Electronic structure and magnetic properties of co2taal from ab initio calculations

Journal of Science: Advanced Materials and Devices (2016) 286e289 Contents lists available at ScienceDirect Journal of Science: Advanced Materials and Devices journal homepage: www.elsevier.com/locate/jsamd Original Article Electronic structure and magnetic properties of Co2TaAl from ab initio calculations Saadi Berri Laboratory for Developing New Materials and Their Characterizations, University of Setif 1, Algeria a r t i c l e i n f o a b s t r a c t Article history: Received 23 April 2016 Received in revised form 27 May 2016 Accepted 27 May 2016 Available online June 2016 A first-principles approach is used to study the structural, electronic and magnetic properties of the Co2TaAl Heusler compound with CuHg2Ti-type structure The investigation was done using the (FPLAPW) method where the exchange-correlation potential was calculated with the frame of GGA by Perdew et al (Phys Rev Lett 77 (1996) 3865) At ambient conditions our calculations predict that Co2TaAl is half-metallic ferromagnet (HMF) with a magnetic moment of mB/fu and HM flip gap of 0.58 eV In addition, the ferromagnetic phase is found to be energetically more favorable than paramagnetic phase Therefore, the Co2TaAl Heusler compound is a candidate material for future spintronic applications © 2016 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: Heusler compound Ab initio calculations Half-metallic Spintronic Electronic structure Introduction Heusler compounds are ternary intermetallic compounds that have the general composition X2YZ In this class, X and Y represent d-electron transition metals, and Z denotes an sp-electron element [1] In recent years, Heusler compounds have been extensively studied, motivated by their gained importance due to advancements in spintronics [2e6] Half-metallic ferromagnets (HMFs) meet all the requirements of spintronics, as a result of their exceptional electronic structure These materials behave like metals with respect to the electrons of one spin direction and like semiconductors with respect to the electrons of the other spin direction Recently, half-metallic ferromagnetism has been found in, (Ca, Sr, Ba)C [7], Co2MnSi [8], Co2MnZ (Z ¼ Ge, Sn) [9], CoFeTiSb [10], Mn2CoAs [11], ZrFeTiAl, ZrFeTiSi, ZrFeTiGe and ZrNiTiAl [12], Co2Mn1ÀxFexSi [13], Co2MnBi [14] and Co2FeZ (Z ¼ Al, Ga, Si, Ge) [15] Generally, Heusler compounds (X2YZ) crystallize in the cubic L21 structure (#225), in which the lattice consists of interpenetrating fcc sub lattices with the positions 4a (1/4 1/4 1/4) for the X, 4d (1/2 1/2 1/2) for the Y and 4c (0 0) for the Z atoms, respectively The crystal structures of these compounds are shown in Fig Our main E-mail address: berrisaadi12@yahoo.fr Peer review under responsibility of Vietnam National University, Hanoi goal in this work is to evaluate examine the validity of the predictions of half metallicity for Co2TaAl Heusler compound, the calculations are performed using ab initio full-potential linearized augmented plane wave (FP-LAPW) within the density functional theory DFT within the generalized gradient approximation GGA Our paper is organized as follows The theoretical background is presented in Section Results and discussion are presented in Section A summary of the results is given in Section Method of calculations The first principles calculations were performed by employing FP-LAPW approach [16], based on the DFT [17] as implemented in WIEN2K code [18] The KohneSham equations are solved selfconsistently using FP-LAPW method In the calculations reported here, we use a parameter RMTKmax ¼ 9, which determines matrix size (convergence), where Kmax is the plane wave cut-off and RMT is the smallest of all atomic sphere radii We have chosen the muffintin radii (MT) for Co, Ta and Al to be 2.4, 2.5 and 2.3 (a.u), respectively The following initial atomic configurations were employed: (Co 3d7 4s2), (Ta 5d3 6s2) and (Al 3s2 3p1) Exchange-correlation effects are