First principles calculations to investigate structural electronic half metallic and thermodynamic properties of hexagonal ux2o6 x¼cr v compounds

Journal of Science: Advanced Materials and Devices (2019) 319e326 Contents lists available at ScienceDirect Journal of Science: Advanced Materials and Devices journal homepage: www.elsevier.com/locate/jsamd Original Article First-principles calculations to investigate structural, electronic, half-metallic and thermodynamic properties of hexagonal UX2O6 (X¼Cr,V) compounds Saadi Berri a, b, * a b Laboratory for Developing New Materials and Their Characterizations, University of Setif 1, Algeria Department of Physics, Faculty of Science, University of M'sila, Algeria a r t i c l e i n f o a b s t r a c t Article history: Received 12 April 2019 Received in revised form 18 May 2019 Accepted 26 May 2019 Available online June 2019 Full potential linearized augmented plane wave plus local orbital's (FP-LAPW ỵ LO) method within density functional theory (DFT) is used to investigate the structural, electronic and half-metallic properties of hexagonal UX2O6 (X ¼ Cr,V) Features such as the lattice constant (a and c), bulk modulus and its pressure derivative are reported The calculated lattice parameters are in good agreement with available experimental results Band structure and overall densities of states have proved UV2O6 as an indirect half-metallic material with a band gap of 2.88 eV and UCr2O6 as a magnetic semiconductor The results obtained, make the hexagonal UX2O6 a candidate material for future spintronic applications Based on the quasi-harmonic Debye model, the thermodynamic properties of the material in question have been predicted taking into account of the lattice vibrations The variation of the lattice constant, bulk modulus and heat capacity as a function of pressure in the range 0e40 GPa and temperatures of 0e1500 K is computed Our findings show that external effects are highly effective in tuning some of the macroscopic properties of the compounds under study © 2019 The Author Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) Keywords: UX2O6 (X¼Cr,V) Half-metallic Magnetic semiconductor Electronic structure Thermal properties Introduction Oxide ceramics materials of general formula AB2O6 attracted a great deal of attention followed by the discovery of exotic properties such as microwave dielectric properties of AB2O6 (e.g., A ¼ Ca, Mg, Mn, Co, Ni, Zn, and B]Nb, Ta) [1], superconductivity (e.g., KOs2O6) [2], antiferromagnet (e.g., CuTa2O6) [3], an ionic solid at high temperatures (!573 K) (e.g., KTaWO6) [4], semiconductor with a narrow band gap (2.70e2.85 eV) (e.g., Bi2WO6) [5], catalyst for selective oxidation of methanol to methylal (e.g., SbRe2O6) [6], the possible vibration modes (e.g., ThTi2O6) [7], ferromagnetic (e.g., ScRe2O6) [8], electrode material in lithium ion batteries (e.g., CdV2O6) [9], magnetic (e.g., PdAs2O6) [10], high-performance supercapacitors (e.g., MnNb2O6) [11], suitable hosts for redemitting phosphors (e.g., Te R2O6 (R ¼ La, Gd)) [12e14], superior electrochemical performances (e.g., ZnSb2O6) [15] * Laboratory for Developing New Materials and Their Characterizations, University of Setif 1, Algeria E-mail address: berrisaadi12@yahoo.fr Peer review under responsibility of Vietnam National University, Hanoi Half-metallic ferromagnets represent a new class of materials which absorbed a lot of attention considering their possible applications in spintronics [16] This material has a complete (100%) spin polarization at the Fermi level because one spin channel is metallic while the other channel is semiconducting Various halfmetallic ferromagnetisms have been predicted by the firstprinciples calculations or experimentally synthesized, such as double perovskites (for example, Sr2GdReO6 [17,18] and Ba2NiUO6 [19]); zinc blende (ZB) CaC and CaN compounds [20]; Suzuki-type compounds Li6TMCl8 [21]; perovskite XAlO3 (X ¼ Cs, Rb and K) [22]; quaternary Heusler compounds (for example, PtZrTiAl, PdZrTiAl, CoMnCrSb, and Ti2RhSn1-xSix) [23e25]; CrO2 [26] and gU3O8 [27] Z Ali et al [28] studied the electronic and magnetic properties of BaUO3using GGA ỵ U from