Nature of the Spin Liquid Ground State in a Breathing Kagome Compound Studied by NMR and Series Expansion

In the vanadium oxyfluoride compound $({\mathrm{NH}}_4{)}_2[{\mathrm{C}}_7{\mathrm{H}}_{14}\mathrm{N}][{\mathrm{V}}_7{\mathrm{O}}_6{\mathrm{F}}_{18}]$ (DQVOF), the ${\mathrm{V}}^{4+}$ ($3d^1$, $S=1/2$) ions realize a unique, highly frustrated breathing kagome lattice composed of alternately sized, corner-sharing equilateral triangles. Here we present an ${}^{17}\mathrm{O}$ NMR study of DQVOF, which isolates the local susceptibility of the breathing kagome network. By a fit to series expansion, we extract the ratio of the interactions within the breathing kagome plane, $J_{\nabla }/J_{\mathrm{\Delta }}=0.55(4)$, and the mean antiferromagnetic interaction $\overline{J}=60(7)\mathrm{K}$. Spin lattice ($T_1$) measurements reveal an essentially gapless excitation spectrum with a maximum gap $\mathrm{\Delta }/\overline{J}=0.007(7)$. Our study provides new impetus for further theoretical investigations in order to establish whether the gapless spin liquid behavior displayed by DQVOF is intrinsic to its breathing kagome lattice or whether it is due to perturbations to this model, such as a residual coupling of the ${\mathrm{V}}^{4+}$ ions in the breathing kagome planes to the interlayer ${\mathrm{V}}^{3+}$ ($S=1$) spins.

Figure 1

${}^{17}\mathrm{O}$ NMR spectrum of DQVOF at 300 K and $H_0=7.5\mathrm{T}$ (black line) and the simulation of the powder spectrum (red dashed line). The blue arrows point to the quadrupolar singularities. The shift reference is ${\nu }_0={}^{17}\gamma /2\pi \times H_0=43.288\mathrm{MHz}$ (${}^{17}\gamma /2\pi =5.772\mathrm{MHz}/\mathrm{T}$). Left inset: Top view of the magnetic lattice with the ${\mathrm{V}}^{4+}$ (light blue spheres) forming the breathing kagome lattice and the interlayer ${\mathrm{V}}^{3+}$ (dark blue spheres). Right inset: Local environments of the vanadium ions.

Figure 2

${}^{17}\mathrm{O}$ NMR spectra over a selected range of temperatures. The spectra are normalized to their maximum value. The black vertical lines show the reference for the spin shift.

Figure 3

Local NMR susceptibility of the kagome layers ${\chi }^{\mathrm{loc}}$. The lines are fits to $A{\chi }_{\mathrm{kago}}^{\mathrm{th}}+C$ (see the text). Inset: SQUID macroscopic susceptibility (circles) and fit to a combination of ${\chi }_{\mathrm{kago}}^{\mathrm{th}}$ ($\alpha =1$) and a paramagnetic contribution from the ${\mathrm{V}}^{3+}$ (line) [24].

Figure 4

Thermal evolution of $1/T_1$. The solid line is a fit as explained in the text. The dashed line shows the $T^{0.3}$ variation. Inset: Recovery curves at 290 and 1.2 K.