Phase transition and electronic properties of Co–As binary compounds at high pressure

Abstract

New stable stoichiometries in the Co–As system are investigated up to 100 GPa by the CALYPSO structure prediction method. In particular, we found three novel stable compounds of Co₂As-Pnma, CoAs₂-Pnnm, and CoAs₃-C2/m at high pressure. According to the theoretical electronic band structures, the structures of Co₂As-Pnma, CoAs₂-Pnnm, and CoAs₃-C2/m have metallic characters, and a pressure-induced electronic topological transition was found in CoAs₃-C2/m, which is not shown in other stoichiometries of the Co–As system. The calculated results of the electron localization function show that there are polar covalent bond interactions between Co atoms and As atoms in CoAs₂-Pnnm and CoAs₃-C2/m. The present results can be helpful for understanding diverse structures and properties of Co–As binary compounds under high pressure.

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1 Introduction

With several decades of effort, great achievements have been made in the field of condensed-matter physics. However, materials with better properties under extreme conditions are still being sought and studied. High pressure can provide a good way to search for new materials with new crystal phases, nonconventional stoichiometry, and outstanding properties.^1–5 For instance, unexpected stable stoichiometry of some binary systems were predicted under pressure.^6,7 Furthermore, the pressure-induced electronic topological transition in the structure of IrP has been uncovered by Ma by first-principles calculations.⁸ The study shows that pressure has a strong influence in tuning the electronic properties and can also enhance the properties of materials.^9–11

Compared with main group V compounds, the arsenide has been focused and researched under pressure since it exhibits unique structural features. For example, the arsenide is an important member of topological superconductors. Pressure-induced topological superconducting phases are observed in Cd₃As₂ and SrAs₃.^12,13 A non-monotonic pressure dependence of thermal conductivity was noticed in BAs due to the pressure-induced competing responses of three-phonon and four-phonon interactions, which has never been predicted or experimentally observed for any other materials.^14,15 To the best of our knowledge, the Co–As system has rarely been reported under pressure. On the basis of the interesting properties of above arsenide, it is necessary to explore the structure characters and chemical bonding of the Co–As binary compounds under pressure.

In the present paper, by means of first-principles swarm-intelligence structure search, we explored the binary Co–As phase diagram at 0–100 GPa. The previously reported structures of Co₂As-P6̄2m, CoAs-Pnam, CoAs₂-P2₁/c, and CoAs₃-Im3̄ were successfully reproduced at ambient conditions. Furthermore, three novel stable compounds (Co₂As-Pnma, CoAs₂-Pnnm, and CoAs₃-C2/m) were predicted under high pressure. At the same time, the details of electronic properties exhibit different bonding characters in these compounds under pressure. Interestingly, pressure-induced electronic topology transitions in CoAs3-C2/m phase have been confirmed. Our result represents a significant step toward understanding structural and electrical behaviour of the binary Co–As system under extreme condition.

2 Computational methods

CALYPSO method is the swarm-intelligence based particle swarm optimization (PSO) algorithm,^16–18 on which we predicted Co–As binary compounds under pressure of 0–100 GPa. In the framework of density functional theory, the structural optimizations, electronic structure and phonon calculations were performed. The generalized gradient approximation Perdew–Burke–Ernzerhof (GGA-PBE)¹⁹ was employed to treat exchange-correlation energy as implemented in the Vienna ab initio simulation package (VASP) code,²⁰ and projector-augmented-wave method²¹ was employed for cobalt and arsenic with 3d⁸4s¹ and 4s²4p³ as valence states, respectively. The cutoff energy of 800 eV and Monkhorst–Pack scheme with 2π × 0.04 Å⁻¹ were chosen to ensure that all of the enthalpy calculations were well converged to better than 1 meV per atom.^22,23 The full potential linearized augmented plane-wave approach developed in the WIEN2k package (Fig. S0†) is used to assess the correctness of the generalized gradient approximation Perdew–Burke–Ernzerhof utilized at high pressure.²⁴ The DFT + U method was used to evaluate the effect of the U value for the transition metal element Co(ESI Fig. 6. and ESI Table 2†), the result proved that U had less impact on the Co–As system. The chemical stability of the Co–As system is examined by using the ab initio molecular dynamics (AIMD) simulations in the constant-temperature and constant-volume ensemble. The temperature is controlled at 300 K. The time step is set as 1 fs and each simulation lasts 5 ps. We used electron localization function (ELF)²⁵ to investigate the bonding characteristics between atoms, and calculated phonons by supercell approach of PHONOPY program to determine dynamic stability of structure.^26,27

3 Results and discussion

3.1. Crystal structure

The variable-cell simulation with cell sizes of 1–4 formula units (f.u.) was performed structure prediction for CoAs_x (x = 1/2; 1; 2; 3) at 0–100 GPa. We calculated the enthalpy of formation (ΔH_f) of each stoichiometric compound, as shown in Fig. 1, to study thermodynamic stability of predicted Co–As compounds. The relative thermodynamic stability of different Co–As compounds with respect to elemental solids Co and As is calculated according to following equation: ΔH_f(CoAs_x) = [H(CoAs_x) − H(Co) − xH(As)]/(x + 1). In the formula, H(M) represents the enthalpy of structure at corresponding pressure (M = CoAs_x, Co, As). In Fig. 1, solid star indicates thermodynamically stable phases and unstable or metastable phases are expressed by hollow star.

