Ferromagnetically Coupled Shastry-Sutherland Quantum Spin Singlets in $(\mathrm{CuCl}){\mathrm{LaNb}}_2{\mathrm{O}}_7$

A thorough crystal structure determination at very low temperature of $(\mathrm{CuCl}){\mathrm{LaNb}}_2{\mathrm{O}}_7$, originally proposed as a spin-$1/2$ square-lattice antiferromagnet, is reported thanks to the use of single-crystal x-ray diffraction and powder neutron diffraction. State-of-the-art calculations (maximum entropy method) reveal that $(\mathrm{CuCl}){\mathrm{LaNb}}_2{\mathrm{O}}_7$ is orthorhombic with $Pbam$ symmetry. First-principles calculations demonstrate that the dominant magnetic interactions are antiferromagnetic between fourth nearest neighbors with a Cu-Cl-Cl-Cu exchange path, which lead to the formation of spin singlets. The two strongest interactions between the singlets are ferromagnetic, which makes $(\mathrm{CuCl}){\mathrm{LaNb}}_2{\mathrm{O}}_7$ the first system of ferromagnetically coupled Shastry-Sutherland quantum spin singlets.

Figure 1

Inelastic neutron scattering data obtained at 70 mK from the powder sample. (a) Energy dependence of the triplet excitations for $B=0\mathrm{T}$ (blue) and $B=11.5\mathrm{T}$ (red). (b) $Q$ dependence for $B=0\mathrm{T}$. Lines are described in the text.

Figure 2

Single crystal x-ray and powder neutron diffraction data. (a) The x-ray CCD image of the $ab$ plane at 14 K. The single crystal was twinned; thus $a$ and $b$ axes are interchangeable. The spots with green circles are the allowed integer Bragg reflections for the original tetragonal structure; the other spots are the half-integer reflections. (b) Rietveld plot against neutron diffraction data at 2 K. The indices in the inset are in the tetragonal notation.

Figure 3

Crystal structure and magnetic exchange interactions of $(\mathrm{CuCl}){\mathrm{LaNb}}_2{\mathrm{O}}_7$. (a) Projection of crystal structure in bc plane, (b) ac plane. Purple, red, blue, and green spheres represent La, O, Cu, and Cl ions, respectively. The dark green polygons represent $\mathrm{Nb}{\mathrm{O}}_6$ octahedra. The grey lines show the unit cell. (c) Exchange interactions in the $ab$ plane. The O ions are located above and below the Cu ions. The lines connecting Cu atoms represent exchange bonds: $J_{1a}$ (blue), $J_{2a}$ (solid cyan), $J_{2b}$ (dotted cyan), $J_4$ (solid red), and $J_4^{\prime }$ (dotted red). See Table . $J_{1b}$ is not plotted for clarity. (d) Six ordered AFM spin states used to extract the spin exchange parameters by $\mathrm{GGA}+U$ calculations. Only the ${\mathrm{Cu}}^{2+}$ ions are shown, and the open and filled circles represent the up and down spins, respectively. The relative energies (in meV per 4 f.u.) of the ordered spin states (with respect to the FM spin state) are given in the parentheses.