treated using GGA as parameterized by Perdew et al [19] Self-consistent calculations are considered to be converged when the total energy of the system is stable within 10À6 Ry The convergence criteria for total energy and force are taken as 10À5 and 10À6 eV/Å, respectively The valence wave functions inside the http://dx.doi.org/10.1016/j.jsamd.2016.05.006 2468-2179/© 2016 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/) S Berri / Journal of Science: Advanced Materials and Devices (2016) 286e289 ground state properties, such as equilibrium lattice constant a, bulk modulus B and its pressure derivative B' The calculated structural parameters of Co2TaAl are reported in Table The optimal lattice parameters obtained by this procedure is in agreement with the experimental value [22] In the absence of the experimental data regarding the bulk modulus and its pressure derivative B0 of the material of interest, and hence our results are predictions We also include in Table the bulk modulus B and its pressure derivative B0 data for Co2CrAl, Co2CrGa, Co2FeAl and Co2FeGa [23] for comparison purpose In addition, the ferromagnetic phase is found to be energetically more favorable than paramagnetic phase At T ¼ K, the calculated spin-polarized band structures of Co2TaAl compound at the theoretical equilibrium lattice constant along high-symmetry directions of the first Brillouin zone are displayed in Fig The total and partial densities of states, in which the spin-up and spin-down sub-bands are shown in Fig The Fermi level set as eV In Fig 3, it is clear that the majority-spin band is metallic, the conduction band minimum (CBM) is found to be mixed with the valence band maximum (VBM) along the (GX) direction, while the minority spin band shows a semiconducting gap around the Fermi level In the minority-spin band, the valence band maximum (VBM) is located at À0.58 eV and the conduction band minimum (CBM) at 0.18 eV The energy gap for spin-down electrons at around the Fermi level is 0.74 eV and close to the energy gap values for the Co2MnSi compound [13] The half-metallic gap [24,25], which is determined as the minimum between the lowest energy of minority (majority) spin conduction bands with respect to the Fermi level and the absolute values of the highest energy of the minority (majority)spin valence bands, is 0.58 eV, for Co2TaAl compound 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 In the absence of both experimental and theoretical data of the energy gap for the material of interest, to the best of our knowledge, no comment can be ascribed to the accuracy of the used method and hence our result may serve only for a reference Fig shows the total density of states and partial density of as a function of energy for the Co2TaAl compound at its equilibrium lattice constant To illustrate the nature of the electronic band structures, we have plotted the partial density of states (DOS) of Co eg and t2g, Ta eg and t2g and Al-p electrons for the spin-up and spindown sub-bands For Co2TaAl compound, in both spin channels, significant contributions to the total density of states in the energy range between À5.0 and À1.0 eV, come from p electrons of Al element hybridized with eg electron of Co and t2g states of Ta atom At the Fermi energy the situation is markedly different, where the t2g orbital of Co and Ta atoms creates fully occupied bands These values of polarization are similar to those already published for Co2VZ (Z ¼ Al and Ga) full Heusler compounds calculated with a full-potential linearized augmented plane wave method [26] In the energy range between 1.0 and 4.0 eV, the eg were states of Ta atoms contribute to the majority and minority spin states The origin of Fig Crystal structure of Co2TaAl Heusler compound -37311,80 Ferromagnetic Paramagnetic Energy(Ry) -37311,82 Murnaghan EOS -37311,84 -37311,86 -37311,88 -37311,90 300 320 340 360 380 400 287 420 Vol(a.u ) Fig Volume optimization for the Co2TaAl Heusler compound spheres are expanded up to lmax ¼ 10 while the charge