Metal–Metal Bonding Stabilized Ground State Structure of Early

Article pubs.acs.org/JPCC

Metal−Metal Bonding Stabilized Ground State Structure of Early Transition Metal Monoxide TM−MO (TM = Ti, Hf, V, Ta) Linggang Zhu,†,‡ Jian Zhou,† Zhonglu Guo,†,‡ and Zhimei Sun*,†,‡ †

School of Materials Science and Engineering, Beihang University, Beijing 100191, China Center for Integrated Computational Materials Engineering, International Research Institute for Multidisciplinary Science, Beihang University, Beijing 100191, China

‡

S Supporting Information *

ABSTRACT: It is commonly believed that early transition metal monoxides (TM−MOs) crystallize in simple rock-salt structures (symmetry FM3̅M) for their ground states. Here, by combining structure-searching algorithm and first-principles calculations, we identified structures that are more stable than the ideal rock-salt for the early TM−MOs (TM = Ti, Hf, V, Ta). For TiO, HfO, and TaO, ground state symmetries of P6̅2M), I41/AMD and P1̅ are obtained, respectively, which have distinct structural and electronic properties compared to the rock-salt structure. However, it is rather complex for the case of VO due to the existence of magnetic ordering. For VO, magnetic ordering behavior exists in the rock-salt and the predicted P1̅ structure according to the hybrid functional calculations. After relaxation, the magnetic ordering causes local distortion in the original rock-salt structure, leading to a R3M ̅ symmetry, which becomes more stable than the predicted P1̅ structure. Furthermore, the ionic TM−O bonding of the predicted phases is rather weaker than that of their rock-salt counterparts. While the enhanced metal−metal bonding characterized by the distances between the nearest-neighboring metallic atoms is found to be responsible for the stabilization of the ground state structures discovered here. Our findings deepen the understanding of the ground state of early TM−MOs, which is vital for the unraveling of the complete physical picture for transition metal monoxides.

1. INTRODUCTION Transition metal monoxides (TM−MOs) have a quite special position in condensed matter physics, for instance, they are regarded as prototypes for the study of exchange-correlation effects between electrons. In these systems, the d orbital of the cations are partially occupied, which is believed to be the reason for various physical properties such as antiferromagnetism, electrically conductivity, etc.1 Determination of the crystal structures of TM−MOs is the basis and thus very crucial for any further studies on these systems. Until now, this classic geometry issue of TM−MO still attracts the attentions of the researchers. Recently, Derzsi et al.2 summarized the crystal structures of TM−MOs: early TM− MOs including TiO, VO, CrO, TaO, and ZrO adopt perfect rock-salt (B1) structure; late TM−MO including CuO, PdO, PtO, and HgO exhibit various symmetries, while surprisingly they can all be viewed as the distorted B1. Derzsi et al.2 also demonstrated that the distortions from perfect B1 of late TM− MO structure are due to the interplay between electronic and nuclear degrees of freedom, for example, the monoclinic C2/c structure of CuO3 arises from the antiferromagnetic interactions between unpaired electron on the Cu2+ cation. In essence, these structural distortions of late TM−MOs arise from the so-called Jahn−Teller (JT) effect,4 i.e., the geometrical distortion that removes the degeneracy of the electronic ground © XXXX American Chemical Society

state like eg orbitals in the octahedral complexes will stabilize the system. JT effect is more pronounced when the eg orbitals are unevenly occupied. Considering the partially occupied t2g orbitals and empty eg orbitals of early TM−MOs where JT effect is much less noticeable,5 their crystallization into perfect B1 structure seems reasonable. Indeed, a few early TM−MOs with B1 structure have been observed in experiments, including TiO,6 VO,7 and TaO.8 However, it should be noted that, compared to the late transition metals, the early transition metals can form more oxides in which valence state of the cations are different. For example, in the phase diagram of Ti−O,6 Ti2O, TiO, Ti2O3, and TiO2 all exist, while for Cu, only two oxides can be formed, CuO and Cu2O.9 In other words, the ion-packing of metallic atom and oxygen in the early transition metal oxides can be versatile, which can also be a trigger of the distortion from a high symmetry structure in addition to JT effect.5 In fact, monoclinic TiO with C2/M symmetry that exists in low temperature has been confirmed by experiments, named as αTiO,6 which is lower in energy than its rock-salt counterpart according to simple DFT calculations. Very recently, Amano et Received: March 20, 2016 Revised: April 27, 2016

