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Spin-state crossover beyond a conventional ligand-field theory has been a fundamental issue in condensed matter physics. Here, we report microscopic observations of spin states and low-energy dynamics through orbital-resolved NMR spectroscopy in the prototype compound LaCoO$_3$. The $^{59}$Co NMR spectrum shows the preserved crystal symmetry across the crossover, inconsistent with $d$ orbital ordering due to the Jahn-Teller distortion. The orbital degeneracy results in a pseudospin ($\tilde{J} = 1$) excited state with an orbital moment observed as $^{59}$Co hyperfine coupling tensors. We found that the population of the excited state evolves above the heart crossover temperature. The crossover involves critical spin-state fluctuations emerging under the magnetic field. These results suggest that the spin-state crossover can be mapped into a statistical problem, analogous to the supercritical liquid in liquid-gas transition., 5 pages, 5 figures

A thermally-induced spin-state transition in RC0O3 (R = La, Pr, and Nd) is investigated by single-crystal 59Co NMR measurements. In contrast to LaCoO3, PdCoC3 and NdCoC3 exhibit no clear transition but a crossover from a nonmagnetic state to a paramagnetic phase. Subtracting a rare-earth contribution to the 59Co Knight shift in PrCoC3 and NdCoC3, we obtain the hyperfine coupling constant between a 59Co nuclear spin and 3d spins in the paramagnetic state with the finite 3d spin susceptibility.