Half-metallic electronic feature and thermophysical properties of the Ba2CoMoO6 perovskite-like cobalt molybdate

1. Introduction

Perovskite-like ceramics with ideal formula ABX3, wherein A represents alkaline earth and rare earth elements, B is a transition element cation and X is an anion, usually oxygen, evidence numerous physical properties which are particularly sensitive to inhomogeneities like distortions from their ideal cubic structure, vacancies and chemical substitutions [1]. One of these anomalies, which raises the complex perovskite with A2BB’O6 formula, results from the ordering of B and B’ cations on the octahedral site of the primitive perovskite unit cell.

The importance of complex perovskites is in the possibility of creating new magnetic materials A2BB’O6, with B and B’ constituted by magnetic 3d cations. Recently, the study of these materials has increased due to the possibility of applying them in the design and technology of magnetic devices for applications in high capacity magnetic information storage devices and RAM memories [2-3], prototypes for the transport of polarized currents [4], hard magnets [5], magnetic sensors [6], systems based on magnetic nanoparticles [7], among others. Likewise, during the last years, the calculations of first principles based on the Functional Theory of Density (DFT) have become a usual and very precise method for the theoretical prediction of diverse properties of perovskite-type materials, such as the crystallographic structure, electric transport mechanisms (considering the polarization of spin) and the distribution of valence electrons around the Fermi level that allow characterizing the material as an insulator, semiconductor, conductor or half-metallic.

In addition, this type of calculation allows establishing the contribution of the different electronic orbitals to the magnetic and electrical properties, as well as the eventual ferroelectric response of the materials [8]. On the other hand, theoretical simulations have proved to be a very interesting method for the prediction of thermodynamic properties at high pressure, as a function of temperature, for perovskite-like materials [9]. This is possible because the macroscopic thermodynamic properties are strongly correlated with the microscopic dynamics of the atoms of the material. Thus, the collective vibrations of crystalline networks in solids take place in discrete packets of energy, or energy quanta, known as phonons.

This kind of fundamental excitations in solids, as well as the electrons, is responsible for the thermodynamic properties of materials. The most relevant role of phonons occurs for insulators and semiconductors, where they contribute directly to properties such as specific heat and thermal expansion, as well as their dependence on temperature. When speaking of phonons, it is assumed that the crystal vibrations are of harmonic character, which can be considered valid at low temperatures, more specifically below the Debye temperature of the solid. For this reason, theoretical methods are used as a complementary tool that allows the study of atomic dynamics at high temperatures, facilitating the calculation of the thermodynamic properties of materials, through approximations such as the quasi-harmonic Debye model [10].

The results obtained through this method have been surprisingly close to the experimental values reported for some specific materials [11]. The growing interest for the double perovskite materials based on Co and Mo has to do with the tuning of the physical characteristics from its composition and the type of hybridizations of the electronic orbitals 3d and 4d, from which they can be generated properties that suggest its applicability in spintronics [12] and solid oxide fuel cells [13], among other modern technology devices.

From experimental results of the structural, electrical and magnetic behavior of the Ba₂CoMoO₆ double perovskite were reported [14] and the authors claim that this material crystallizes in a cubic structure, belonging to the Fm3̅. (#125) space group. DFT calculations in this material with spin polarization revealed a conductor behavior for both up and down spin orientations when calculated by considering exchange and correlation potentials within the GGA and LSDA approximations [15].

In this work theoretical results of the structural and electronic characteristics of the double perovskite Ba₂CoMoO₆ are reported, which have been made in the search of information that allows to infer the mechanisms responsible for the magnetic and transport properties of this material, through the analysis of the crystallographic parameters, the band structure, the density of electronic states, and the behavior of the specific heat, the thermal expansion, the Debye temperature and the Grüneisen parameter as functions of temperature and pressure.

2. Calculation method

It was used the Wien2k [16] within the framework of the Kohn-Sham Density Functional Theory (DFT) [17], applying the Full-Potential Linear Augmented Plane Wave method (FP-LAPW) and adopting the Generalized Gradient Approximation (GGA) for the exchange-correlation energy due to Perdew, Burke y Ernzerhof and also the Local Density Approximation (LDA) [18].

The self-consistent process in the numeric package Wien2k allows the total energy calculation for constituent elements and alloys.

