Coexisting commensurate and incommensurate charge ordered phases in CoO

Abstract The subtle interplay of strong electronic correlations in a distorted crystal lattice often leads to the evolution of novel emergent functionalities in the strongly correlated materials (SCM). Here, we unravel such unprecedented commensurate (COM) and incommensurate (ICOM) charge ordered (CO) phases at room temperature in a simple transition-metal mono-oxide, namely CoO. The electron diffraction pattern unveils a COM ( $$q_{1}$$ q 1 = $$\frac{1}{2}(1,1,{\bar{1}})$$ 1 2 ( 1 , 1 , 1 ¯ ) and ICOM ( $$q_{2}=0.213(1,1,{\bar{1}})$$ q 2 = 0.213 ( 1 , 1 , 1 ¯ ) ) periodic lattice distortion. Transmission electron microscopy (TEM) captures unidirectional and bidirectional stripe patterns of charge density modulations. The widespread phase singularities in the phase-field of the order parameter (OP) affirms the abundant topological disorder. Using, density functional theory (DFT) calculations, we demystify the underlying electronic mechanism. The DFT study shows that a cation disordering ( $$\mathrm {Co}_{1-\textit{x}}\mathrm {O}, \text {with }{} \textit{x} = 4.17 \%$$ Co 1 - x O , with x = 4.17 % ) stabilizes Jahn-Teller (JT) distortion and localized aliovalent $$\mathrm {Co}^{3+}$$ Co 3 + states in CoO. Therefore, the lattice distortion accompanied with mixed valence states ( $$\mathrm {Co}^{3+}, \mathrm {Co}^{2+}$$ Co 3 + , Co 2 + ) states introduces CO in CoO. Our findings offer an electronic paradigm to engineer CO to exploit the associated electronic functionalities in widely available transition-metal mono-oxides.