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DOI: 10.1021/acs.jpcc.6b02871 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C al.10 synthesized another polymorph of TiO with the symmetry of P6̅2M, named as ε-TiO, which is the most stable one among all polymorphs. They found that a Bi flux is necessary in the fabrication process of ε-TiO, which may explain why this phase has been overlooked so far. In spite of the progress in the structure characterization of TiO, the perfect B1 structure is still commonly accepted as the ground state for many other early TM−MOs, which makes a more detailed study on the structure characterization very urgent and essential. Moreover, for vanadium, the neighbor of Ti in the periodic table, its monoxide always keeps the cubic symmetry, and no lower symmetry with vacancy ordering can be fabricated using similar heat treatment methods as the TiO.11 Therefore, the early TM−MOs where only t2g orbitals are occupied also exhibit abundant physics, which wait to be unraveled. In this study, we revisit the ground states of early transition metal monoxides TM−MOs (TM= Ti, Hf, V, Ta) with the electronic configurations d2 and d3. More stable phases compared to the ideal B1 structure are found for the TM− MOs by using structure-searching algorithm. The dynamic stabilities for the predicted structures are confirmed by phonon calculations. Furthermore, for the stabilization mechanism of the discovered symmetries, the metal−metal bonds are found responsible.

Figure 1. Phonon dispersion curves for the early TM−MOs with ideal B1 structure. Negative frequencies indicate soft modes.

cation and anion sublattice. It has been demonstrated that for the late transition metal monoxides, their B1 structures have the largest negative frequencies at point L (1/2, 1/2, 1/2), corresponding to the distortions in the oxygen sublattice,2 while the modes at point L for the early TM−MOs all have positive frequencies as shown in Figure 1. This discrepancy shows that patterns of atomic displacements that compensate the soft modes are very different for the early and late TM−MOs, which may imply different structural distortion mechanism. 3.2. Predicted TM−MO Structures. The stable structures obtained in the three-step calculation process (as mentioned in the Calculation Details Section) are shown in Figure 2. Table 1 summarizes the symmetry and energetic data for all these structures.

2. CALCULATION DETAILS To figure out the correct ground state structures of early TM− MOs, a three-step process is designed. First, the automatic structure searching is done using evolutionary algorithm as implemented in the code USPEX.12,13 Then, a series of geometries are constructed manually, based on the symmetries that already exist in the database for the transition metal monoxides. Finally, effects of spin−orbital coupling (SOC) and d-electron localization are considered to confirm the relative stability between the B1 phase and the stable structures found in the first two steps. All the structure optimization and energy calculations are done using VASP code,14−16 in conjunction with projector augmented wave potentials within the generalized-gradient approximation (PAW-GGA).17 Spin polarization is turned on for all the calculations. Cutoff energy for the plane wave basis set is 450 eV. K-point meshes for structures with different symmetry are carefully tested to ensure the convergence of the energy data. Regarding the localization of the d electrons in the transition ions, the hybrid functional HSE0618 is employed to check the relative stability of various structures and in the study of electronic properties. Previous study on late TM−MOs has shown that the hybrid functional can reproduce the relative stability between various polymorphs well.2 Phonon calculation is performed in the framework of harmonic approximation using Phonopy19 in order to study the dynamic stability of the structures.

