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We show that short-range resonating-valence-bond correlations and long-rangeorder can coexist in the ground state (GS) of a frustrated spin system. Ourstudy comprises a comprehensive investigation of the quantum magnetism on thestructurally disorder-free single crystal of Cu$_2$(OH)$_3$NO$_3$, whichrealizes the $s$ = 1/2 Heisenberg model on a spatially anisotropic triangularlattice. Competing exchange interactions determined by fitting themagnetization measured up to 55 T give rise to an exotic GS wavefunction withcoexistence of the dominant short-range resonating-valence-bond correlationsand weak long-range stripe order (ordered moment $M_0$ = $|\langles_i^z\rangle|$ $\sim$ 0.02). At low temperatures, a first-order spin-floptransition is visible at $\sim$ 1-3 T. As the applied field further increases,another two magnetic-field-induced quantum phase transitions are observed at$\sim$ 14-19 and $\sim$ 46-52 T, respectively. Simulations of the Heisenbergexchange model show semi-quantitative agreement with the magnetic-fieldmodulation of these unconventional phases, as well as the absence of visiblemagnetic reflections in neutron diffraction, thus supporting the GS of the spinsystem of Cu$_2$(OH)$_3$NO$_3$ may be approximate to a quantum spin liquid. Ourstudy establishes structurally disorder-free magnetic materials with spatiallyanisotropic exchange interactions as a possible arena for spin liquids.

physical review. b./physical review. b

Possible coexistence of short-range resonating-valence-bond and  long-range stripe correlations in the spatially anisotropic  triangular-lattice quantum magnet Cu$_2$(OH)$_3$NO$_3$