Coexisting commensurate and incommensurate charge ordered phases in CoO

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 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q_{1}$$\end{document}q1=\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{1}{2}(1,1,{\bar{1}})$$\end{document}12(1,1,1¯) and ICOM (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q_{2}=0.213(1,1,{\bar{1}})$$\end{document}q2=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 (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {Co}_{1-\textit{x}}\mathrm {O}, \text {with }{} \textit{x} = 4.17 \%$$\end{document}Co1-xO,withx=4.17%) stabilizes Jahn-Teller (JT) distortion and localized aliovalent \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {Co}^{3+}$$\end{document}Co3+ states in CoO. Therefore, the lattice distortion accompanied with mixed valence states (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm {Co}^{3+}, \mathrm {Co}^{2+}$$\end{document}Co3+,Co2+) 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.


Results and discussions
Probing lattice distortions in reciprocal space. CoO crystallizes in a NaCl-type rock-salt structure with the cubic space-group of Fm3 m . It is an antiferromagnetic (AFM) insulator with a lattice constant of ∼ 4.27 Å (Fig. 1a) 31 . Below the Neel temperature T N ≈ 290 K, the magnetic moments of Co atoms stack along the (111) crystal plane. Such magnetic ordering commonly refereed as AFM-II ordering 32 . The HR-TEM image of a CoO thin film shows the epitaxial nature of the thin film (Fig. 1b). The EDP further affirms single crystallinity of the thin film (Fig. 1c). Surprisingly, the EDPs acquired from the distinct regions in the CoO thin film readily indicate the coexisting electronic phase inhomogeneity ( Fig.1d-f). The apparent additional spatial frequencies in the EDP explicitly evidence the periodic lattice deformation and CO in the CoO lattice 33,34 . The quantified spatial frequencies reveal a COM ( q 1 = 1 2 (1, 1,1) and ICOM ( q 2 = (0.213(1, 1,1)) ) ( Fig. 1d,e) CO phase. However, in some regions in the thin film, the EDP also suggests the coexisting superlattices ( Fig.1 f). The coexisting nature of the COM and ICOM superlattice phases in a SCM also reported 23,35 . The EDP also suggest the compositional modulation in the thin film. The theory of spinodal-decomposition can provide an additional insight on the free-energy associated to the compositional-modulation to justify the stability of such coexisting CO phases in CoO 36 . However, this study lies beyond the scope of the present investigation and is reserved for future investigations. Nevertheless, the present experimental observation inspires to explore the aspects of a spinodaldecomposition for CoO and for other similar TMOs. Furthermore, a cohesive energy analysis indicates that at higher temperatures cation vacancies can easily form in CoO ("First principles calculations") Such a vacancy can form at a temperature of (900 • ) during thin-film growth 37 . Although an anion vacancy can also be formed, the ordering of cation vacancies is energetically more preferable then anion-vacancy ordering 38 . Moreover, a cation deficiency in CoO implies the formation of mixed-valence charge states ("First principles calculations", Fig. S15). The mixed-valence states accompanied with a lattice distortion offer the prospect of CO (Supplementary Information). Therefore, the superlattice spots in the EDP represent a cation-disordering-induced CO in CoO. The underlying electronic mechanism of CO is elaborated in "First principles calculations". The occurrence of COM and ICOM CO phase at room temperature in CoO is a unique observation and suggests a yet unexplored prospect in such simple rock-salt structured transition-metal mono-oxides. The capability of tailoring such composition modulation by controlled defect engineering in the widely available TMOs offers potential opportunities for leveraging electronic properties associated to the CO.
