Successive magnetic phase transitions in $\alpha -{\mathrm{RuCl}}_3$: XY-like frustrated magnet on the honeycomb lattice

The layered compound $\alpha -{\mathrm{RuCl}}_3$ is composed of a honeycomb lattice of magnetic ${\mathrm{Ru}}^{3+}$ ions with the $4d^5$ electronic state. We have investigated the magnetic properties of $\alpha -{\mathrm{RuCl}}_3$ via magnetization and specific heat measurements using single crystals. It was observed that $\alpha -{\mathrm{RuCl}}_3$ undergoes a structural phase transition at $T_t\simeq 150$ K accompanied by fairly large hysteresis. This structural phase transition is expected to be similar to that observed in closely related ${\mathrm{CrCl}}_3$. The magnetizations and magnetic susceptibilities are strongly anisotropic, which mainly arise from the anisotropic $g$ factors, i.e., $g_{ab}\simeq 2.5$ and $g_c\simeq 0.4$ for magnetic fields parallel and perpendicular to the $ab$ plane, respectively. These $g$ factors and the obtained entropy indicate that the effective spin of ${\mathrm{Ru}}^{3+}$ is one-half, which results from the low-spin state. Specific heat data show that magnetic ordering occurs in four steps at zero magnetic field. The successive magnetic phase transitions should be ascribed to the competition among exchange interactions. The magnetic phase diagram for $H\parallel ab$ is obtained. We discuss the strongly anisotropic $g$ factors in $\alpha -{\mathrm{RuCl}}_3$ and deduce that the exchange interaction is strongly XY-like. $\alpha -{\mathrm{RuCl}}_3$ is magnetically described as a three-dimensionally coupled XY-like frustrated magnet on a honeycomb lattice.

Figure 1

Monoclinic crystal structure ($C2/m$) of $\alpha -{\mathrm{RuCl}}_3$ at room temperature (a) viewed perpendicular to the $ab$ plane and (b) viewed along the $b$ axis. Small purple and large green spheres are ${\mathrm{Ru}}^{3+}$ and ${\mathrm{Cl}}^{-}$ ions, respectively. Thin solid lines denote the chemical unit cells. (c) Trigonal crystal structure ($R\overline{3}$) of ${\mathrm{CrCl}}_3$ in the low-temperature phase viewed along the $c$ axis, which is expected to be the same as the low-temperature crystal structure of $\alpha -{\mathrm{RuCl}}_3$.

Figure 2

Temperature dependence of (a) magnetic susceptibilities $\chi =M/H$ and (b) inverse magnetic susceptibilities in $\alpha -{\mathrm{RuCl}}_3$ measured at $H=0.1\text{T}$ for $H\parallel ab$ and $H\perp ab$. The arrow indicates the structural phase transition temperature $T_{\mathrm{t}}$.

Figure 3

Hysteresis in magnetic susceptibility observed around $T=150$ K for $H\perp ab$.

Figure 4

(a) Low-temperature magnetic susceptibilities in $\alpha -{\mathrm{RuCl}}_3$ measured at $H=0.1\text{T}$ for (a) $H\parallel ab$ and (b) $H\perp ab$. Arrows indicate the anomalies caused by magnetic phase transitions.

Figure 5

Low-temperature magnetic susceptibilities in $\alpha -{\mathrm{RuCl}}_3$ measured at various magnetic fields for $H\parallel ab$. The susceptibility data are shifted upward by multiples of $2\times {10}^{-3}$ emu/mol. Arrows indicate the transition temperatures determined from the specific heat anomaly. (b) Derivative of $\chi$ with respect to $T$ measured at $H=6$ T. Arrows indicate the transition temperatures determined from the specific heat anomaly, which are close to those giving local maxima or minima of $d\chi /dT$.

Figure 6

Magnetic field dependence of the magnetization $M$ and its field derivative $dM/dH$ measured at 1.3 K for $H\parallel ab$ in $\alpha -{\mathrm{RuCl}}_3$ for the highest fields of (a) 57.5 and (b) 14 T. Arrows indicate the transition fields.

Figure 7

Magnetic field dependence of the magnetization $M$ and its field derivative $dM/dH$ measured at 1.3 K for $H\perp ab$ in $\alpha -{\mathrm{RuCl}}_3$ with the highest fields of (a) 57.5 and (b) 20 T. Arrows indicate the transition fields.

Figure 8

Low-temperature specific heat $C$ and $C/T$ in $\alpha -{\mathrm{RuCl}}_3$ measured at various magnetic fields for $H\parallel ab$. The specific heat data and $C/T$ are shifted upward by multiples of 2 J/mol K and 0.2 J/$\mathrm{mol}{\mathrm{K}}^2$, respectively. Arrows show the anomalies indicative of magnetic phase transitions.

Figure 9

Temperature dependence of $C_{\mathrm{mag}}/T$ in $\alpha -{\mathrm{RuCl}}_3$ measured at zero magnetic field. The solid curve represents the magnetic entropy $S_{\mathrm{mag}}$.

Figure 10

Field scans of the specific heat in $\alpha -{\mathrm{RuCl}}_3$ measured at 1.3, 2.4, and 3.5 K for $H\parallel ab$. Arrows show the anomalies indicative of magnetic phase transitions.

Figure 11

Magnetic phase diagram for $H\parallel ab$. The circular and triangular symbols are transition points determined from the temperature and field dependencies of specific heat, respectively, and the rectangular symbols are those determined from the magnetization process. Solid and dashed lines are visual guides.

Figure 12

Energy levels of $E_{\mathrm{l}}$ and $E_{\mathrm{q}}^{\pm }$ as a function of $\delta /{\lambda }^{\prime }$.

Figure 13

(a) $g$ factors as a function of $\delta /{\lambda }^{\prime }$. (b) Enlargement of the $g$ factors between $\delta /{\lambda }^{\prime }=0$ and 2. The two horizontal lines are experimental $g$ factors estimated from the high-field magnetization process. Open circles and squares represent two sets of the $g$ factors suitable for $\alpha -{\mathrm{RuCl}}_3$.

Figure 14

Classical configuration of spins ${\mathit{s}}_i$ and ${\mathit{s}}_j$ and coordinate systems. The $y$ direction is chosen to be parallel to the bond vector ${\mathit{r}}_{12}$ and $\mathit{D}$.