We perform a comprehensive theoretical study of the pressure-induced evolution of the electronic structure, magnetic state, and phase stability of the late transition metal monoxides MnO, FeO, CoO, and NiO using a fully charge self-consistent DFT+dynamical mean-field theory method. Our results reveal that the pressure-induced Mott insulator-to-metal phase transition in MnO-NiO is accompanied by a simultaneous collapse of local magnetic moments and lattice volume, implying a complex interplay between chemical bonding and electronic correlations. We compute the pressure-induced evolution of relative weights of the different valence states and spin-state configurations. Employing the concept of fluctuating valence in a correlated solid, we demonstrate that in MnO, FeO, and CoO a Mott insulator-metal transition and collapse of the local moments is accompanied by a sharp crossover of the spin-state and valence configurations. Our microscopic explanation of the magnetic collapse differs from the accepted picture and points out a remarkable dynamical coexistence (frustration) of the high-, intermediate-, and low-spin states. In particular, in MnO, the magnetic collapse is found to be driven by the appearance of the intermediate-spin state (IS), competing with the low-spin (LS) state; in FeO, we observe a conventional high-spin to low-spin (HS-LS) crossover. Most interestingly, in CoO, we obtain a remarkable (dynamical) coexistence of the HS and LS states, i.e., a HS-LS frustration, up to high pressure. Our results demonstrate the importance of quantum fluctuations of the valence and spin states for the understanding of quantum criticality of the Mott transitions.
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