Taking the experimental unit cell data as input, all the structures studied in this work were fully relaxed with respect to their lattice parameters and the internal degrees of freedom compatible with the space group symmetry of the crystal structure. The resulting energies versus volume functions have been fitted to the equation of state due to Murnaghan [19] in order to obtain de minimum energy value, the bulk modulus, its pressure derivative and the equilibrium lattice parameters and associated volume.

The muffin-tin radius of the elements was 2.4, 1.8, 1.8 and 1.8 (in au) Ba, Co, Mo and O respectfully, angular momentum up to l = 10 inside the muffin-tin sphere, a maximum vector in the reciprocal space of Gmáx =12.0, RMKAX=7, and a mesh of 1500 points in the first Brillouin zone (equivalent to a maximum of 56 k points in the irreducible Brillouin zone). Finally, the convergence criteria for the self-consistent calculation were 0.0001 Ry for the total energies, 0.0005 u.a in the charge and 1.0 mRy/u.a. in the internal forces. Spin polarization was included in the calculations. The quasi- harmonic Debye model is applied in order to calculate the thermophysical properties of the material as a function of temperature, such as the specific heat at constant volume and pressure, the thermal expansion of the crystal, the Debye temperature and the Grüneisen parameter [20].

3. Results and discussion

A preliminary approach to the structure of a perovskite- type material can be made from the SPuDS structure prediction diagnostic software [21], which has been designed for this family of materials. Using this tool, it is possible to establish an approximate value of the network parameters of the crystal, which for this case was carried out considering the Fm3̅. (#225) space group. Then, using the code PowderCell (PCW) [22], the respective diffraction pattern was theoretically generated. The obtained picture, which is presented in figure 1, shows the characteristics of a perfect complex cubic structure.

The ideal double cubic perovskite A2BB'O6 is characterized by the formation of a superstructure in which the cations B and B' are organized alternately along the crystallographic axes, coordinated with six oxygens that define the octahedral distribution of the structure. The presence of the superstructure can be determined by X-ray diffraction through the occurrence in the diffractogram of reflection peaks with indexes (311), (331), (511) and (531), which are observable in the theoretical diffraction pattern of figure 1.

In the superstructure, the positions occupied by B and B' are not equivalent and for this reason the reflection lines mentioned above appear in the diffraction pattern [23]. In the case of the double cubic perovskite with formula A2BB'O6, when all the atoms are located in the ideal position, the intensity of the peaks, particularly of (111), is proportional to the difference in the scattering power of the atoms B and B' [24]. If the cations B and B 'were located randomly in the structure, the peaks (111), (311), (331), (511) and (531) would have zero intensity, that is, they would not appear in the diffractogram. In that Ba2CoMoO6 material, the order of the Co²⁺ and Mo⁶⁺ cations in positions B and B' can be clearly distinguished through the occurrence of the peaks mentioned above, whose intensities are significant.

The cell constant of Ba₂CoMoO₆, calculated from the simulation is a=7.8121 Å, which corresponds to 96.6% of the experimentally reported [14]. Figure 2 shows the ideal structure expected for this material. In the picture it is observed the Co²⁺ and Mo⁶⁺ cations adopt octahedral correlations with its nearest neighbors, consisting of O^2- anions. It is observed in figure 2, that the octahedra with Co²⁺ and Mo⁶⁺ are perfectly interspersed throughout the crystallographic structure, generating a salt-rock superstructure, according to the Miller planes.

Figure 3 illustrates the energy as a function of volume. Each one of the squared points constitutes an individual calculation and the line corresponds to a fitting with the Murnaghan state equation, which was carried out by using the concept of the least-square fitting method [25]. The minimum of the energy is obtained for - 44347.453444 Ry, the volume modulus Bo = 129.7 GPa, and the equilibrium volume is 485.358 ų . This value is close to that predicted from the SPuDS, which is 476.764 Å^{3 .} From the minimization of energy as a function of the volume of figure 3 within the GGA approximation it was calculatedthe lattice parameter Bo=7.8587 Å, which corresponds to 0.5% above the value predicted by the SPuDS. On the other hand, when the LDA approximation is used the equilibrium volume is 387.8990 ų , which corresponds to a lattice parameter of a=7.293 Å, that turns out to be 7.0% different from the SPuDS prediction. This result is not uncommon considering that the application of LDA usually leads to an underestimation of the crystal lattice constants with respect to the GGA application, where the bulk lattice constants increase due to the presence of a more repulsive core-valence exchange [26]. In table 1 comparison between the atomic positions for the different theoretical procedures is showed.

