The elusive magnetic ground state of sodium superoxide (NaO2)

doi:10.21203/rs.3.rs-756659/v1

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The elusive magnetic ground state of sodium superoxide (NaO2)

https://doi.org/10.21203/rs.3.rs-756659/v1

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An alternative energy storage solution to Li-ion batteries is a higher alkali metal superoxide, namely NaO₂. It is well-known that the transport properties of this alkali superoxide are governed by the transfer of charge between O₂ dimers. Although it goes through a plethora of structural phase transitions, its electronic and magnetic ground state remains shrouded. In this work, we perform first-principles density functional theory (DFT) calculations in order to understand the electronic structure, the source of the ‘unconventional’ magnetic properties and its effect on conductivity in Na superoxide. Finally, we explore the connection between magnetogyration and the magnetic ground state of NaO₂ remaining undetected till date.

Medical Physics

Ecological Modeling

Sodium superoxide

Oxygen dimers

Density function theory (DFT)

Orbital ordering (OO)

Magnetogyration effect

Super exchange mechanism

Sodium superoxide (NaO₂) has gained considerable attention in recent years as the main discharge product in Na-air battery because of its higher specific energy over Li-ion battery. The performance and stability of Na-O₂ batteries predominantly depend on the discharge products. The discharge products for the Na-O₂ batteries are Na₂O₂ and NaO₂, which have specific energies 1.6 kWh/kg and 1.1 kWh/kg respectively. On the other hand, the discharge product Li₂O₂ for Li-O₂ batteries has a higher specific energy of 3.5 kWh/kg. Since lower specific energy implies performance is higher, Na-O₂ batteries have better performance over the Li-counterpart, Li-O₂ batteries. At the standard state condition (300 K and 1 atm), NaO₂ is a stable compound in the Na-O₂ systems but LiO₂ is not a stable compound for the Li-O₂ systems [1, 2]. Furthermore, the relative stability of Na-O₂ batteries is higher than Li-O₂ batteries. These issues make Na-O₂ batteries the central point of attraction in the battery community. As the stable state of NaO₂ is accessible, NaO₂ can be produced from the reaction of superoxide and Na ions in a Na-O₂ batteries [3, 4]. However, in Li-O₂ batteries, it is the toughest challenge to produce solid LiO₂. Moreover, Li-O₂ batteries have a poor life cycle as well as low round-trip efficiency. The low round-trip efficiency arises from high over potentials during charging. These are great problems associated with Li-O₂ batteries. However, there is a solution to overcome these problems and can be minimized by using Na-O₂ batteries. The Na-O₂ batteries have high over potentials during charging. Furthermore, cells that discharge to NaO₂ have much lower over potentials, typically less than 200 meV over Li-ion batteries [5, 6–8]. Therefore, NaO₂ is widely using as an alternative energy storage solution to Li-ion batteries. Since NaO₂ is the chief discharge product in Na-air battery, ample concentrations have been dedicated to investigate its structures and physical properties [9, 10].

The material NaO₂ is exclusive among the alkali-metal superoxide in which the molecular complex O₂⁻ performs the role of anion and displays a diversity of phenomena, which are unswervingly associated with the properties of superoxide ions. This material has widespread applications, for example, it can be utilized in developing oxygen regeneration devices [11–15]. Nevertheless, NaO₂ phase exhibits several polymorphs [1]. At room temperature (RT), NaO₂ has an orientational disorder in the cubic Fm-3m structure. Upon cooling to about 230 K, the Fm-3m structure transforms to a rock salt-type pyrite (Pa-3) structure. Finally, NaO₂ adopts the orthorhombic FeS₂-type (space group Pnnm) structure in the temperature range of 43 to 196 K, which is also called the marcasite phase. The chief difference amongst the three phases arises from the superoxide O₂⁻ complex ordering in NaO₂. This material exhibits a rich variety of magnetism arising from the superoxide molecules. The origin of magnetism in this compound is distinctly dissimilar compared to that of the transition metals or rare-earth elements [1]. The magnetism of NaO₂ is dominated by the relative orientation of the O₂⁻ complexes [16, 17] and the state of partially occupied O-π^* orbitals. The O-π^* orbitals are composed of the anti-bonding components of O-p_x and p_y orbitals. At RT (cubic phase) and 200 K (pyrite phase), the system is paramagnetic having magnetic moments of 1.97 and 1.79 μB respectively. The magnetic susceptibility reduces first drastically to 200 K, thereafter gradually upon cooling, indicating some kind of magnetic order. Neutron diffraction experiments suggest that this order is not long-range. At 0–43 K range, magnetic orders are obscure. Nevertheless, the rise of the magnetic susceptibility at lower temperatures implies a dilute paramagnet having a concentration of about one mole per cent [18, 19].