density was Fourier expanded up to Gmax ¼ 14 The Monkorst-Pack special kpoints were performed using 104 special k-points in the irreducible Brillion zone [20] Results and discussion Our basic procedure in this work is to calculate the total energy as a function of the unit-cell volume around the equilibrium cell volume V0 for Co2TaAl Heusler compounds in both paramagnetic and ferromagnetic phases We present, in Fig 2, structural optimization curves obtained in both phases, and the data are fitted to the Murnaghan's equation of state [21] so as to determine the Table Lattice constant a (Å), bulk modulus B (in GPa), pressure derivative of bulk modulus B0 , total and partial magnetic moment (in mB) for Co2TaAl Heusler compound Compound a B B0 mCo mTa Co2TaAl(FM) Co2TaAl(PM) Co2TaAl(EX) [22] Co2CrAl [23] Co2CrGa [23] Co2FeAl [23] Co2FeGa [23] 5.96 5.93 5.93 5.70 5.72 5.69 5.71 205.43 215.53 e 207.23 208.81 215.87 198.85 4.94 5.43 e e e e e 1.040 e 0.75 e e 2.74 2.76 À0.008 e e e e e e mAl 0.002 e e À0.038 À0.029 À0.038 À0.028 minterstitial mTotal À0.075 e e e e e e 2.00 e 1.5 3.00 3.028 4.99 5.02 288 S Berri / Journal of Science: Advanced Materials and Devices (2016) 286e289 4 Energy (eV) Spin-up Spin-down 3 2 1 0 -1 -1 -2 -2 -3 -3 -4 W L Γ WK X -4 EF L W Γ X W K Fig The band structures of the Co2TaAl Heusler compound for the spin-up and spin-down electrons the band gap results from eg orbital of Co atoms on the valence band and t2g orbital of Co atoms on the conduction band In other word, it requires the total valence electrons to be 26 or 28, with the Fermi level locating in between 2eg and 3t2g or 2eu and 2eg orbitals [27] The calculated total and atom-resolved magnetic moments of Co2TaAl compound are listed in Table For Half-Heusler compounds with three atoms per formula unit, the SlaterePauling rule is given by mtot ¼ Nve18 In the case of X2YZ Heusler material, there Total -3 -6 Density of States (St/eV spin f.u) -1 -2 -3 1,0 Co- dteg Co-deg 0,5 0,0 -0,5 -1,0 Ta-deg Ta- dteg 0,2 0,1 0,0 -0,1 Al-p -0,2 -4 -2 Energy(eV) Fig Spin-polarized total densities of states (TDOS) and partial densities of states (DOS) of Co2TaAl Heusler compound S Berri / Journal of Science: Advanced Materials and Devices (2016) 286e289 are four atoms per unit cell leading to the formula mtot ¼ NvÀ24, rule The total spin moment is mB for the Co2TaAl compound which have 26 valence electrons per unit cell Thus Co2TaAl compound follow the SlaterePauling behavior and the “rule of 24” [28] The present study shows that the total magnetic moment of this compound is mB Our results for the magnetic moments are in good agreement with experimental data [22] The main contribution to the total magnetic moment is due to Cobalt and the magnetic moment on the Tantalum and Aluminum atoms are small For Co2TaAl compound, the large exchange splitting of the Co-3d states leads to a large magnetic moment Conclusion The electronic structure and magnetic properties of the Co2TaAl Heusler compound have been calculated using the first-principles full-potential linearized augmented plane waves (FPLAPW) method At the equilibrium lattice constant, our calculations predict that Co2TaAl is half-metallic ferromagnet (HMF) with a magnetic moment of mB/fu and HM flip gap of 0.58 eV, respectively The calculated equilibrium lattice constant and the magnetic moment of the material of interest are found to be in good agreement with experiment data Therefore, the Co2TaAl Heusler compound is a candidate material for future spintronic applications References [1] P.J Webster, K.R.A 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Tantalum and Aluminum atoms are small For Co2TaAl compound, the large exchange splitting of the Co-3d states leads to a large magnetic moment Conclusion The electronic structure and magnetic properties. .. 1.0 and 4.0 eV, the eg were states of Ta atoms contribute to the majority and minority spin states The origin of Fig Crystal structure of Co2TaAl Heusler compound -37311,80 Ferromagnetic Paramagnetic