which they found that it is a half-metal with a ferromagnetic behavior Meantime, theoretical studies based on density functional theory have been conducted to predict the properties including phase stability, electronic structure and Half-Metallic properties [29e35] In this paper, we investigated the structural, electronic, halfmetallic and thermodynamic properties of UV2O6 and UCr2O6 compound using the first principle methods The remaining of the paper is organized as follows: The theoretical background is https://doi.org/10.1016/j.jsamd.2019.05.002 2468-2179/© 2019 The Author Publishing services by Elsevier B.V on behalf of Vietnam National University, Hanoi This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) 320 S Berri / Journal of Science: Advanced Materials and Devices (2019) 319e326 described in Section Results are presented and discussed in Section A summary of the results is given in Method of calculations As mentioned already, we have considered the experimental crystal parameters as reported by Kovba [36], Hoekstra and Siegel [37] UX2O6 (X ¼ V, Cr) compounds crystallize in the hexagonal space group P-31m (No.162), Z ¼ The crystal structures of UX2O6 (X ¼ V, Cr) compounds is shown in Fig The present computations are performed through the FP-LAPW ỵ LO method using DFT as implemented in WIEN2K code [38] In the study of structural properties, the exchange correlation energy is treated within the GGA as parameterized by Perdew, Burk and Emzerhop Perdew (PBE)-GGA method [39] The threshold energy between valence and core states is set to be À6.0 Ry Here, the KohneSham equations are solved by expanding the wave functions in the spherical harmonics form inside the atom spheres A plane wave expansion has been used in the interstitial regions of atoms inside the unit cell We have used lmax ¼ 10 for angular momentum expansion and RMTKmax ¼ as a plane wave cut-off with 1400 k points for hexagonal phase Here RMT is the average muffin-tin (MT) radius and Kmax is the wave function cut-off The radii RMT of the muffin tins (MT) are chosen to be approximately proportional to the corresponding ionic radii The energy between successive iterations is converged to 0.0001 Ry and forces are minimized to mRy BohrÀ1 The 5f(U) and 3d (V and Cr) was treated using the GGA ỵ U approach [40] The GGA þ U calculations used an effective parameter Ueff ¼ U þ J, where U is the Hubbard parameter and J is the exchange parameter As a matter of fact, the use of the Hubbard parameter (GGA ỵ U) approaches so as to treat the exchangecorrelation potential is very efficient for studying strongly correlated electrons where the energy band gap of the material of interest can be evaluated more accurately In these cases, the core electrons are taken to be relativistic whereas the valence electrons are considered to be as semi-relativistic This is probably best suited for our system and for a full potential method The Ueff is taken to be 5.01 eV and 4.97 eV for U(5f) and X(3d) atoms similarly to Refs [41,42], respectively To investigate the thermodynamic properties of hexagonal UX2O6 (X ¼ V, Cr) compounds we apply the quasi-harmonic Debye model [43] In this model, the non-equilibrium Gibbs function G*(V;P,T) is expressed as follows, GÃ ðV; P; Tị ẳ EVị ỵ PV ỵ AVibẵqVị; T (1) where E(V) is the total energy per unit cell, PV corresponds to the constant hydrostatic pressure condition, qðVÞ is the Debye temperature, and Avib is a vibrational term that can be written using the Debye model of the phonon density of states as [44], Avib q; Tị ẳ nkT    9q ỵ ln eq=T Dq=Tị 8T  (2) where n is the number of atoms per formula unit and Dðq=TÞ is the Debye integral For an isotropic solid, q is given as [45], h i1=3 qD ẳ Z 6p2 V 1=2 n f rị s BS Mk2B (3) where M is the molecular mass per unit cell and BS is the adiabatic bulk modulus The latter is approximated by the static compressibility as, BS y BVị ẳ V d2 EVị dV (4) f rị in Eq (3) is reported in Refs [46] The Poisson ratio n is taken to be 0.25 [47] Thus, the non-equilibrium Gibbs function G*(V;P,T) versus (V; P, T) is minimized with respect to the volume V as,   * vG V; P; Tị ẳ0 vV P;T Fig Crystal structure for