Balancing orbital effects and on-site Coulomb repulsion through Na modulations in ${\mathrm{Na}}_{x}\mathrm{V}{\mathrm{O}}_{2}$

Editors' Suggestion

Balancing orbital effects and on-site Coulomb repulsion through Na modulations in ${Na}_{x} V O_{2}$

Xi Chen, Hao Tang, Yichao Wang, and Xin Li

Phys. Rev. Materials 5, 084402 – Published 6 August 2021

Abstract

Vanadium oxides have been highly attractive for over half a century since the discovery of the metal insulator transition near room temperature. Here ${Na}_{x} V O_{2}$ is studied through a systematic comparison with other layered sodium metal oxides with early $3 d$ transition metals, first disclosing a unified evolution pattern of Na density waves through in situ x-ray diffraction analysis. Combining ab initio simulations and theoretical modelings, a sodium-modulated Peierls-like transition mechanism is then proposed for the bonding formation of metal ion dimers. More importantly, the unique trimer structure in ${Na}_{x} V O_{2}$ is shown to be very sensitive to the on-site Coulomb repulsion value, suggesting a delicate balance between strong electronic correlations and orbital effects that can be precisely modulated by both Na compositions and atomic stackings. This unveils a unique opportunity to design strongly correlated materials with tailored electronic transitions through electrochemical modulations and crystallographic designs, to elegantly balance various competition effects. We think the understanding will also help further elucidate complicated electronic behaviors in other vanadium oxide systems, as well as help improve electrochemical performances in layered metal oxides for Na ion battery applications.

Received 21 December 2020
Revised 29 June 2021
Accepted 19 July 2021

DOI:https://doi.org/10.1103/PhysRevMaterials.5.084402

Physics Subject Headings (PhySH)

Electrochemistry Electronic transitions Materials Structural properties

Vanadates

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Xi Chen^*, Hao Tang ^*, Yichao Wang, and Xin Li ^†