Presently, there are very limited reports [15, 19] dealing with magnetic disorder and orientation of superoxide complexes in NaO₂. Therefore, it is decisively important to realize the magnetic disorder in room-temperature NaO₂, which is further crucial for determining the electronic structure, surface energetics, and growth properties of Na-O₂ batteries. In this spirit, we concentrated to fill the gaps in the present-day understanding of the electronic structure and magnetic properties of NaO₂. Furthermore, we explored that the crystal has an orientational disorder at RT cubic Fm-3m structure. The extra single electron of O₂^- that is donated by Na⁺ is equally distributed among the degenerate O-π^* orbitals. In the pyrite structure, the molecular anions aligned disorderly. In this structure, weak isotropic antiferromagnetic interactions between the molecules are observed. However, degeneracy of O-π^* orbitals is still observed. The O-atoms are aligned parallel in alternative planes in the marcasite structure. In the marcasite phase, degeneracy in the O-π^* orbitals suppresses, leading to long-range orbital ordering (OO) and the formation of quasi-one-dimensional antiferromagnetic spin chains.

We have carried out self-consistent calculations for the electronic, magnetic and structural properties of NaO₂ for RT, pyrite and marcasite structures by using density functional theory (DFT) [20, 21], which is implemented in the tight-binding linearized-muffin-tin orbitals (TB-LMTO) method [22, 23]. The local density approximations (LDA) method [23, 24] is further employed for the exchange-correlation interactions. The lattice parameters for the RT structure are a = b = c = 5.49 Å and the primitive unit cell contains one Na and two equivalent O-atoms [25]. The lattice parameters used for the pyrite phase are a = b = c = 5.48 Å and its primitive unit cell contains four equivalent Na and eight equivalent O atoms [25]. Finally, lattice parameters for the marcasite structure are a = 4.26 Å, b = 5.54 Å and c = 3.44 Å. The primitive unit cell consists of two equivalent Na and four equivalent O atoms [25]. The Na atoms are located at (0, 0, 0) in all the three structures, whereas O atoms are located at (0.25, 0.25, 0.25), (0.439, 0.439, 0.439) and (0.119, 0.42, 0) respectively for the RT, pyrite and marcasite structures [25].

In NaO₂, after acqiring an extra electron from Na, each O₂⁻ complexes have nine electrons in the configuration of σ²π⁴π^*3σ^*0. The partially occupied anti-bonding π^* molecular states essentially determine the electronic and magnetic properties of NaO₂. The extra electron in the π^*orbital generates the magnetic moment of 1.0 μB per O₂⁻ molecule. Nevertheless, in comparison with the regular oxygen molecule, the O₂⁻ complex has one extra electron in the degenerate π^* orbital that is composed of anti-bonding components of O-p_x and p_y orbitals. Consequently, the properties of NaO₂ crucially depend on where this adopted electron will reside.

3.1. Electronic, magnetic and structural properties of cubic NaO₂

At room temperature (RT), NaO₂ adopts the cubic Fm-3m structure. It has two superoxide ions in the primitive unit cell. Figure 1(a) displays the total densities of states (TDOS) in the nonmagnetic LDA calculations for high symmetry cubic structure. It is evident from this figure that the total DOS is predominated by the O-2p character, while the contributions from the 2p, 2s character of Na are negligible. The partial DOS (PDOS) of O-2p states exhibit perfect molecular splitting between σ, π, π^* and σ^* states. The finite DOS at the Fermi level (E_F) arises from the π^* states, indicating the metallic behaviour of NaO₂. The band structure of NaO₂ is depicted in Fig. 1(b). Within the orbital picture of the ground state of O-2p bands, the two highest occupied orbitals are π^* anti-bonding orbitals, with one electron in each orbital. The O- π^* orbital remains as the highest occupied molecular orbital for O₂⁻ complex, which is filled by three electrons after acquiring an extra electron from the Na ion. This means, each O₂⁻ complex has one unpaired electron, making O₂⁻ magnetic. But it is observed in the band structure calculations that the anti-bonding π^* states are exactly degenerate due to high symmetry in the crystal structure. Because of this orbital degeneracy, the external electron added to the O₂ molecule has an equal probability to occupy each π^* orbital. It is also unambiguous from Fig. 1(b) that there is no local band formation and the bands are extended. We also observed no s-p hybridization in the band structure calculations, which however indicates no local moment and hence no magnetism.