Band structure calculations along high symmetry directions of the first Brillouin zone for the Ba2CoMoO6 double perovskite are presented in figure 4 for the up and down spin configurations. In the picture, the energy of electrons as a function of wave vector k, along W-L- Λ-Γ-D-X-W directions is observed. From this figure, it is possible to infer that the Ba2CoMoO6 material evidences a conductive character for a spin channel and an insulating nature for the other spin orientation, with a strong contribution of the 3d orbital of the Co cations in the valence band close to the Fermi level.

Partial DOS for Ba, Co, Mo and O atoms are presented in figure 5 for the up and down spin channels. It is observed in the pictures (figures 4 and 5) that the band structure is non-symmetrical around the Fermi level, which implies that there exists an effective magnetic moment. It was qualitatively determined orbitals Co.3d (t₂g) are directly responsible for this response and the value of the effective magnetic moment was found to be 3.0 m.. The most relevant observation is relative to the exotic property of half-metallicity, which is characterized by the differentiated conducting response of the spin up and spin down orientations, and an integer value of the effective magnetic moment. The density of states as a function of energy clearly evidences that the majority spin component shows an energy gap at the Fermi level, as the insulating materials, and the other spin orientation is continuous at the Fermi level, due to the strong hybridization of Co.3d (t₂g) and O-2p states. On the other hand, it is observed that the crystalline field evidences a splitting between t₂g and eg levels of Co-3d.

Exchange splitting between t_2g up and t_2g down, and between eg up and eg down are also observed. In general, the contribution of t_2g states to DOS is significantly longer than eg states for both spin orientations. In figure 5, it was clearly observed the superposition of partial density of states for localized Mo d-t_2g and delocalized Mo d-eg levels, which characterize the splitting of crystalline field between t_2g and eg states, and exchange splitting between t_2g up and t2g down levels, and between e_g up and eg down states.

Figure 5 describes the exchange and crystalline field splitting behaviors of Co.3d and Mo.4d levels, respectively, for the Ba₂CoMoO₆ compound. This result can be summarized by means of the qualitative scheme of figure 6, through the well-known Sarma model [27].

The left part of the figure describes the Co-3d states, where it is observed a strong exchange splitting between up and down spin configurations for both e_g and t_2g electronic states. Meanwhile, the splitting of the crystalline field is not as strong as the exchange splitting. On the other hand, Mo-4d levels are described on the right side of this diagram. It is interesting to note that states e_g show energy values that are higher than those observed for the states of the Co. In addition, in the case of Mo, the exchange splitting cannot be observed because of the superposition between its t_2g levels for the spin down configuration, while the crystalline field is significantly large. A clear scheme related to the hopping interactions, which are considered responsible for the hybridization of the Co-3d and Mo- 4d states, can be consulted in C.M. Bonilla et al [28].

A fact of significant relevance is that the delocalized Co-t_2g states for the spin-up orientations are located below the Fermi level, while the t_2g states for the spin- down configuration are closer to the Fermi level. In this way, the shift of the spin-up and spin-down states induces a spin polarization of the mobile electrons due to the hopping interactions between the localized electrons and the conduction states. On the other hand, for both spin up and spin-down orientations, the eg states are strongly pulled down as a result of the hybridization, but these remain above the Fermi level.

In order to study the thermophysical properties of Ba₂CoMoO₆, this was considered that variations in pressure modify the thermodynamic response of materials. For this purpose, these properties were calculated as a function of temperature, under the application of several pressure values up to 35 GPa, using as a starting point the state equation, and following the quasi-harmonic approximation of the Debye model. [29]. In figure 7, the results of the specific heat at constant volume (figure 7(a)) and at constant pressure (figure 7(b)) as a function of the temperature up to T=1500 K and under the application of pressures up to 35 GPa are exemplified. In these figures, it is possible to observe that the two curves show very similar behaviors in the low-temperature regime (up to 400 K) for all the applied pressure values. It is clear from figure 7(a) that the specific heat at constant volume tends strongly to adopt a value independent of temperature (for very high-temperature values), in the regime known as the Dulong-Petit limit. This characteristic is observed for all applied pressure (up to 35 GPa) with a value for the Dulong-Petit limit of 246.3 J/mol.K. On the other hand, figure 7(b) reveals that this tendency is not universal for the case of specific heat at constant pressure. This occurs because at high temperatures it is expected that the quasi- harmonic model of Debye will fail, so that the divergences presented in figure 7(b) would not essentially constitute a response of the material [10]. Meanwhile, under the application of relatively low pressures (less than 20 GPa) a certain tendency towards a Dulong-Petit limit between 263.1 J/mol.K and 274.4 J/mol.K can be established.