Fig. 1 Relative enthalpies of formation of Co–As phases with respect to elemental cobalt and arsenic solids. The convex hulls connecting stable phases (solid star) are shown by solid lines. Metastable phases are shown by open star.

The built pressure-composition phase diagram of the Co–As system is shown in Fig. 2, with stable structures identified using colours and space groups. The metallic and non-metallic phases are represented by cyan and red colours, respectively. As can be seen in the Fig. 2, all predicted stable structures are metal phase under pressure. The structural parameters and atomic coordinates of predicted structures are presented in Table 1. The predicted stable structures at ambient pressure are in good agreement with the experimental results,^28–31 validating the applicability to the Co–As system of our adopted structure searching method and PBE functional.

Fig. 2 Predicted pressure-composition phase diagram of Co–As crystal phases. Cyan and red colours represent the metallic and non-metallic phases, respectively. The solid (dash) lines represent stable (metastable) phases.

Table 1 The lattice parameters and the Wyckoff position of predicted structures in the Co–As system

Space group pressure	Lattice parameters	Atomic coordinates (fractional)				Sites
Pnma-Co2As 1.28 GPa	a = 5.611 Å	Co1	0.039	0.250	0.317	4c
	b = 3.693 Å	Co2	0.648	0.250	0.565	4c
	c = 5.883 Å	As1	0.739	0.250	0.882	4c
	α = β = γ = 90.0°
Pnnm-CoAs2 74.5 GPa	a = 4.867 Å	Co1	0.500	0.000	0.500	2c
	b = 5.433 Å	As1	0.823	0.139	1.000	4g
	c = 2.636 Å
	α = β = γ = 90.0°
C2/m-CoAs3 45.7 GPa	a = 8.882 Å	Co1	0.176	0.000	0.923	4i
	b = 4.348 Å	As1	0.055	0.000	0.288	4i
	c = 5.404 Å	As2	0.108	0.500	0.851	4i
	α = γ = 90.0°	As3	0.827	0.500	0.596	4i
	β = 92.06°

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Pressure exhibits unique advantages in finding new materials,^32–36 thus the crystal structure and electron properties of these structures under high pressure will be examined in detail next. The full information of the initial pressure structures and phase diagrams of stable structures at different pressures are shown in ESI Fig. 1, 2, 3, and ESI Table 1,† respectively. The morphologies of predicted structures are presented in Fig. 3. The stoichiometric Co₂As has the lowest-enthalpy structure with I4/mmm, then at 1.28 GPa, it gives to the Pnma phase. Simultaneously, the distance between Co atoms and As atoms changes from 2.346 Å to 2.370 Å. Our calculation indicates that Co₂As-Pnma will be stable up until 100 GPa. Turning to CoAs, CoAs₂, and CoAs₃, Co atoms and As atoms in all predicted crystal structures form a Co–As octahedral environmental configuration, in which Co atoms occupy the center of the body and As atoms occupy the vertices. In the CoAs₂-Pnnm, there are As–As bonds with bond lengths is 2.292 Å. CoAs₃ is crystallized in a skutterudite-type structure at ambient pressure. The bond length of Co–As is 2.363 Å, and As atoms formed rectangular As₄ ring with As–As distances of 2.655 Å and 2.529 Å. Our calculations show that the cubic CoAs₃-Im3̄ will be stabilized up to 34.5 GPa. With the increase of pressure, the structure changes from Im3̄ phase to metastable C2/c phase, and in the C2/c phase, the As atoms are in the form of chains with the distance of 2.359 Å, and the distance between Co atoms and As atoms turns into 2.242 Å. As pressure increases to 45.7 GPa, the structure changes to the C2/m phase, and distances between Co–As and As–As change to 2.286 Å and 2.510 Å, respectively. To judge their stability, the phonon dispersion curves for Co₂As-Pnma, CoAs₂-Pnnm, and CoAs₃–C2/m are calculated, as presented in Fig. 4. All above phases are dynamically stable in their accessible pressures since no imaginary vibrational modes are observed in the Brillouin zone.^37–41 To confirm the thermodynamic stability of the predicted structure, the AIMD at finite temperatures for Co₂As-Pnma, CoAs₂-Pnnm, and CoAs₃–C2/m are calculated, as presented in ESI Fig. 4.†^42,43

Fig. 3 Structures of predicted Co–As system for (a) Co₂As-Pnma at 1.28 GPa; (b) CoAs₂-Pnnm at 74.5 GPa, and (c) CoAs₃-C2/m at 45.7 GPa. The blue and pink spheres are Co atoms and As atoms, respectively.

Fig. 4 Phonon dispersion relations and phonon density of states projected on Co atoms and As atoms for (a) Co₂As-Pnma at 1.28 GPa (b) CoAs₂-Pnnm at 74.5 GPa, and (c) CoAs₃-C2/m at 45.7 GPa.