Next, we carried out the FM electronic structure calculations. The calculated TDOS and PDOS of Na-2p, 2s and O-2p are illustrated in Fig. 2(a). The system is insulating in the up-spin channel with a semiconducting gap of ~ 7.0 eV, while the down-spin channel is metallic but the Fermi level (E_F) falls almost into a pseudogap. The semiconducting gap appears between the occupied π^* and unoccupied σ^* states. The semiconducting gap in the up-spin channel indicates 100% spin polarization. It is also evident that the total DOS is O-2p dominated and the contributions from 2p and 2s states of Na are insignificant. The electronic band structure of O-2p states in both spin channels are also shown in Figs. 2(b) and (c). From both DOS and band structure calculations, it is clear that all of σ, π and π^* states are occupied for the up-spin channel, whereas σ and π states are observed occupied but π_g^* states are observed unoccupied for the down-spin channel that is accompanied by spin polarization. The calculated total, Na and O magnetic moments are 3.0 μB. 0.03 μB and 1.47 μB respectively, which indicates magnetism in the RT phase of NaO₂.

Further, we concentrated on the structural properties of NaO₂ in the RT cubic phase. The crystal structure of NaO₂ is exhibited in Fig. 3(a). In this phase, sodium has eight oxygen coordination. We observed uniform Na-O bond distances. The uniform Na-O bond distance is 2.3772 Å. The < Na-O-Na and < O-Na-O bond angles are also uniform. The magnitudes of < Na-O-Na and < O-Na-O angles are 109.47º and 70.529º respectively. Besides, each O atom has four Na coordination forming a square [see Fig. 3(b)] having uniform Na-Na distances in the diagonal position = 3.8820 Å. These four Na-atoms form four uniform < Na-O-Na bond angles having a magnitude of 109.471º, which results in high symmetry and hence degeneracy in the π^* orbitals. More interestingly, O₂⁻ species freely rotate to have an Fm-3m structure. This kind of O₂⁻ orientation is responsible for the disorder in NaO₂.

3.2. Electronic, magnetic and structural properties of pyrite NaO₂

The pyrite phase of NaO₂ is realized above 196 K. The primitive unit cell of pyrite NaO₂ contains two formula unit (f.u.), hence four superoxide ions in the primitive unit cell. Figure 4(a) represents TDOS and PDOS of Na-s, p and O-p states in the nonmagnetic calculations. It is observed that total DOS is dominated by the O-p states, while the contributions from s and p states of Na are negligible. The low energy states that appear around − 10 to -8.8 eV and − 8.8 to -7.3 eV correspond to bonding components of σ and π states respectively. The π^*-like anti-bonding molecular orbitals (MOs) are observed around E_F. It is observable from the figure that the electron contributions from the anti-bonding components of π^* states are responsible for the metallic character of pyrite NaO₂. The nonmagnetic electronic band structure of π^* orbitals of oxygen is depicted in Fig. 4(b). The FM DOS calculated in the LDA approximations are illustrated in Fig. 5(a). In the spin-up channel, the bonding components of σ and π orbitals are observed around − 10.4 to -9.3 eV and − 9.3 to -7.3 eV respectively. The anti-bonding components of π^* and narrow σ^*-like orbitals are observed around − 2.2 to -0.4 eV and 14.3 to 14.6 eV respectively. In the down-spin channel, σ, π, π^* and narrow σ^* states are observed around − 9.7 to -8.3 eV, -8.3 to -7.3 eV, -1.9 to 0.8 eV and 15.6 to 15.9 eV [not shown in Fig. 5(a)] respectively. It is visible from this figure that a minute but finite DOS is observed at E_F for both spin channels, which results in the metallic nature of NaO₂ in the pyrite phase. It is further noticeable that Na-s and O-π^*-states are hybridized near E_F. The electronic band structures of O-π^* -like states are represented respectively in Figs. 5(b) and 5(c) for two spin states. The anti-bonding π^* orbitals split into two components. These two components lie immediately below E_F for spin-up states, while for spin-down states they lie both above and below E_F. Nevertheless, the degeneracy of π^* states is still maintained. The O-π^* states are localized in such a manner that results in a substantial magnetic moment in the π^*-orbital. The total magnetic moment calculated as 0.98 μB, which ensures magnetism in the pyrite phase of NaO₂.