These values agree with those reported for other double perovskites belonging to highly symmetric space groups [20]. Likewise, the predominance of a purely electronic response in specific heat is expected at low temperatures, while at high temperatures the phonics response should be predominant. The results of density of states and structure of bands presented in figures 4 and 5 reveal the majority presence of Co-3d-t_2g and minority orbitals 4d-Mo-t_2g and 2p-O in the vicinity of the Fermi level, which supplies the most relevant electronic contributions to the specific heat. On the other hand, the contribution due to the 6s-Baorbitals is very incipient. In view of the foregoing, as the temperature of the material increases, the vibration of the cations and anions around their equilibrium positions, which results from the absorption of heat, makes an additional contribution to the total specific heat. In the case of the actual compound Ba₂CoMoO₆, some variations in the results may take place because of the polycrystalline character of this material, so that the specific heat must have dependencies of the porosity. This inference is made here because it is expected that the thermal energy needed to increase the temperature in denser materials is higher than in the more porous ones [30].

The Debye temperature as a function of temperature, Q _D(T), was calculated for different pressure values (up to 35 GPa) as shown in figure 8(a). It is observed in the figure, that an increase in pressure produces a gradual increase in the elastic waves of the system, resulting in an increase in the temperature of Debye. The observed Debye temperature at T=0 K is in the range between 494.4 K for P=0 GPa and 693.3 K for P=35 GPa. In the same way, Q _D(T) evidences a continuous non-linear decreasing behavior with the increase in temperature for all applied pressures, reaching values ranging from 424.8 K for P=0 GPa to 660.5 K for P=35 GPa (at T=1500 K). A decrease of this type in Q _D(T) with the increase in temperature, accompanied by an increase with the growth of pressure has been reported for materials of double perovskite-type. [31].

The Debye temperature is understood as the highest value of temperature that can be obtained for a single normal vibration, for which it is possible to predict that the application of the pressure on Q _D(T) produces the effect of increasing the vibration frequencies of the bonds between the cations and the oxygen, i.e., octahedral bonds Co-O₆ and Mo-O₆ , and cuboctahedral Ba-O₁₂ bonds. Therefore, the expansion of the structure due to the increase in temperature manifests itself as an increase in the wavelength of the vibrations, so that the frequency decreases, thus generating a decrease in the Debye temperature.

Figure 8(b) represents the dependence of the coefficient of thermal expansion, α(T), with the temperature under the application of different pressure values, up to 35 GPa. The picture shows a systematic decrease of α(T) when the pressure is increased. This decrease is more pronounced at high temperatures, where a change can be perceived from 6.4.10^-5.-1 to 2.3.10^-5.-1 for a temperature of T=1500 K. Likewise, it can be seen in the figure that at low temperatures, in the regime between 0 K and 200 K, the coefficient of thermal expansion increases abruptly when the temperature is increased. At T>200 K, this increase is smooth, reaching an approximately linear trend at very high temperatures. The Ba₂CoMoO₆ material has a cubic structure, with its crystallographic parameters a=b=c, so that it has a perovskite-like nature corresponding to an isometric structure, so no large differences are expected in the values of thermal expansion as along the three crystallographic directions as would be expected for the case of more anisometric materials [32].

This behavior is correlated with the typical structural distortions of perovskite-type materials, where changes in temperature and pressure cause rotations and inclinations of the CoO₆ and MoO₆ octahedra, as well as elongations or compressions in certain directions of the crystallographic cell. Thus, the results obtained for α(T) have to do with the types of distortion or structural transitions that are characteristic of the changes in temperature and pressure to which the material is subject. Therefore, it is expected that there will be possible differences between the theoretical results presented in Figure 8b and the real experimental response that could be measured in the laboratory. The very low value of the coefficient of thermal expansion for this material suggests that it can be applied at low temperatures as material for fuel cell anodes [33].