Figure 2. Structures of the predicted phases (CIF files for these geometries can be found in the Supporting Information). Red balls are oxygen atoms, while the others represent metallic cations.

As shown in Table 1, according to the results using PBE functional, the predicted phases are much more stable than the B1 geometry with identical composition. No imaginary frequencies exist in the phonon dispersion curves of the predicted phases calculated using PBE functional as shown in Figure 3, indicating the dynamic stability of these systems. For the spin−orbital coupling (SOC), it is known that its effects on the 5d transition metal oxides is much more pronounced than the 3d oxides.20 In consistence with these conclusions, we found that the energy changes induced by SOC

3. RESULTS AND DISCUSSIONS 3.1. Soft Modes in B1 Structure. The phonon dispersion curves along selected high-symmetry direction in the Brillouin zone calculated using PBE functionals are plotted in Figure 1. The dynamic instability of the perfect B1 structure for all the four monoxides can be indicated from the calculated imaginary frequencies. The modes with largest negative frequencies mainly locate at the points X (1/2, 0, 1/2) and W (1/2, 1/4, 3/4), which correspond to the cooperative movements of B

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is given in the Supporting Information. As for the P1̅ type VO, which can be viewed as vacancy ordered format of B1 (see Figure S1 in Supporting Information) and has lower energy than R3M ̅ (distorted B1) structure according to PBE result, no AFM is found at the PBE level. However, results calculated by using the HSE06 functional indicate that the P1̅ VO is also antiferromagnetic, and it becomes energetically unfavorable compared to R3M ̅ . Figure 4 shows the magnetic configurations

Table 1. Energy of the Predicted Phases Per MO Unit Compared to B1 Structurea composition

TiO

HfO

VOb

TaO

symmetry PBE PBE + SOC HSE06

P6̅2M −0.59 −0.55 −0.66

I41/AMD −1.15 −1.14 −1.38

P1̅ −0.60 −0.56 +0.33

P1̅ −2.0 −2.0 −2.4

a In unit of eV. Energetic data are obtained with different functional and parameter setting, such as PBE, PBE plus SOC effect, and hybrid functional HSE06. Negative values mean that the predicted phase is more stable than B1 structure, while positive value indicates the stability of B1. bAfter full relaxation, B1 symmetry of VO is reduced to R3M ̅ due to the magnetic ordering, i.e., for VO, the energetic data listed is the relative value compared to the R3̅M structure instead of ideal B1.

Figure 4. Spin configurations for (a) R3M ̅ (distorted B1 after full relaxation) and (b) P1̅ type VO obtained by HSE06 calculations. The directions of the magnetic moments on V are labeled using black arrows.

for R3̅M and P1̅ VO obtained by using HSE06 calculations. Normally the scale of the relative energy change in TM−MO polymorphs induced by the exchange-correlation effect is quite small even when the more advanced random phase approximation (RPA) technique is used.22 Apparently, here the magnetic ordering triggered by the electron-correlation effects is the main reason for the ground state structure evolution in the case of VO, which also makes VO different from TiO. To further elucidate the effects of electron spin on the phase ordering in VO, the spin of electrons is restricted by performing nonspin polarization calculations. It is found that even at HSE06 level, the P1̅ structure is more stable than B1, and the energy difference is as large as 0.67 eV per MO unit. The significant effects of electron spin and magnetic ordering on the relative stability of VO polymorphs can thus be concluded. However, according to the experimental studies, the electronic and magnetic properties of VO depend on the temperature and its practical composition. Nominally stoichiometric VO is found to be a paramagnetic metal, while Austin noted that VO becomes nonmetallic at temperature below 123 K.23 With a wide composition and temperature range, VOx presented antiferromagnetic (AFM) behaviors for x = 1.25 and 1.147 at the temperatures of 7.0 and 4.6 K, respectively.24 Meanwhile, their electrical conductivity also strongly relies on the value of x.25 It has been found that the low-energy elementary excitation spectrum of VO is dominated by some spin fluctuation without long-range order, and experimental data suggested that VO tends to develop local magnetic moments in the vicinity of a metal−insulator transition (Mott− Hubbard transition).11 Therefore, considering the nonmetallic property at low temperature and signal of local magnetic moments observed in the above-mentioned experiments, our finding using advanced HSE06 calculations that ground state of VO is an AFM insulator with structure of R3̅M (distorted B1) is reasonable. So far, given the structural searching results and the effects of magnetic ordering, the ground state symmetries for these TM− MOs can be summarized: P6̅2M for TiO, I41/AMD for HfO, P1̅ for TaO, and R3̅M with AFM behavior for VO. An interesting question here is whether there are some connections