The crystal structure of NaO₂ in the pyrite phase is illustrated in Fig. 6(a). The formation of oxygen dimers is observed in this phase. It is obvious from this figure that O-O dimers are oriented randomly in all possible directions. The O-O dimer length is 1.158 Å. It is found that every O-O dimer has six Na coordination. Four of these Na atoms lie in the plane (basal plane) cutting the oxygen dimer, while the remaining two lies along the line (apical plane) joining two oxygen atoms of the dimer [see Fig. 6(b)]. All Na-O distances are found uniform (= 2.4517 Å). All the < Na-O-Na angles are also uniform (= 104.417^o). Therefore, the crystal is tilted slightly but still maintains high symmetry for which degeneracy in the π^* -like molecular orbitals still maintains. It is observed that each Na has six oxygen coordination. The < O-Na-O bond angles are 91.065^o (×2) and 88.935^o (×2) for the basal plane. Besides, <O-Na-O bond angle for the apical plane is 180^o, which facilitates a super exchange mechanism and hence the system exhibits anti-ferromagnetism in the pyrite phase.

3.3. Electronic, magnetic and structural properties of marcasite NaO₂

The marcasite phase of NaO₂ is realized below 196 K. The primitive unit cell of pyrite NaO₂ contains four formula units i.e. eight superoxide ions in the primitive unit cell. The TDOS and PDOS of Na-s, p and O-p states in the nonmagnetic calculations are presented in Fig. 7(a). From this figure, it clear that TDOS is O-2p dominated and contributions from s and p states of Na are insignificant. The σ and π-like orbitals are separated by a small energy gap ~ 0.12 eV. These two states are respectively observed around 5.98 to 6.77 eV and 4.35 to 5.86 eV below E_F. The π^*-like anti-bonding molecular orbitals (MOs) are observed both below and above E_F (-1.5 to 0.3 eV). Therefore, this system is metallic due to electron contributions from the anti-bonding components of π^* states around E_F. The electronic band structures of O-2p orbitals are illustrated in Fig. 7(b). It is clear from these figures that the degeneracy in the O-π^* orbitals is suppressed due to the symmetry loss accompanied by the structural phase transition to the marcasite phase. Therefore, the O-π^* orbitals split, leading to long-range OO is observed. The spin-polarized ferromagnetic LDA DOS are shown in Fig. 8(a). The up-spin channel is insulating and the down-spin channel is metallic. Therefore, the system is half-metallic. The semiconducting gap observed is ~ 1.2 eV. In the spin-up channel, σ and π -bonding components are observed between − 6.5 to -7.25 eV and − 4.9 to 6.38 eV respectively. In the down-spin channel, the corresponding components are found around − 6.6 to -5.85 eV and 5.8 to 4.2 eV respectively. The π^*-like molecular orbitals are observed around − 1.85 to -0.30 eV and − 1.25 to 0.45 eV respectively for up and down-spin channels.

Our next effort was to study the electronic band structures of marcasite NaO₂. The total band structures of O-π^* -like orbitals for both spin channels are shown in Figs. 8(b) and (c). The band structures of O-2p_x/y are also illustrated in Figs. 9(a) and (c) for the up and down-spin channel respectively. The O-p_z band structures for the corresponding channels are also represented in Figs. 9(b) and (d) respectively. Due to the structural transition, two π* orbitals are energetically separated. Therefore, degeneracy in the O-π* orbitals lifts due to structural transition. Therefore, suppression of degeneracy in the π^*-like orbitals occurs due to the transition in the marcasite phase. As a result, orbitals split and long-range OO is observed [Figs. 9(b) and (d)]. This long-range OO gives rise to magnetization in the marcasite NaO₂. The O-π^* states are therefore localized, which results in a substantial magnetic moment in the π^*-orbital. The calculated magnetic moment per Na and O ions are − 0.15 μB and − 0.42 μB respectively.

