak position obtained at two temperatures, 1.7 and 8 K. A peak is observed at 1.7 K. A large sloping background is due to the unscattered neutron beam. (b) Temperature dependence of the integrated intensity of the peak shown in (a). A background scan obtained at 20 K was subtracted from the raw data before the counts were added up. The solid line is a fit to $\sim {(T_c-T)}^{2\beta }$ with $\beta =0.2\pm 0.1$ and $T_c=8.2\left(5\right)\text{K}$. (c) $L$ dependence of the magnetic peak at two temperatures. The error bars in the figure represent one standard deviation. The solid line is based on the Hendricks-Teller calculation as described in the text. The inset shows the unit vectors in real and reciprocal space, and spin arrangements in the zigzag and stripe ordering pattern.

Figure 4

Magnetization isotherm at 1.7 K measured with magnetic fields applied perpendicular to the honeycomb lattice. The inset shows $\Delta M$ for both positive (empty circles) and negative (filled circles) field directions, obtained by subtracting linear dependence (dashed line) from the raw data.