Gapless Spin Liquid Ground State in the $S\mathbf{=}1/2$ Vanadium Oxyfluoride Kagome Antiferromagnet $\left[{\mathrm{NH}}_4{]}_2\right[{\mathbf{C}}_7{\mathbf{H}}_{14}\mathbf{N}\left]\right[{\mathbf{V}}_7{\mathbf{O}}_6{\mathbf{F}}_{18}]$

The vanadium oxyfluoride $[{\mathrm{NH}}_4{]}_2[{\mathrm{C}}_7{\mathrm{H}}_{14}\mathrm{N}][{\mathrm{V}}_7{\mathrm{O}}_6{\mathrm{F}}_{18}]$ (DQVOF) is a geometrically frustrated magnetic bilayer material. The structure consists of $S=1/2$ kagome planes of ${\mathrm{V}}^{4+}$ $d^1$ ions with $S=1$ ${\mathrm{V}}^{3+}$ $d^2$ ions located between the kagome layers. Muon spin relaxation measurements demonstrate the absence of spin freezing down to 40 mK despite an energy scale of 60 K for antiferromagnetic exchange interactions. From magnetization and heat capacity measurements we conclude that the $S=1$ spins of the interplane ${\mathrm{V}}^{3+}$ ions are weakly coupled to the kagome layers, such that DQVOF can be viewed as an experimental model for $S=1/2$ kagome physics, and that it displays a gapless spin liquid ground state.