Microscopic structural features of CO. The Fourier filtered electron micrograph of COM phase ( q 1 ) displays a unidirectional charge density modulation along the [112] zone-axis (Fig. 2a). These unidirectional www.nature.com/scientificreports/ density modulations are referred as charge-stripe pattern. Such stripe pattern are recognized as a characteristic microscopic structural features of a CO material 39 . These unidirectional charge density stripes also serve as a real-space evidence of broken translational and rotational symmetry in a CO transition 40 ( Supplementary  Information, Fig. S2). In contrast, the ICOM phase shows bidirectional charge density modulations (Fig. 2b). These density stripes mutually intertwine. The checkerboard-type CO materials also exhibits a similar stripe patterns [40][41][42][43] ( Supplementary Information, Fig. S3). Furthermore, a detailed microscopic inspection allows us to witness a region, which exhibits an intriguing pattern of segregated charge density modulations. A similar nature of charge density modulation has been reported for various CDW materials [44][45][46] . The segregated charge density presumably manifest the highly localized Coulomb interaction 47 . A previous theoretical study has established that a cation imperfection in CoO leads to a charge-state disproportions 48 . Therefore, a broken spatial symmetry and mixed-valence charge-states poses a prospect of CO in Co 1−x O . We align our investigation with such insights and explore the feasibility of CO in Co 1−x O . The potential of such an assumption is substantiated by simulating the HR-TEM image of Co 1−x O at 300 kV TEM. The non-stochiometric crystal structure constructed by creating a Co vacancy at the center of a ( 2 × 2 × 2 ) supercell of CoO. The simulated HR-TEM images displays a qualitatively resemblance with the experimental image. The simulated HR-TEM demonstrates the exact segregated charge density modulation pattern at corresponding locations ( Fig. 2c,d). A qualitative similarity and a quantitative comparison of the experimental and simulated micrographs consolidates the aforementioned assumption of cation disordering ( Supplementary Information, Fig. S15). Next, we explore the spatial uniformity of the CO domains, along different crystal plane ((200 ), ( 1 11 ), ( 111 )) directions along the [011] zone-axis. The unperturbed CoO lattice shows a regular atomic modulation (Fig. 2e). However, the CO domains demonstrate a wrinkled nature of the atomic modulation. The bending and breaking nature of CO modulation can be radially identified ( Fig. 2f-h). The bending and breaking nature of density modulation signifies the dislocations in the modulation of CO domains. A similar bending and breaking nature of CO domains also reported recently in a complex CO magnetite 49 . Our previous study also traced the CO in CoO 29 . However, the present detailed investigation unveils the unexplored rich microscopic structural features of CO and further provides an invaluable insight on the relative dominance nature of such CO phase ("Spatial distribution of order parameter"). Furthermore, an extensive theoretical analysis provides a deeper understanding on the operating electronic mechanism, and elaborates the previously unnoticed JT distortion and orbital reconstruction next to vacancy site ("First principles calculations").
Spatial distribution of order parameter. The order parameter is an important measure to gauge the degrees of order in the phase transition process. Therefore, we compute the spatial fluctuation map of the OP by using the phase-lock method 49,50 (Supplementary Information, Section II). The OP associated to the complexfield of the modulation can be approximated by the equation; ψ q (�r) ≈ R{A(r) * exp i(q·r+φ(r)) } , where A(r) is an displacement amplitude of the modulation. The vector q is a modulation vector of the superlattice reflection and φ(r) represents the phase-field of the modulation. φ(r) also encapsulates the information of the localized disorder, i.e. emergent topological defects. Topological defects are unavoidable emergent excitation, which originate during the structural phase transition process. The topological disorder can be perceived in the form of a www.nature.com/scientificreports/ phase singularity in φ(r) , which winds 2π around the core of the topological defect. These phase singularities are similar to the quantum fluxoid and vortices in superconductors 51 (Fig. 3b). These topological defects cost a finite energy, which contributes to stabilize the COM phase 6 . Therefore, the phase-map provides an insight on the relative spatial stability of such CO phase. The A(r) vanishes at the core of the localized topological defect. The phase mapping is an effective approach, which qualitatively shows the relative dominating nature of the coexisting electronic phases 6 (Supplementary Information). Figure 3a-c, exemplify the extraction of the φ(r) and A(r) fields of a complex-field associated to the unidirectional lattice modulation. A topological discontinuity in the OP is identifiable by a 2π winding phase singularity in φ(r) . Consistently, the computed spatial A(r) field precisely locate the minimum intensity at the corresponding location of the phase singularity and the core of topological disorder. The COM phase with q 1 exhibits an abundance of dislocations in the unidirectional density modulation (Fig. 3d,g). The corresponding φ(r) map shows an interconnected network of phase-singularities (Supplementary Information). The COM phase possesses more phase singularities than the coexisting ICOM CO phase (Fig. 3e,h), signifying the large lattice-order disruption in the COM order. The intensity of A(r) vanishes at a locations of the core of phase singularities (Fig. 3f,i). The spatial phase-fluctuation maps indicate a relative higher lattice order degradation of the COM phase. Moreover, a thermodynamic study of such CO can also firmly establish the competing nature of such coexisting CO phase 23,33 .