UX2O6 Fig Calculated normalized energy as a function of volume for UX2O6 compound (5) S Berri / Journal of Science: Advanced Materials and Devices (2019) 319e326 321 Table Lattice constant a (Å), c (Å), bulk modulus B (in GPa), and first-pressure derivative of bulk modulus B0 for UX2O6 compounds Compounds Method UV2O6 GGA EXP [36] GGA EXP [37] GGA [50] UCr2O6 CaTa2O6 Point group P-31m P-31m P-31m P-31m Pm3m Pnma a(Å) b(Å) c(Å) B (GPa) B0 5.00 4.988 5.06 4.988 3.8024 11.068 5.00 4.988 5.06 4.988 3.8024 7.505 4.78 4.768 4.96 4.620 3.8024 5.378 213.8177 e 212.8447 e 145.256 288 4.3805 e 4.3221 e e e By solving Eq (5), one can obtain the thermal equation-of state (EOS) V(P,T) The heat capacity CV and the thermal expansion coefficient a are given by [48],     q 3q=T À q=T CV ¼ 3nk 4D T À1 e (6)  i h q À ln À eÀq=T S ¼ nk 4D T (7) a¼ gC V BT V (8) } neisen parameter, which is defined as, where g is the Gru g¼ À d ln qðVÞ d ln V (9) Through the quasi-harmonic Debye model, one could calculate the thermodynamic quantities at any given temperatures and pressures of UX2O6 (X ¼ V, Cr) compounds from the obtained EeV data at T ¼ and P ¼ Results and discussion The main objective in this work is to calculate the total energy as a function of the unit-cell volume around the equilibrium cell volume V0 for UX2O6 (X ¼ V, Cr) compounds in the spin-polarization (FM state) Fig shows the total energy as a function of the unit-cell volume The equilibrium lattice constant (a and c), bulk modulus B and its first-order pressure derivative B0 have been computed using Murnaghan's equation of state (EOS) [49] The equilibrium lattice parameters (a and c), Fig The band structure of the UCr2O6 and UV2O6for the spin-up and spin-down electrons 10 10 -2 -4 -6 -2 -4 -6 -8 -8 -10 -10 -8 -6 -4 -2 Energy(eV) Total U V O UV2O6 Total densitiy of states (TDOS) Total densitiy of states (TDOS) Total U Cr O UCr2O6 -8 -6 -4 -2 Energy(eV) Fig Spin-polarized total densities of states (TDOS) for UX2O6 322 S Berri / Journal of Science: Advanced Materials and Devices (2019) 319e326 0,8 U-DX2Y U-DZ2 0,4 0,6 PDOS(States/eV/atom) PDOS(States/eV/atom) 0,6 0,2 0,0 U-f -0,2 -0,4 -0,6 0,2 0,0 -0,2 -0,4 -0,6 -0,8 -8 1,2 PDOS(States/eV/atom) O-p 0,4 -6 -4 -2 -8 -6 -4 Cr-DX2Y -2 8 Energy (eV) 0,8 Cr-DZ2 0,4 (a) 0,0 -0,4 -0,8 -1,2 -8 -6 -4 -2 Energy (eV) 0,6 0,8 0,4 0,6 PDOS(States/eV/atom) PDOS(States/eV/atom) U-DX2Y U-DZ2 0,2 0,0 -0,2 U-f -0,4 -0,6 0,2 0,0 -0,2 -0,4 -0,6 -0,8 -8 PDOS(States/eV/atom) O-p 0,4 -6 -4 -2 -8 -6 -2 V-DZ2 0,4 (b) 0,0 -0,4 -0,8 -8 -6 -4 Energy (eV) V-DX2Y 0,8 -4 -2 Energy (eV) Fig Spin-polarized partial densities of states (DOS) for (a) UCr2O6 and (b) UCr2O6 S Berri / Journal of Science: Advanced Materials and Devices (2019) 319e326 Total densitiy of states (TDOS) 15 (a) P=0 GPa UCr2O6 P=15 GPa 10 P=30 GPa -5 -10 -15 -6 -4 -2 Energy (eV) Total densitiy of states (TDOS) the bulk moduli B and their corresponding pressure derivatives B0 , along with the experimental results where available [36,37], are listed in Table The predicted values of the optimized structural parameters and their equivalent experimental ones yields excellent agreement as listed in Table To our knowledge, there are no experimental or theoretical data reported for the bulk modulus and its pressure derivative for the material of interest, and hence our results are predictions We have also included in Table the bulk modulus for CaTa2O6 [50] for comparison purpose Figs and show respectively the self-consistent scalar relativistic spin-polarized band structures and total density of states of U(V, Cr)2O6 in its Hexagonal phase The partial densities of states, in which the spin-up and spin-down sub-bands, are shown in Fig The Fermi level set as eV The band structure and density of states computed via the GGA approach are shown as a prototype given the fact that the band profiles obtained from GGA approach are quite similar to those calculated via GGA ỵ U method with a negligible difference in details Based on the lattice symmetry, the integration paths G-K-M-G-A are performed so as to treat the band structure for Hexagonal phase For the UV2O6 compound, one can observe the absence of a gap at