Frustration, ring exchange, and the absence of long-range order in ${\mathrm{EtMe}}_3\mathrm{Sb}{\left[\mathrm{Pd}{\left(\mathrm{dmit}\right)}_2\right]}_2$: From first principles to many-body theory

We parametrize Hubbard and spin models for ${\mathrm{EtMe}}_3\mathrm{Sb}{\left[\mathrm{Pd}{\left(\mathrm{dmit}\right)}_2\right]}_2$ from broken symmetry density functional calculations. This gives a scalene triangular model where the largest net exchange interaction is three times larger than the mean interchain coupling. The chain random phase approximation shows that the difference in the interchain couplings is equivalent to a bipartite interchain coupling, favoring long-range magnetic order. This competes with ring exchange, which favors quantum disorder. Ring exchange wins. We predict that the thermal conductivity $\kappa$ along the chain direction is much larger than that along the crystallographic axes and that $\kappa /T\to 0$ as $T\to 0$ along the crystallographic axes, but that $\kappa /T\to \mathrm{aconstant}>0$ as $T\to 0$ along the chain direction.

Figure 1

We find three significant antiferromagnetic nearest-neighbor couplings within the layers of [Pd(dmit)${}_2{]}_2$ dimers (a). The largest, $J_B$, is in the dimer stacking direction. The others, $J_r\ne J_S$, lead to a scalene lattice (b). We show that the physics of this model differs importantly from the isosceles triangular lattice relevant to the closely related BEDT-TTF salts (c). We also calculate the three- and four-site ring exchange interactions $K_3$, $K_4$, $K_4^{\prime }$, and $K_4^{\prime \prime }$ (a). The interlayer coupling $J_z$ is approximately perpendicular to the page.

Figure 2

Illustration of the decomposition of the magnetic exchange coupling calculation. Blue and red circles represent magnetic orbitals (singly) occupied by spin-up and spin-down electrons, respectively. Horizontal black lines and vertical arrows represent nonmagnetic occupied orbitals (also known as core orbitals).

Figure 3

Numerical calculation of the ordering temperature as a function of each parameter in Eq. (2). Each line corresponds to varying one parameter $X$ and keeping the others constant. In (a), all parameters (except for $X$) are set to our values for ${\mathrm{EtMe}}_3\mathrm{Sb}$. In this case, solutions for $T_N$ are only positive when $K_4$ is very small or $\delta J_y$, $J_z$ are large. Solutions for $T_N$ become negative and complex when $2K_4>|\delta J_y|+|J_z|$ (for these unphysical solutions only the real part is shown). The vertical black lines indicate the parameter values for which this transition occurs. In (b), we set $K_4=0.06J_B$ and $\delta J_y=0.2J_B$ as an example of the regime $2K_4<|\delta J_y|+|J_z|$. In both cases, the solution is exactly reproduced with Eq. (5); it is independent of the magnitudes of $\overline{J_y}$, $K_4^{\prime }$, and $K_4^{\prime \prime }$

Figure 4

Numerical calculation of the ordering temperature as a function of the interchain ring exchange $K_4$ and the unfrustrated interchain couplings $\delta J_y$ and $J_z$. Our calculated parameters for ${\mathrm{EtMe}}_3\mathrm{Sb}$ are marked by the green cross. We have used our calculated values for the other couplings in Eq. (2); ${\overline{J}}_y=135$ K, $K_3=18$ K, $K_4^{\prime }=76$ K, and $K_4^{\prime \prime }=66$ K. The gray area indicates where there is no real positive solution for $T_N$. This occurs when $2K_4>|\delta J_y|+|J_z|$ (as shown with the blue dashed line). For all points on this graph, $k_0$ and $k_y+\pi /2$ are both less than ${10}^{-4}$.