Final emphasis was given to investigate the structural properties of NaO₂ in the marcasite phase. In this structure, formation of O-O dimer is also observed. The O-O dimers are arranged orderly in the alternative planes as depicted in Fig. 10(a). The O-O dimer length observed is 1.3467 Å, that means dimer length reduces by 0.1881 Å upon the structural phase transition from pyrite to marcasite. Each oxygen dimer is surrounded by six Na atoms. Four of these atoms lie in the plane cutting the oxygen dimer, while the other two lies along the line joining two oxygen atoms of the dimer [see Fig. 10(b)]. All Na-O distances are at uniform distances (= 2.3814 Å). Since the electron density on the O atoms increases after acquiring an extra electron from Na atom, they tend to move apart from each other due to electrostatic grounds. Eventually, this movement is hindered beyond a certain point due to the presence of Na-atoms. The strong electrostatic repulsion of the electrons of Na and O atoms prevents this movement of the latter in the z-direction. Consequently, oxygen dimers are rotated as schematically shown in Fig. 10(b). Indeed, this rotation of O-O dimers exerted a net force on Na-atoms that are found on the plane joining the two O atoms of a dimer such that Na atoms have long/short < Na-O-Na (108.88 Å/91.263 Å) angles [see Fig. 10(b)] with O atoms of the dimers. These results strongly confirm a significant reduction in symmetry of the crystal. Therefore, symmetry lowering would occur via coherent tilting of the O₂⁻ molecular axes i.e. rotation of oxygen dimer, the so-called magnetogyration effect which however facilitates OO in the degenerate π_g^* -like molecular orbitals. Also, each Na atom has six-fold oxygen coordination. The Na-O bond distances are 2.4061 Å (×4) (in the basal plane) and 2.3814 Å (×2) (in the apical plane). The calculated < Na-O-Na bond angles are 108.88^o (×2) and 91.263^o (×2) (in the basal plane) i.e. large tilting in < Na-O-Na is observed, which also lifts crystal symmetry. Lifting of symmetry suppresses degeneracy in the O-π* orbitals. The apical < O-Na-O bond angle observed is 180^o which however favours the super exchange mechanism. Therefore, NaO₂ is antiferromagnetic (AFM) in the marcasite phase.

In this study, we concentrated to fill the gaps in the present-day understanding of the electronic structure and magnetic properties of NaO₂. Furthermore, we explored that the crystal has an orientational disorder at RT cubic Fm-3m structure. The extra single electron of O₂⁻ that is donated by Na⁺ is equally distributed among the degenerate O-π^* orbitals. In the pyrite structure, the molecular anions aligned disorderly. In this structure, weak isotropic antiferromagnetic interactions between the molecules are observed. The degeneracy in the O-π^* orbitals still survives. The O-atoms are aligned parallel in alternative planes in the marcasite phase. The transition to the marcasite phase suppresses the degeneracy in the O-π^* orbitals leading to long-range OO and formation of quasi-one-dimensional antiferromagnetic spin chains. Nevertheless, the magnetogyration effect between Na and O atoms of dimers results in OO in the degenerate π_g^* -like molecular orbitals. Finally, the super exchange mechanism stabilizes AFM in the marcasite phase.

Acknowledgments

The authors thank the West Bengal State University, Kolkata-700126 and Department of Higher Education, W.B, India for financial and infrastructure support to carry out this work.

Code availability

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Authors contribution

S. B.: Framed the works, calculations, simulations, investigations, conceptualization, writing-original draft. M.D.R.: Framed the works, calculations, simulations, investigations, project administration, supervision, technical support, writing-original draft.

Funding

This research was supported by the West Bengal State University, Kolkata-700126 and Department of Higher Education, W.B, India

Availability

All the analyzed and generated data used for this study are available along with this manuscript.

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Not applicable.

Conflict of Interest

The authors declare that they have no conflict of interest.

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You are reading this latest preprint version

The elusive magnetic ground state of sodium superoxide (NaO2)

Status:

Version 1

Abstract

Figures

1. Introduction

2. Computational Methods

3. Results And Discussion

3.1. Electronic, magnetic and structural properties of cubic NaO₂

3.2. Electronic, magnetic and structural properties of pyrite NaO₂

3.3. Electronic, magnetic and structural properties of marcasite NaO₂

4. Conclusions

Declarations

References

Supplementary Files

Status:

Version 1

The elusive magnetic ground state of sodium superoxide (NaO2)

Status:

Version 1

Abstract

Figures

1. Introduction

2. Computational Methods

3. Results And Discussion

3.1. Electronic, magnetic and structural properties of cubic NaO2

3.2. Electronic, magnetic and structural properties of pyrite NaO2

3.3. Electronic, magnetic and structural properties of marcasite NaO2

4. Conclusions

Declarations

References

Supplementary Files

Status:

Version 1

3.1. Electronic, magnetic and structural properties of cubic NaO₂

3.2. Electronic, magnetic and structural properties of pyrite NaO₂

3.3. Electronic, magnetic and structural properties of marcasite NaO₂