the Fermi level for the majority-spin band, which confirms the metallic behavior found for the spin-up, while the minority spin band shows a semiconducting gap around the Fermi level Hence, in this compound the minority-spin band, the valence band maximum (VBM) is located at the G point and the conduction band minimum (CBM) is located in the K direction The half-metallic gap [17], which is determined as the minimum between the lowest energy of majority (minority) spin conduction bands with respect to the Fermi level and the absolute values of the highest energy of the majority (minority) spin valence bands, is 2.88 eV This energy gap in the minority-spin band gap leads to 100% spin polarization at the Fermi level, resulting in the half-metallic behavior at equilibrium state For the UCr2O6 compound, there is a energy band gap in both spin channel but the two gaps are not located at the same energy region and the Fermi Note that, there is a difference in the band structure plot for the two spin channel For the majority-spin band, both the valence band maximum (VBM) and the conduction band minimum (CBM) occur at the high-symmetry point K in the Brillouin zone Hence, the material being studied here is a direct bandgap semiconductor However, as far as the minority-spin channel is concerned, the VBM occurs at G point and the CBM is located at the K point Therefore, the material in question is an indirect band-gap semiconductor Fig illustrates the total density of states of UX2O6 in the hexagonal (P-31m) structure at three different pressures (0.0, 15.0 and 30.0 GPa) Table presents our obtained energy band gap values for UX2O6 compound calculated using PBE-GGA approache at various pressures, namely 0.0, 15.0 and 30.0 GPa Accordingly, one can see that the energy band gap increases with increasing pressure For the UV2O6 compound, one can note a preserved half-metallic nature in the stress range of 0.0 GPa up to 30.0 GPa The nature of the electronic band structure has been elucidated by calculating the total and partial densities of states (DOS) of UX2O6 compound for an energy range ranging from À8 to eV (see Fig 5) At low energies and in particular in the core states the main contribution is due to O-p state; the second part which is beyond the Fermi level, where the contribution is due to X DX2Y and X DZ2 states The conduction band is above the Fermi level This bond is essentially composed of U DX2Y and U DZ2 orbitals hybridization with U 5f states 323 15 (b) P=0 GPa UV2O6 P=15 GPa 10 P=30 GPa -5 -10 -15 -6 -4 -2 Energy (eV) Fig Spin-polarized total densities of states (TDOS) for (a) UCr2O6 and (b) UCr2O6 at various pressures Normally, exchange interactions are very short-ranged, confined to electrons in orbitals on the same atom or nearest neighbor atoms but longer-ranged interactions can occur via intermediary atoms and this is termed superexchange The double-exchange mechanism is a type of a magnetic exchange that may arise between ions in different oxidation states First proposed by Clarence Zener [51] and later developed by Anderson Table Calculated static constants and energy band gap for UX2O6 compounds at different pressures Compounds UV2O6 UCr2O6 Up ([) Down (Y) Up ([) Down (Y) 0.0 GPa 15.0 GPa 30.0 GPa e 2.88 0.54 2.12 e 2.97 0.56 2.19 e 3.03 0.69 2.28 Table Individual and net magnetic moments (mB) of UX2O6 (A ¼ Cr, Mo) from GGA and GGA ỵ U method UV2O6 UCr2O6 Method mCr/V mU mo minterstitial mTotal GGA GGA ỵ U GGA GGA ỵ U 1.20023 1.19956 2.49963 2.49884 1.16116 1.16366 0.37332 0.37552 À0.01953 À0.02038 À0.00794 À0.00800 0.59170 0.59209 0.66150 0.66269 4.00 4.00 6.00 6.00 324 S Berri / Journal of Science: Advanced Materials and Devices (2019) 319e326 and Hasegawa [52], is generally agreed to provide a description of the FM ground state this theory predicts the relative ease with which an electron may be exchanged between two species Electronic structures from a full-potential linearized augmented plane wave method also demonstrated that the half-metallic character is not caused by direct U-U or X-X interactions but by indirect OeXeOeU ped and pef couplings, which are simultaneously responsible for their ferrimagnetic