Spin-state transition, also known as spin crossover, plays a key role in diverse systems, including minerals and biological materials. In theory, the boundary range between the low- and high-spin states is expected to enrich the transition and give rise to unusual physical states. However, no compound that realizes a nearly degenerate critical range as the ground state without requiring special external conditions has yet been experimentally identified. This study reports that, by comprehensive measurements of macroscopic physical properties, X-ray diffractometry, and neutron spectroscopy, the Sc substitution in LaCoO$_3$ destabilizes its nonmagnetic low-spin state and generates an anomalous paramagnetic state accompanied by the enhancement of transport gap and magneto-lattice-expansion as well as the contraction of Co--O distance with the increase of electron site-transfer. These phenomena are not well described by the mixture of conventional low- and high-spin states, but by their quantum superposition occurring on the verge of a spin-state transition. The present study enables us to significantly accelerate the design of new advanced materials without requiring special equipment based on the concept of quantum spin-state criticality.
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