John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA

^*These authors contributed equally to this paper.
^†lixin@seas.harvard.edu

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 5, Iss. 8 — August 2021

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) In situ XRD (Mo source) measurement of ${Na}_{x} Cr O_{2}$ with three continuously moving superstructure peaks. The charging process of the in situ battery cell ends at $x = 1 / 2$ . (b) Comparison of the in situ XRD (blue lines) and the spectra simulated from the solved superstructures (black lines) for two intermediate compositions $x = 4 / 7$ and 3/5 of ${Na}_{x} Cr O_{2}$ . The major and superstructure peaks are all consistent, confirming the solved structures. (c) Simulated superstructure XRD peak evolution of ${Na}_{x} Cr O_{2}$ from our solved structures. (d) Superstructure evolution of ${Na}_{x} Ti O_{2}$ from both the in situ XRD (Mo source) experiments and solved structure simulations. The in situ XRD data are from the previous work [24] where three peaks were observed. The solved Na orderings for ${Na}_{x} Ti O_{2}$ are also fully supported by our ex situ synchrotron XRD analysis. (e) Superstructure evolution of ${Na}_{x} V O_{2}$ from both the in situ XRD (Cu source) experiments and solved structure simulations. The in situ XRD data are from the previous work [23]. (f) Illustration of the mechanism of how the XRD peak position continuously moves together with NDW wavelength during the (de-) intercalation process.
Reuse & Permissions
Figure 2
Superstructure evolution and Na density wave (NDW) in ${Na}_{x} TM O_{2}$ ( $TM = Ti$ , V, Cr). (a) Superstructure evolution in ${Na}_{x} Cr O_{2}$ for $x$ in $(1 / 2, 2 / 3)$ . The Na ions are denoted by yellow disks on the hexagonal lattices. Antiphase boundaries and NDW with continuously varying wavelengths are denoted by red zigzag lines and green wave patterns, respectively. (b) Superstructure evolution of ${Na}_{x} Ti O_{2}$ . (c) Superstructure evolution of ${Na}_{x} V O_{2}$ . The yellow and orange disks denote Na ions from two neighboring Na layers in the corresponding two-layer supercells. The transition metal types and Na compositions are denoted on the top and left-hand sides of the figures, respectively. The stacking of Na along the transition metal layers is along the $c$ direction, following the O′3, P2, and P′3 types of oxygen stacking in the O′3-Ti, P2-V, and P′3-Cr, respectively. The notations of O′3, P2, and P′3 and the corresponding interlayer stackings are explained in Fig. S1 and Table S1 in the Supplemental Material [34].
Reuse & Permissions
Figure 3
Dimer and orbital interactions of NDW structures. (a) Na density wave and the corresponding bonds and charge density wave of ${Na}_{2 / 3} Ti O_{2}$ . The Ti ions in a specific layer are represented by the blue disks, and the Na ions above and below the $Ti O_{2}$ layer are represented by the dark yellow and bright yellow disks, respectively. The labeled distances between the Ti atoms are in units of Å. (b) Positive and negative isosurface of charge density difference around Ti atoms. Electrons transfer from the purple $d_{y z}$ and $d_{x z}$ orbitals to the yellow $d_{x y}$ orbital. (c) Charge density difference between the NDW phase and the uniform phase without dimer (see Methods). Electrons are introduced to red areas which indicate $d_{x y}$ orbitals and σ bonds. (d) PDOS of ${Na}_{0.6} Ti O_{2}$ projected on the $d$ orbitals of an atom involved in a dimer. The states from about –0.5 to 1.5 eV are from $t_{2 g}$ orbitals, while the states from about 2 to 3.5 eV are from $e_{g}^{*}$ orbitals. (e) Displacement of oxygen atoms in the $z$ direction vs the number of adjacent Na ions from statistics of a series of solved superstructures of ${Na}_{x} Ti O_{2}$ . Negative $Δ z$ is the distortion toward the Na layer direction. (f) Relationship between the distance of the two oxygen atoms on different sides of the Ti ion layer and the corresponding TM dimer length. (g) Illustration of quantities defined in (e), (f).
Reuse & Permissions
Figure 4
Mechanism of the instability-induced dimer and material trend. (a) Illustration of the simplified 1D and 2D models. In the 1D model, a single $d_{x y}$ orbital (yellow lobes) is considered for each TM ion (green disks). The Na (yellow disks) distribution modulates both the illustrated orbital energy $ε$ and the hopping integral $t$ of electrons. Empty circles indicate Na vacancies. In the 2D model, we consider the three $t_{2 g}$ orbitals for each TM ion shown by yellow, green, and red lobes, respectively, as well as the hopping integrals between adjacent TM orbitals pointing to each other. (b) Energy coefficient $f_{k}$ of NDW formation in the wave vector space. (c) The effective potential of the interaction between Na ions at Na composition $x = 1 / 2$ given by the 1D model. The blue curve shows the screened Coulomb interaction (see Methods) between Na ions, while the red curve is given by our model with the electronic interaction added. The inset shows the continuous change of the Na-Na distance at the first minimum in the main plot with the Na composition $x$ . (d) Charge introduced into $d_{x y}$ bonding orbitals for O′3- ${Na}_{2 / 3} Ti O_{2}$ , O′3- ${Na}_{1 / 2} V O_{2}$ , P2- ${Na}_{1 / 2} V O_{2}$ , and $P^{'} 3 - {Na}_{1 / 2} Cr O_{2}$ . Electrons transfer to the reddish area upon the formation of dimer or trimer bonds. (e) Tight-binding model simulated dimer displacement or bond length variation (brown), and the dimer-induced variation of electrons in bonding orbitals, i.e., orbital polarization (blue), for different materials. The dashed black line is the 1D model calculated trend with the continuous change of electron numbers. (f) Comparison between bonding length change and bonding order of the dimer bond formation, i.e., orbital polarization, for different TM and Na composition $x$ from DFT. The O′3- ${Na}_{1 / 2} V O_{2}$ is considered in (e), (f).
Reuse & Permissions
Figure 5
Vanadium trimers of P2- ${Na}_{1 / 2} V O_{2}$ . (a) Optimized structure of P2- ${Na}_{1 / 2} V O_{2}$ by the GGA functional ( $U = 0$ ). Trimer bonds of V atoms exist with opposite local magnetic moments at corners (A) and top (B) sites. (b) Interorbital charge transfer and magnetic interaction $J$ in trimer bonds. Charge transfers from the blue area to the purple area. The gray and red digits represent the value of $J$ in units of eV for low $U$ (1.5 eV) and high $U$ (2.5 eV), respectively. Positive and negative values indicate ferromagnetic (FM) and antiferromagnetic (AFM) couplings, respectively. (c) Average magnetic moment on TM sites and dimer/trimer bond length as a function of Hubbard $U$ value for $TM = O^{'} 3 - Ti$ , P2-V, and P′3-Cr at Na composition $x = 1 / 2$ , as well as for P2-V at $x = 0.6$ . (d) Projected DOS of P2- ${Na}_{1 / 2} V O_{2}$ calculated by the $GW$ method, projected to the top V ( $B$ ) and Corner V ( $A$ ) in the trimer. The bands are divided into bonding orbitals, nonbonding orbitals, and antibonding orbitals in the trimer bonds.
Reuse & Permissions
Figure 6
Mechanism of trimer formation in P2- ${Na}_{1 / 2} V O_{2}$ . (a) Na-coupled TM orbital interaction in O′3- ${Na}_{1 / 2} V O_{2}$ with the ground-state ionic dimers from our tight-binding models. The blue disks are V ions. The red circles and orange disks are Na ions on the top and bottom layers. (b) The local potential of the labeled ions in O′3- ${Na}_{1 / 2} V O_{2}$ along the local $x$ axis in (a). The red curve and blue curve describe the case with and without Na. (c) Ground-state ionic trimers in P2- ${Na}_{1 / 2} V O_{2}$ from our tight-binding models. The blue disks are V ions. The red circles and orange disks are Na ions in the top and bottom layers. (d) The local potential of the labeled ions in P2- ${Na}_{1 / 2} V O_{2}$ along the local $x$ and $y$ axes in (c). The red curve and blue curve describe the case with and without Na. Red and blue arrows in (a,c) indicate the displacement directions of several selected ions. Orange lobes illustrate the type of TM-TM bonding. $- ε$ and $+ Δ t$ indicate the decrease of orbital energy and increase of the hopping integral induced by sodium. The results are consistent with our DFT simulations.
Reuse & Permissions

Physical Review Materials

Balancing orbital effects and on-site Coulomb repulsion through Na modulations in NaxVO2

Xi Chen, Hao Tang, Yichao Wang, and Xin Li

Phys. Rev. Materials 5, 084402 – Published 6 August 2021

Abstract

Physics Subject Headings (PhySH)

Authors & Affiliations

Article Text (Subscription Required)

Supplemental Material (Subscription Required)

References (Subscription Required)

Issue

Access Options

Authorization Required

Other Options

Download & Share

Images

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Log In

Search

Article Lookup

Paste a citation or DOI

Enter a citation

Balancing orbital effects and on-site Coulomb repulsion through Na modulations in ${Na}_{x} V O_{2}$