Figure 3. Phonon dispersion curves for the predicted early TM−MOs: (a) TiO, (b) VO, (c) HfO, and (d) TaO. The data is based on the calculation using PBE functional, and VO has the P1̅ symmetry at PBE level.

for 5d oxides HfO and TaO are 0.6 and 0.8 eV, respectively. However, its influence on the relative stability of the predicted structures and B1 are negligible. While for 3d compounds TiO and VO, effect of SOC is very tiny for each phase as well as their relative stability. The stabilities of predicted structures are further verified by the HSE06 calculations for TiO, HfO, and TaO. For TiO, the stability of the recently observed P6̅2M phase over B1 phase and other polymorphs is thus confirmed. We found that the energy of TiO with structure P6̅2M is 0.1 eV/MO-unit lower than that of C2/M, consistent with the results calculated by Amano et al.10 By calculating the free energy of the two polymorphs, we noticed that the stability of P6̅2M over C2/M still remains at T = 600 K. Ground State of VO. Interestingly, for ground state of 3d3 compound VO, as shown in Table 1, contradicted results are obtained by PBE and HSE06 functional: at PBE level, the P1̅ structure is more stable, while for HSE06 calculations, the R3̅M (distorted B1) becomes the more stable structure. We found that this discrepancy is caused by the magnetic ordering of the system. As for B1 type VO, PBE calculation leads to an antiferromagnetic (AFM) conductor, while addition of Hartree−Fock exchange effect as in HSE06 results in an AFM insulator. Our results about the B1 structure agree with other theoretical calculations.21 After the full geometrical relaxation, the repulsion/attraction between atoms with parallel/antiparallel spin will lead to nonuniform deformation and reduce the B1 symmetry to R3M ̅ . CIF file of R3M ̅ structure C

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The Journal of Physical Chemistry C between these structures and B1. First, the C2/M phase of TiO can be viewed as the vacancy ordered structure of B1, where the same amount of Ti and oxygen ions are missing. While for the most stable P6̅2M structure, Ti atoms are coordinated by the oxygen atoms with triangular-prismatic and regular triangular arrangements, showing very different geometry compared to B1. Then for HfO and TaO, there is no apparent resemblance between the predicted structure and B1, and it cannot be referred to as distorted B1. Finally, for VO, R3̅M is in fact the AFM type B1 after full relaxation, where lattice parameters show deviation from ideal B1. The structural similarities/ differences of these phases compared to B1 can also be reflected by the simulated XRD patterns (Figures S2 and S3 in Supporting Information). 3.3. Electronic Structure of the Predicted TM−MOs. The electronic property of transition metal oxides is important for their applications, such as the utilization in the resistance random access memories.26−31 Figure 5 shows the calculated

