Charge and spin interplay in a molecular-dimer-based organic Mott insulator

Triangular lattice quasi-two-dimensional Mott insulators based on the bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF) molecule and its analogies present a possibility to produce exotic phases by coupling charge and spin degrees of freedom. In this work we discuss magnetic properties of one such material, $\kappa$-(BEDT-${\mathrm{TTF})}_2\mathrm{Hg}{\left(\mathrm{SCN}\right)}_2\mathrm{Cl}$, which is found at the border of the phase transition between a Mott insulator into a charge ordered state. Our magnetic susceptibility and cantilever magnetization measurements demonstrate how the charge degree of freedom defines magnetic properties for few different charge phases observed in this material as a function of temperature. Between $T_{\text{CO}}=30\text{K}$ and $T_{\text{S}}=24\text{K}$ we observe charge and spin separation due to one-dimensional charge stripes formed in this material below $T_{\text{CO}}=30\text{K}$. Below $T_{\text{S}}=24\text{K}$ charge and spin degrees of freedom demonstrate coupling. Spin-singlet correlations develop below 24 K, however, the melting of charge order below 15 K prevents the spin-singlet-state formation, leaving the system in the inhomogeneous state with charge ordered spin-singlet domains and charge and spin fluctuating ones.

Figure 1

(a) A projection of the structure of (BEDT-${\mathrm{TTF})}_2$ layer of $\kappa$-(BEDT-${\mathrm{TTF})}_2\mathrm{Hg}{\left(\mathrm{SCN}\right)}_2\mathrm{Cl}$ on $bc$ crystallographic plane. Dashed line circles indicate dimers of (BEDT-${\mathrm{TTF})}_2$. (b) A schematic representation of the 2D layer of (BEDT-${\mathrm{TTF})}_2$ dimers. Thick black lines represent BEDT-TTF molecules bound in a dimer by a shared orbital (grey oval). In both (a) and (b) the red triangle shows a unit of triangular lattice.

Figure 2

(a) Temperature dependence of the specific heat ${\mathrm{C}}_p$(T) of $\kappa$-(BEDT-${\mathrm{TTF})}_2\mathrm{Hg}{\left(\mathrm{SCN}\right)}_2\mathrm{Cl}$ at 0 T. The inset shows heat capacity in the range 200 mK to 3 K. Note $\gamma =0$ within the error of the measurements. (b) Temperature dependence of ${\chi }_M\left(T\right)$. Three regimes related to the charge degree of freedom [9] are indicated by color. Schematic charge distribution on the orbital of (BEDT-${\mathrm{TTF})}_2$ dimer is shown, where grey indicates homogeneous charge in the metallic state above $T_{\text{CO}}=30\text{K}$, red are the charge-rich, and blue are the charge-poor molecules in the charge-ordered insulating state. Low-temperature mixed state below 15 K consists of components with homogeneous charge distribution and dimers where charge order is preserved as static or slowly fluctuating, as depicted by blurred colors.

Figure 3

(a) Scheme of cantilever torque magnetometery experiment with the rotation direction for the $ab$ plane shown with blue arrow and magnetic field direction shown in black. (b) Angle dependence of paramagnetic component of torque ${\tau }_{2\theta }$ at 5 T, rotation in the $ab$ plane for temperatures related to the different charge states of $\kappa$-(BEDT-${\mathrm{TTF})}_2\mathrm{Hg}{\left(\mathrm{SCN}\right)}_2\mathrm{Cl}$. (c) Temperature dependence of the paramagnetic torque amplitude ${\tau }_{2\theta }$ in $ac$ plane and $ab$ planes. (d) Temperature dependence of the phase ${\theta }_2$ in the $ac$ and $ab$ planes.

Figure 4

Magnetization of $\kappa$-(BEDT-${\mathrm{TTF})}_2\mathrm{Hg}{\left(\mathrm{SCN}\right)}_2\mathrm{Cl}$ measured my magnetic cantilever torque magnetometery. (a) Magnetic field dependence of torque signal at 120 mK for magnetic field $H$ in the range from 0 to 17.5 T. (b) Field dependence of ${\tau }_{2\theta }$.

Figure 5

Magnetic susceptibility of $\kappa$-(BEDT-${\mathrm{TTF})}_2\mathrm{Hg}{\left(\mathrm{SCN}\right)}_2\mathrm{Cl}$ polycrystal sample measured by SQUID magnetometer using H=1 T in the temperature range from 300 to 2 K.

Figure 6

Upper panel: Cantilever magnetic torque data analysis and example for the data for the rotation in $ab$ plane at 5 K in magnetic field of 5 T. The figure shows original data and ${\tau }_{\theta }\sin (\theta -{\theta }_1$), and ${\tau }_{2\theta }\sin 2(\theta -{\theta }_1$) components with the respective fitting curves. Lower panel: Raw data of $\kappa$-(BEDT-${\mathrm{TTF})}_2\mathrm{Hg}{\left(\mathrm{SCN}\right)}_2\mathrm{Cl}$ obtained by cantilever magnetic torque measurements. Measurements are done for rotation in $ab$ plane, $H=5$ T. Angle dependence of ${\tau }_{2\theta }$ extracted from these measurements is presented in Fig. 3.