3.2. Electronic properties

As shown in Fig. 5, we calculated band structures and the partial density of states (DOS) to investigate electronic properties of various Co–As compounds. Under high pressure, predicted structures exhibit metallic feature by evidence of overlap between conduction bands and valence bands at the Fermi level. In the structures of Co₂As-Pnma, the majority of the occupied states come from Co-d states near Fermi level (Fig. 5(a)), while in CoAs₂-Pnnm and CoAs₃-C2/m, there exist strong hybridization between Co-d and As-p states (−2 to 2 eV). In CoAs₂ and CoAs₃, the pressure-induced transition from non-metal to metal was recognized. As is shown in ESI Fig. 5,† compared with the typical arsenide GaAs under the high pressure, all the novel phases of high pressure exhibit similar metallic properties. Due to the pressure, the electrons become unlocalized, making the material exhibit metallic properties.

Fig. 5 Electronic band structure and the projected electronic DOS on Co atoms and As atoms for (a) Co₂As-Pnma at 1.28 GPa; (b) CoAs₂-Pnnm at 74.5 GPa; (c) CoAs₃-C2/m at 45.7 GPa, and (d) CoAs₃-C2/m at 48 GPa. Note that Zero energy is at the Fermi level.

It is worth noting that the electronic topological transition has a significant impact on the corresponding physical and chemical properties and can occur when the Fermi surface of the electronic system is changed by doping, high pressure, temperature or other external reagents.^44–46 Therefore, we have checked the potential pressure-induced electronic topological transition in Co–As system. Attractively, the electronic topological transition exists in CoAs₃-C2/m as shown in Fig. 5(c), it is found that there is no band along the A–B direction at 45.7 GPa. The band moves down and approaches to Fermi level at A–B direction when pressure increases. Fig. 5(d) clearly shows that the red band along the A–B direction is not fully occupied at 48 GPa and will form a hole pocket near the Fermi surface. An electronic topological transition in CoAs₃-C2/m structure is clearly observed since the noteworthy changes in the surface pro files Fermi at high pressure.

The electron localization function (ELF),⁴⁷ as depicted in Fig. 6, is used to understand bonding character of the Co–As compounds. Generally speaking, the regions with higher tendency of electron pairing (such as cores, and lone pairs) have large ELF values (>0.5), which indicates the formation of covalent bonds. However, the non/less electron localization have small values (<0.5), which indicates that there are ionic/metallic bonds between atoms. There is a mixed behaviour of ionic and metallic bonds simultaneously exits in Co₂As-Pnma phases. Note that in Fig. 6(b) and (c), the great ELF values about 0.8 between the Co and As atoms in CoAs₂-Pnnm and CoAs₃-C2/m structures, which suggests the covalent bonding character. The above statement is in good agreement with DOS. The DOS shows a large overlap between 3d states of Co and 4p states of As (Fig. 5(b) and (c)). Interestingly, in CoAs₂-Pnnm and CoAs₃-C2/m structure, it can be observed that there is electronic localization between As and As that does not favour either side, indicating the existence of nonpolar covalent bonds. It is more obvious that As atoms exist in chain form in CoAs₃-C2/m. To quantify the amount of charge belonging to each atom at different stoichiometries, we use the Bader charge analysis, which offers a description of electron transfer.⁴⁷

Fig. 6 Contours of the ELF for the structures of (a) Co₂As-Pnma at 1.28 GPa; (b) CoAs₂-Pnnm at 74.5 GPa, and (c) CoAs₃-C2/m at 45.7 GPa with isosurface of 0.8.

4 Conclusions

In summary, three novel stable compounds (Co₂As-Pnma, CoAs₂-Pnnm, and CoAs₃-C2/m) of Co-As compounds are discovered under high pressure using unbiased structure searching combined with density functional theory calculations. The theoretical phonon dispersion curves suggest that all these phases are dynamically stable. The calculated electronic band structures and density of states suggest that the Co₂As-Pnma, CoAs₂-Pnnm, and CoAs₃-C2/m phases are metallic. Moreover, with the increase of pressure, the CoAs₂ and the CoAs₃ realize the transition from semiconductor to metal at 74.5 GPa and 45.7 GPa, respectively. A pressure-induced electronic topological transition has been found in CoAs₃-C2/m phase. The electron localization function results show that there are ionic bonds and metal bonds in the predicted structures. Further analysis of the bonding nature shows that, there are polar covalent bonds between Co atoms and As atoms in CoAs₂-Pnnm, and CoAs₃-C2/m. Our results are important for understanding the structures and properties of Co–As system under high pressure.

Author contributions

Conceptualization, A. Z., H. L.; methodology, S. L., Y. D., Y. H. and A. Z.; validation, A. Z., J. Y. and J. L.; writing—original draft, A. Z.; writing—review and editing, A. Z., Y. L. and T. C. All authors have read and agreed to the published version of the manuscript.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The authors thank the financial support from the Natural Science Foundation of China (Grant No. 11764043).

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Footnote

† Electronic supplementary information (ESI) available. See https://doi.org/10.1039/d2ra02114e

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