Microscopic model of $\left(\text{CuCl}\right){\text{LaNb}}_2{\text{O}}_7$: Coupled spin dimers replace a frustrated square lattice

We present a microscopic model of the spin-gap quantum magnet $\left(\text{CuCl}\right){\text{LaNb}}_2{\text{O}}_7$, previously suggested as a realization of the spin-$\frac{1}{2}$ frustrated square lattice. Taking advantage of the precise atomic positions from recent crystal structure refinement, we evaluate individual exchange integrals and construct a minimum model that naturally explains all the available experimental data. Surprisingly, the deviation from tetragonal symmetry leads to the formation of spin dimers between fourth neighbors due to a Cu-Cl-Cl-Cu pathway with an antiferromagnetic exchange $J_4\simeq 25\text{K}$. The total interdimer exchange amounts to 12–15 K. Our model is in agreement with inelastic neutron-scattering results and is further confirmed by quantum Monte Carlo simulations of the magnetic susceptibility and the high-field magnetization. We establish $\left(\text{CuCl}\right){\text{LaNb}}_2{\text{O}}_7$ as a nonfrustrated system of coupled spin dimers with predominant antiferromagnetic interactions and provide a general perspective for related materials with unusual low-temperature magnetic properties.

Figure 1

(Color online) Crystal structure of $\left(\text{CuCl}\right){\text{LaNb}}_2{\text{O}}_7$: the overall view (left panel) and the [CuCl] “layers” in the $ab$ plane (right panel). The couplings are labeled according to the Cu-Cu distances: the subscript 1 denotes the interactions between first neighbors, the subscript 2 denotes the interactions between second neighbors, etc.

Figure 2

(Color online) Tight-binding fit (thick dark lines) of the LDA band structure (thin light lines).

Figure 3

(Color online) A sketch of the $\left(\text{CuCl}\right){\text{LaNb}}_2{\text{O}}_7$ spin lattice in the $ab$ plane. The FM coupling $J_1$ is denoted by the dotted line, the AFM couplings $J_2$, $J_4$, and $J_4^{\prime }$ are shown by the dashed, thick solid, and thin solid lines, respectively. The couplings $J_{\perp }$ run along the $c$ axis and connect the neighboring planes. The shading denotes the spin dimer. The open and filled circles show the columnar AFM ordering in the case of weak dimerization.

Figure 4

(Color online) Fits of the experimental data with $J_4=25\text{K}$ and $J_2/J_4=0.3$: temperature dependence of the magnetic susceptibility $\left(\chi \right)$ in the primary figure and field dependence of the magnetization $\left(M\right)$ in the inset. Experimental data are shown with dots, dark lines are the fits.