First principles calculations. Our TEM-based investigations have evidently proved the CO in real and reciprocal space, respectively. We further computationally pursue to uncover the underpinning electronic mechanism, which can justify the observed unconventional CO in CoO. It is well established that a functional ionic deficiency profoundly modifies the local structural, chemical and magnetic environment in transitionmetal mono-oxides 27 . Such electronic modifications can induce diverse electronic properties, e.g. half-metallicity, spin-blockade, spin-state crossover, ferromagnetism, etc, even in a simple stoichiometric transition-metal mono-oxides, e.g. CaO, MnO, NiO, CoO 38,48,52-55 . Therefore, motivated by an exceptional agreement between our experimental and simulated HR-TEM observations, and further guided by the earlier theoretical insights,   37 . Although, the anion vacancy can be easily created at such a temperature, a cation-vacancy ordering is energetically preferable over anion-vacancy ordering 38 . Moreover, a stable non-stochiometric TMO crystal can even possess a much higher defect density than the representative minimal defect density considered in present theoretical investigations 52,56 .
CoO is a charge-transfer insulator with a band gap of ∼ 2.7 eV. Our calculation results show an agreement with previous investigation 57 . The hybridized nature of Co-3d−O-2p states in CoO is evident from the DOS (Fig. 4a). The complementary populated spin-up and spin-down states signify the AFM ordering in CoO. The profound influence of V Co in Co 1−x O is distinguishable at Fermi level ( E F ). The energetically emerged hybridized Co-3d−O-2p states surpass E F . Interestingly, only a unidirectional spin-channel, i.e. the spin-up channel, shows the metallic nature (Fig. 4b). Such electronic states are commonly referred as half-metallic (HM) states and are considered to be extremely important for various spintronics applications. Cation defect-induced HM is also reported in other similar transition-metal mono-oxides, e.g. NiO, MnO, CaO 38,52,53,55 . The asymmetric nature of the DOS profile implies a deviation from the AFM nature. We further appraise the origin of the halfmetallic state by analyzing the DOS of Co-d and O-p adjacent to and at a distance from the disorder atomic site. The DOS unequivocally demonstrates that a Co and O atoms adjacent to V Co exclusively contributes the HM states (Fig. 4c-f). Further, to gain a deeper insight on the orbital reconstruction at E F , the orbital decomposed DOS is evaluated. The valence band maximum of CoO is populated by nearly uniform contribution of all Co-d www.nature.com/scientificreports/ partial orbital states (Fig. 4g). However, in Co 1−x O , the energetic distribution of the partial orbitals substantially alters and surpass E F . The energetic orbital states introduces the half-metallic states in Co 1−x O (Fig. 4h). The energetically emerged states signify an extended orbitals overlapping and thus prone to destabilize the crystalfield environment. The modified orbital states at disorder site reflects a perturbed structural, magnetic, and chemical environment. The hole compensation and the electrostatic interaction between defect site and loosely bound holes elongate the defected O h to reduce the in-plane (lateral) Co-O bond from 2.11 Å to 1.95 Å at two nearest O h . However, the O h elongation concurrently increase the Co-O bond in out-of-plane (axial) direction by ∼ 0.10 Å. The perturbed Co-O bond lengths concomitantly distort the O h symmetry. The O h distortion can modify the chemical nature of the ionic states therefore, we gauge the chemical state by computing the ionic charges by performing Bader charge analysis 58 . The computed ionic charges on pure CoO are q Co = +1.34 e − and q O = −1.34 e − , respectively. However, in Co 1−x O , we identify higher ionic charges q ′ Co = +1.50 e − at vertically inverted and adjacent to disorder sites. The enhanced ionic charge indicates a localized charge-state transition. Interestingly, the chemical identity of two V Co -adjacent O atoms persists nearly identical to the O atom of pure CoO, i.e. q ′ O = −1.36 e − . The chemical identity remains preserved by the charge transfer from the elevated charge state. The charge transfer essentially compensates the hole formation and leads to an charge state disproportion by introducing localized aliovalent Co 3+ state. The V Co -induced Co 3+ state is also supported by some earlier theoretical investigations 48 . Moreover, we also experimentally validated the mix-valence Co states in Co 1−x O , by electron energy-loss spectroscopy ( Supplementary Information, Section I(D)). The localized structural and chemical distortion simultaneously influence the corresponding magnetic nature. We identify that the spin magnetic moment of two Co atoms enhances from initial 2.75 to 3.15 µ B . These two Co atoms reside vertically opposite from the cation deficient atomic site, undergo a higher charge-state transition and reduce the bonding distance. Moreover, the uplifted magnetic frustration also induces a minute moment of 0.21 µ B on two V Co -adjacent O atoms. However, the Co and O atoms located far from the V Co remain nearly unmodified.