character [53] The calculated total and atom-resolved magnetic moments of UCr2O6 and UV2O6 in the GGA and GGA ỵ U methods are summarized in Table The total magnetic moments per unit cell of 6.00 and 4.00 mB for UCr2O6 and UV2O6 compound are close to an integer which agrees with the half metallicity of these materials The main source of magnetization in these compounds is thus the unfilled U (5f), Cr and V (3d) states and small contributions from the interstitial region, whereas the moments of the Oxygen are small Our results for magnetic moment for uranium atoms which is in agreement with previous studies [27] The magnetic moments of the Cr and V atoms are in agreement with theoretical data [54] In this computational work, to investigate the thermodynamic properties of UCr2O6 and UV2O6 compounds under high temperature and high pressure, we apply the quasi-harmonic Debye approximation As a first step, a set of total energy calculation versus primitive cell volume (EeV) was carried out, in the static approximation The results are then fitted with a numerical EOS in order to determine its structural parameters at P ¼ and T ¼ 0, and to derive the macroscopic properties as a function of pressure and temperatures from standard thermodynamic relations The diagrams that represent the volume unit cell-temperature at various pressures and lattice constant-pressure at different temperatures for UCr2O6 and UV2O6 compounds being studied here are shown in Fig Note that for a given pressure, the volume unite cell increases monotonically with raising temperature Nevertheless, the rate of increase seems to be very moderate On the other hand, for a given temperature, the volumes unite cell decreases with increasing pressure In the present work, our calculated volumes for UCr2O6 and UV2O6 compounds at zero pressure and room temperature is found to be 704.04 and 703.54 (u.a.)3, respectively In Fig 8, the relationships between bulk modulus (B) and temperatures (T) are all nearly linear at various pressures from to 40 GPa One can notice that the bulk modulus is an important parameter to define its resistance to volume change under compression The bulk modulus decreases monotonically and very moderately when the temperature increases At room temperature and zero pressure, the bulk modulus for UCr2O6 and UV2O6 compound is 843.61 GPa and 849.29 GPa, respectively Fig Temperature dependence of the volume at various pressures Fig Temperature dependence of the Bulk modulus B at various pressures S Berri / Journal of Science: Advanced Materials and Devices (2019) 319e326 325 Fig Variation of the heat capacities Cv with temperature at various pressures The evolution of the heat capacity at a constant volume CV as a function of temperature at various pressures ranging from to 40 GPa is displayed in Fig Note that CV increases with raising temperature The behavior appears to be rapid at low temperatures but becomes slow at high temperatures For temperatures less than 1100 K, CV depends on both temperature and pressure At high temperatures, CV approaches approximately 215.40 and 215.96 J molÀ1 KÀ1 for UCr2O6 and UV2O6 compounds, respectively The details in this change seem to depend on pressure The behavior of CV for all compounds of interest exhibits similar features in a wide range of pressures and temperatures At zero pressure and a temperature of room temperature, our findings yielded values of CV of about 108.62 and 108.08 J molÀ1 KÀ1 for UCr2O6 and UV2O6 compounds, respectively Conclusion In conclusion, first-principle calculations have been performed using WIEN2K with GGA and GGA ỵ U exchange correlation to investigate the structural, electronic and half-metallic properties of the hexagonal UX2O6 (X ¼ Cr,V) under different pressures It was found that the UV2O6 is an indirect half-metallic material with a band gap of 2.88 eV, whereas the UCr2O6 is a magnetic semiconductor The half metallicity is attributed by the doubleexchange interaction mechanism via the U(f)eO(p)eX(d)-p bounding The results obtained, make the hexagonal UX2O6 a candidate material for future spintronic applications This 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