level is also much reduced compared to the B1 structure. Therefore, the low electron conductivity and high resistance for these predicted structures can be expected. Additionally, we found that C2/M TiO has a band gap of 0.2 eV (Figure S4 in Supporting Information). The distinct electronic structures among these polymorphs indicate strong phonon−electron coupling. 3.4. Bonding and Stabilization Mechanism of Predicted Phases. Ionic bonding involving the charge transfer can be easily formed between the transition metal and oxygen, which should play an important role in the stabilization of the oxides. The coordination number of the cation in the predicted phases ranges from 3 to 6, smaller than that in the ideal B1 structure, which is 6. The coordination geometries can be seen in Figure S5 of the Supporting Information. The decrease in coordination numbers might be a signal of weakening ionic bonding in the predicted phases, and to confirm this, the Bader charge analysis32 is performed. Bader charge is the accumulation of the electrons inside the Bader volume enclosed by a zero flux surface on which the charge density is a minimum perpendicular to the surface. The variance of the Bader charge represents the charge transfer. Table 2 list the Bader charge of Table 2. Bader Charge (in e) of the Metallic Cations for Various Oxides, Relative to the Charge of the Neutral Atomic Statea predicted phase B1

TiO

HfO

VO

TaO

1.1, 1.4 1.48

1.39, 1.33 1.63

1.32, 1.30 1.46

1.38, 1.03 1.51

a

The data for the predicted phases and ideal B1 are compared. The positive value means the electron donation. The charge on different cation positions in each oxide are all listed. For VO, the predicted phase in this table is with P1̅ symmetry, while R3̅M structure has the same Bader charge as B1.

the metallic ions in the oxides relative to the atomic states. Larger value (representing more electron donation) indicates stronger ionic bonding. As can be seen in Table 2, the cations in the predicted phases for all oxides donate fewer electrons compared to the B1 structure, meaning weaker ionic bonding in the predicted phases. It is surprising to see that the more stable oxides have weaker ionic bonds. Therefore, the heteropolar TM−O bond does not account for the relative stability of various phases found here. Although the ionic bonding in the predicted phases is relatively weaker, they are still more stable in the cases of TiO, HfO, and TaO. One mechanism for the stabilization might be the strengthening of other type of bonding, such as the bonding between cations. To verify this hypothesis, the metal−metal distances in various structures are measured. Figure 6 summarizes the distances between the nearest-neighboring metallic atoms in the oxides. For TiO, HfO, and TaO, it is obvious that in the predicted phases the distances between the nearest-neighboring metallic atoms are smaller than those in B1 structure, independent of the functionals used in the calculations. In this case, the smaller metal−metal distance represents the stability of the structure. For VO, at the PBE level, the more stable P1̅ structure also has smaller V−V distance than B1 (reduced to R3̅M). Due to the magnetic ordering in HSE06 calculations as mentioned above, the B1 structure (reduced to R3̅M) of VO becomes more stable. Interestingly, as shown in Figure 6, the discrepancy in the V−V

Figure 5. Density of states (DOS) for (a) TiO, (b) HfO, and (c) TaO, and the number of states shown are for each MO formula unit. The left panel is the DOS for the B1 structure, while the right panel for the predicted structures. The vertical line indicates the position of the Fermi level.

density of states for TiO, HfO, and TaO using hybrid functional in which the predicted phase and B1 structure are compared. While for VO, as discussed above, it is an AFM insulator according to the HSE06 results. As shown in Figure 5, when TiO, HfO, and TaO adopt the B1 structures, they exhibit metallic behavior, and their DOS profiles are quite similar. With the filling of d orbitals from Ti (Hf) to Ta, the position of the Fermi Level moves upward to accommodate more d electrons. In contrast to the rather smooth DOS curve near the Fermi level in the B1 structures, DOS of the predicted geometries show many peaks near the Fermi level, which indicate the localization of the electrons. For P1̅ type TaO, the number of the states on the Fermi level is reduced to 0. For TiO with P6̅2M symmetry, the density of electronic states near the Fermi D

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The abrupt variation of the distance between the nearestneighboring Ti atoms is found to be associated with this structure/property transition.3535

