Chasing the spin gap through the phase diagram of a frustrated Mott insulator

The quest for entangled spin excitations has stimulated intense research on frustrated magnetic systems. For almost two decades, the triangular-lattice Mott insulator $\kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$ has been the hottest candidate for a $gapless$ quantum spin liquid with itinerant spinons. Very recently, however, this scenario was overturned as electron-spin-resonance (ESR) studies unveiled a spin gap, calling for reevaluation of the magnetic ground state. Here we achieve a precise mapping of this spin-gapped phase through the Mott transition by ultrahigh-resolution strain tuning. Our transport experiments reveal a reentrance of charge localization below $T^{\star}=6$ K associated with a gap size of 30-50 K. The negative slope of the insulator-metal boundary, $dT^{\star}/dp<0$, evidences the low-entropy nature of the spin-singlet ground state. By tuning the enigmatic '6 K anomaly' through the phase diagram of $\kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$, we identify it as the transition to a valence-bond-solid phase, with typical magnetic and structural fingerprints, that persists at $T\rightarrow 0$ until unconventional superconductivity and metallic transport proliferate.