The calculations carried out have not considered that the increase in temperature can give rise to structural phase transitions and that these transitions modify the response of the thermophysical properties under study. In figure 8(c) the Grüneisen parameter decreases gradually with the increase in applied pressure (from 2.10 for P=0 GPa to 1.80 for P = 35 GPa, at T = 0 K). This behavior is observed for all temperatures that were considered in the calculations. In the meantime, it is also possible to see a continuous, smooth and non-linear growth of the Grüneisen parameter when the temperature is increased. At last, it can be stated that the behavior of the Grüneisen parameter as a function of temperature and pressure is a consequence of the variations produced in the vibration frequencies of the crystalline lattice, as previously discussed [34].

4. Conclusions

It has performed several ab initiocalculations over the Ba₂CoMoO₆ double perovskite. Results show that it has an insulator behavior for the spin-up orientation and conductor for the spin-down configuration, as expected for half-metallic materials. Analysis of electronic structure for Ba₂CoMoO₆ for both spin orientations permitted to infer that the t_2g spin-down states are responsible for the conductivity feature for both Co-3d and Mo-4d states. On the other hand, the insulating behavior of the spin-up configuration can be attributed to the e_g states. Additionally, it was correlated the results with the recent model propose to explain the conduction mechanism in this kind of compound by considering the Mechanism of Sarmafor the magnetic interactions responsible for the magnetism on the Ba₂CoMoO₆ double perovskites.

Another evidence of the half-metallicity is related to the integer value (in Bohr magneton) of the effective magnetic moment, which was determined to be 3.0 mB. It also has calculated the cell dimensions that minimize the total energy for each configuration using the Murnaghan equation state. The results of calculations of thermophysical properties through the application of the state equation, within the framework of the quasi- harmonic approximation of the Debye model, reveal that interatomic vibrations generate a small decrease in specific heat as a function of the applied pressure, with a tendency to the limit of Dulong-Petit, that presents values of the characteristic order of the highly symmetric double perovskites. Additionally, it can be concluded that at temperatures lower than 400 K, the specific heats at constant volume and at constant pressure are very similar, which is justified by the low value of the coefficient of thermal expansion. On the other hand, the temperature of Debye increases with the increase in pressure and decreases with the increase in temperature. Conversely, both the coefficient of thermal expansion and the Grüneisen parameter decrease with pressure and increase slightly as a function of temperature.

In general, the behavior observed in thermodynamic properties is characteristic of double perovskite-type materials. It is important to note that the thermophysical properties depend strongly on the value of the Grüneisen parameter, since it is obtained from a third derivative of the state equation, which is why it is very sensitive to both the numerical errors in the derivation and the softness of the resulting curves. For this reason, the experimental measurement of these properties is very interesting to establish in a more objective way the microscopic mechanisms that originate them.

The scientific relevance of the current work, both in Colombia and in the world, takes place because the study of the electronic properties of this type of new materials allows to expand the general knowledge in science of new materials, suggesting the perspective of experimental investigations that contribute to the formation of highly qualified human resources that corroborates the theoretical predictions made here, also making possible the potential of their possible technological applications in spintronic devices.

Acknowledgments

This work was partially financed by FONCIENCIAS, University of Magdalena and Departamento Administrativo de Ciencia y Tecnología Francisco José de Caldas – COLCIENCIAS, on the project FP80740- 243-2019. One of us (J.I. Villa Hernández) received support by Departamento Administrativo de Ciencia y Tecnología “Francisco José de Caldas”, COLCIENCIAS, on the scholarship program for national doctorates.

References

Author notes

3 Grupo de Estudio de Materiales y Dispositivos Electrónicos (GEMyDE), Universidad Nacional de La Plata, Argentina.

Additional information

How to cite: C.E. Deluque Toro, A.V. Gil Rebaza, J.I. Villa Hernández, D.A. Landínez Téllez, J. Roa-Rojas, “Half-metallic electronic feature and thermophysical properties of the Ba2CoMoO6 perovskite-like cobalt molybdate,” Rev. UIS Ing., vol. 19, no. 1, pp. 213-224, 2020. doi: 10.18273/revuin.v19n1-2020020

Revista UIS Ingenierías
ISSN: 1657-4583
Vol. 19
Num. 1
Año. 2020

Half-metallic electronic feature and thermophysical properties of the Ba2CoMoO6 perovskite-like cobalt molybdate

Críspulo E.Arles V.Jorge I.David A.Jairo Deluque-ToroGil-RebazaVilla-HernándezLandínez-TéllezRoa-Rojas
Universidad del MagdalenaUNLPUniversidad Nacional de ColombiaUniversidad Nacional de ColombiaUniversidad Nacional de Colombia,ColombiaArgentinaColombiaColombiaColombia