4. CONCLUSIONS To summarize, in the present study, the very basic ground state issue of early transition metal monoxides (TM−MO, TM = Ti, Hf, V, Ta) is revisited. It is found that the generally accepted rock-salt (B1) structures for these monoxides are dynamically unstable and that the imaginary phonon modes correspond to the collective displacements of metallic atoms as well as oxygen. By structural searching using the evolution algorithm and comparison with known structures for monoxides, more stable structures for these TM−MOs are found, which are also dynamically stable. The predicted symmetries are P6̅2M for TiO, I41/AMD for HfO, and P1̅ for TaO. DOS profiles show that the electrons in these predicted structures are more localized compared to those in B1. For VO, AFM behavior is found for both B1 and the predicted P1̅ structure, according to the hybrid functional calculations. The magnetic ordering induces the relaxation of B1 structure and the symmetry is reduced to R3̅M, indicating the strong spin−lattice coupling in VO. It is found that, in the predicted structures for TM−MOs, ionic bonding between TM and oxygen is weaker than that in B1, according to the Bader charge analysis. It is noticed that the metal−metal bonding strength, reflected by the atomic distance between metallic atoms, dominates the stabilization mechanism for these predicted structures. Overall, this study shows that for the early TM−MOs, even without complicated physical phenomena such as the Jahn−Teller effects, simple interaction between metallic atoms can also lead to the distortion of the high-symmetry structures and formation of other geometries with different ion-packing patterns. These findings expand the knowledge of transition metal oxides that have important positions in the community of condensed matter and materials science.

Figure 6. Distance between the nearest-neighbor metallic atoms in the oxides. Square and circle represent the data for the B1 structure and the predicted structure, while the solid and empty symbols are the results based on the PBE and HSE calculations, respectively. For VO, B1 structure is reduced to R3̅M with AFM behavior after full relaxation.

distance between P1̅ and B1 at the HSE06 level becomes much smaller even though the value for B1 is a little larger. Again, the close relationship between the metal−metal distance and the stability of the structure is confirmed. Up to now, it can be inferred that the small metal−metal distance, which is closely related to the metallic interactions, can lead to the stability of the structure. Therefore, the interaction between neighboring metallic atoms may account for the stability of the phases in these early TM−MOs. To give a direct picture of the strengthened metallic bonding in the predicted phases, electron localization function (ELF) is calculated. ELF is a measure of the probability of finding an electron in the neighboring space of reference electron located at a given point, originally defined by Becke and Edgecombe in 1990.33 The value of ELF is in the range of [0, 1]. The upper limit ELF = 1 corresponds to perfect electron localization, and the value of 0.5 indicates the electrongas-like behavior, which is normally used to represent the existence of metallic bonding.34 As shown in Figure 7, here for

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b02871. Atomic structures of the oxides and some simulated XRD patterns (PDF)

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Figure 7. Contour plots of calculated electron localization function (ELF) for TiO. (a) B1 symmetry, (011) plane, and (b) P6̅2M symmetry, (110) plane. Positions of Ti and O are labeled.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +86-(0)10-82317747. Notes

a clear presentation, TiO whose two polymorphs are both with quite high symmetry is used as the example. As seen in Figure 7, in the predicted phase where Ti atoms have smaller coordination number and shortened distance in-between, the metallic bonding among these cations (ELF = 0.5) is more significant than that in the B1 structure. In fact, in addition to the monoxides studied here, the significant impact of the metal−metal bonding on the stable atomic geometry also exists in other low-oxidation-state oxides of the early transition metal.5 For example, in Ti2O3, the weakening in Ti−Ti bonding is believed to be responsible for the anomalous lattice parameter change at high temperatures, which is accompanied by a semiconductor to metal transition.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is partially supported by National Natural Science Foundation for Distinguished Young Scientists of China (51225205) and the National Natural Science Foundation of China (61274005, 51401009).

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DOI: 10.1021/acs.jpcc.6b02871 J. Phys. Chem. C XXXX, XXX, XXX−XXX