The computational insights enables to infer that a localized cation deficiency forms two uncompensated hole states in the O-p bands. These holes are compensated by a charge delocalization from partially occupied Co-d states, located vertically opposite to the disordered atomic site. The charge-transfer process transforms the divalent Co ion to a trivalent state ( Co 3+ ). The hole-compensation process also displaces the cation from a high symmetry location in O h geometry. Therefore, lowering the symmetry activates a JT distortion (Supplementary Information). In Co 1−x O , the JT distortion elongates the cation-deficient octahedra ( O V Co h ). The axial elongation of O V Co h reduces the symmetry in adjacent compressed octahedra ( O c h ) and uplift the degeneracy via destabilizing the energy of the d xy , d x 2 −y 2 orbitals (Fig. 4h). However, the O h elongation concomitantly stretches O h in lateral direction (Supplementary Information). The O h compression also facilitates to eliminate the degeneracy of the crystal-field ( octa ) by destabilizing the energy of the d z 2 , d xz , d yz orbitals (Fig. 4h). The computed orbital-decomposed DOS capture the energetic of the crystal-field distortion and corroborates the operating JT mechanism in Co 1−x O (Fig. 4h). Therefore, the energetically destabilized partial orbital states cross E F to form the HM states. Thus, a localized cation imperfection induces a JT displacement and consequent charge-transfer introduces aliovalent states ( Co 2+ , Co 3+ ) (Supplementary Information, Section III(D)). Hence, the DFT calculation justify the experimental observations and suggests that a cation disordering-induced lattice distortion accompanied with mixed-valence charge states leads to the CO in Co 1−x O.

Discussion
To summarize, we unravel COM and ICOM CO phases in CoO. The TEM-based investigations show the characteristics of the CO phase in real and reciprocal space, respectively. Furthermore, the coupled DFT calculations decipher the underlying electronic mechanism. The DFT calculation highlights the cation-disorder-driven functional structural, chemical and magnetic modification, which leads to the mix-valence charge states in CoO. The lattice distortion accompanied with mix-valence states leads to the evolution of CO phases in Co 1−x O . CO shows a close proximity with various important electronic properties. Therefore, our finding suggest that a controlled functional cation-ordering imperfection offers opportunities to engineer and leverage the broad spectrum of emergent functionalities, even in widely available simple transition-metal mono-oxides.

Methods
Thin film growth. Epitaxial thin film of CoO is grown by pulsed laser deposition method 37 . The thin film is grown on the " c " plane of sapphire ( Al 2 O 3 ) substrate. The target pallet of CoO prepared by grinding CoO power (Sigma aldrich 99.99% purity) and further sintering it for 9 h in tube furnace. An excimer LASER (KrF) with ∼ 248 nm wavelength (Laser fluence ∼ 1.5 Jcm −2 ) used to ablate CoO from the target pallet. The target pallet is placed ∼ 5 cm far from the Al 2 O 3 substrate. The oxygen partial pressure in the chamber is maintained at P O 2 ∼ 1 × 10 −5 Torr.
Density functional theory calculations. The electronic structure calculations are based on the spin-polarized density functional theory (DFT), as implemented in the vienna ab-initio simulation package (VASP) 59,60 . The exchange-correlation energy treated within the generalized gradient approximation (GGA) in the form of the Perdew, Burke and Ernzerhof (PBE) functional 61 . The plane-wave basis cut-off was set to 600 eV. The Monkhorst www.nature.com/scientificreports/ respectively 62 . The Co 1−x O structure was constructed by embedding a Co vacancy ( V Co ) in a ( 2 × 2 × 2 ) supercell (48 atoms) of CoO ( Co 1−x O, x = 4.17% ) (Supplementary Information). For structural optimizations, a combination of the conjugate-gradient algorithm and the quasi-Newton force minimization was used. The limit of the force tolerance was set to 5 × 10 −3 eV/Å. The Coulomb repulsion U = 7.1 eV and the local exchange interactions with J = 1 eV, are used for the on−site interaction of Co-3d states 48 .