The half-metallic gap [24,25] , which is determined as the min- imum between the lowest energy of minority (majority) spin conduction bands with respect to the Fermi level and the absolu[r]
Trang 1Original Article
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
Article history:
Received 23 April 2016
Received in revised form
27 May 2016
Accepted 27 May 2016
Available online 8 June 2016
Keywords:
Heusler compound
Ab initio calculations
Half-metallic
Spintronic
Electronic structure
a b s t r a c t
Afirst-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 (FP-LAPW) 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 2mB/fu and HMflip gap of 0.58 eV In addition, the ferromagnetic phase is found to be energetically more favorable than para-magnetic 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/)
1 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
advance-ments 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
ferro-magnetism has been found in, (Ca, Sr, Ba)C [7], Co2MnSi [8],
Co2MnZ (Z¼ Ge, Sn)[9], CoFeTiSb [10], Mn2CoAs[11], ZrFeTiAl,
ZrFeTiSi, ZrFeTiGe and ZrNiTiAl[12], Co2Mn1xFexSi[13], Co2MnBi
[14]and Co2FeZ (Z¼ 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 0) for the Z atoms, respectively The
crystal structures of these compounds are shown inFig 1 Our main
goal in this work is to evaluate examine the validity of the pre-dictions 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 Section2 Results and discussion are presented in Section3 A summary of the results is given in Section4
2 Method of calculations Thefirst 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 self-consistently using FP-LAPW method In the calculations reported here, we use a parameter RMTKmax¼ 9, which determines matrix size (convergence), where Kmaxis the plane wave cut-off and RMTis the smallest of all atomic sphere radii We have chosen the muf fin-tin radii (MT) for Co, Ta and Al to be 2.4, 2.5 and 2.3 (a.u), respec-tively The following initial atomic configurations were employed: (Co 3d74s2), (Ta 5d36s2) and (Al 3s23p1) 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 106Ry The convergence criteria for total energy and force are taken as 105 and 106eV/Å, respectively The valence wave functions inside the
E-mail address: berrisaadi12@yahoo.fr
Peer review under responsibility of Vietnam National University, Hanoi.
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Journal of Science: Advanced Materials and Devices
j o u r n a l h o m e p a g e : w w w e l s e v i e r c o m / l o c a t e / j s a m d
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
Journal of Science: Advanced Materials and Devices 1 (2016) 286e289
Trang 2spheres are expanded up to lmax¼ 10 while the charge density was
Fourier expanded up to Gmax¼ 14 The Monkorst-Pack special
k-points were performed using 104 special k-k-points in the irreducible
Brillion zone[20]
3 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 V0for Co2TaAl Heusler compounds in both paramagnetic
and ferromagnetic phases We present, inFig 2, structural
opti-mization curves obtained in both phases, and the data arefitted to
the Murnaghan's equation of state [21]so as to determine the
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 inTable 1 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 B0of the material of interest, and hence our results are predictions We also include inTable 1the bulk modulus B and its pressure derivative B0 data for Co2CrAl, Co2CrGa, Co2FeAl and Co2FeGa[23]for compari-son purpose In addition, the ferromagnetic phase is found to be energetically more favorable than paramagnetic phase
At T ¼ 0 K, the calculated spin-polarized band structures of
Co2TaAl compound at the theoretical equilibrium lattice constant along high-symmetry directions of thefirst Brillouin zone are dis-played inFig 3 The total and partial densities of states, in which the spin-up and spin-down sub-bands are shown inFig 4 The Fermi level set as 0 eV
InFig 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 at0.58 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 min-imum 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 4shows 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
egand t2g, Ta egand t2gand Al-p electrons for the up and spin-down sub-bands For Co2TaAl compound, in both spin channels, significant contributions to the total density of states in the energy range between 5.0 and 1.0 eV, come from p electrons of Al element hybridized with egelectron of Co and t2gstates of Ta atom
At the Fermi energy the situation is markedly different, where the
t2gorbital of Co and Ta atoms creates fully occupied bands These values of polarization are similar to those already published for
Co2VZ (Z¼ 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 egwere states of Ta atoms contribute to the majority and minority spin states The origin of
Fig 1 Crystal structure of Co 2 TaAl Heusler compound.
300 320 340 360 380 400 420 -37311,90
-37311,88
-37311,86
-37311,84
-37311,82
-37311,80
Vol(a.u 3 )
Murnaghan EOS Paramagnetic Ferromagnetic
Fig 2 Volume optimization for the Co 2 TaAl Heusler compound.
Table 1
Lattice constant a (Å), bulk modulus B (in GPa), pressure derivative of bulk modulus B0, total and partial magnetic moment (inmB ) for Co 2 TaAl Heusler compound.
S Berri / Journal of Science: Advanced Materials and Devices 1 (2016) 286e289 287
Trang 3the band gap results from egorbital of Co atoms on the valence band
and t2gorbital 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 2egand 3t2gor 2euand 2egorbitals[27]
The calculated total and atom-resolved magnetic moments of
Co2TaAl compound are listed in Table 1 For Half-Heusler com-pounds with three atoms per formula unit, the SlaterePauling rule
is given by mtot¼ Nve18 In the case of X2YZ Heusler material, there
-4 -3 -2 -1 0 1 2 3 4
-4 -3 -2 -1 0 1 2 3
4
Spin-up Spin-down
EF
Fig 3 The band structures of the Co 2 TaAl Heusler compound for the spin-up and spin-down electrons.
-6 -3 0 3 6
Total
-3 -2 -1 0 1 2
Ta- dteg
Al-p
Co- dteg
-1,0 -0,5 0,0 0,5 1,0
Energy(eV)
-0,2 -0,1 0,0 0,1 0,2
S Berri / Journal of Science: Advanced Materials and Devices 1 (2016) 286e289 288
Trang 4are four atoms per unit cell leading to the formula mtot¼ Nv24,
rule The total spin moment is 2 mBfor the Co2TaAl compound
which have 26 valence electrons per unit cell Thus Co2TaAl
com-pound follow the SlaterePauling behavior and the “rule of 24”[28]
The present study shows that the total magnetic moment of this
compound is 2mB Our results for the magnetic moments are in
good agreement with experimental data[22] The main
contribu-tion to the total magnetic moment is due to Cobalt and the
mag-netic 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
4 Conclusion
The electronic structure and magnetic properties of the Co2TaAl
Heusler compound have been calculated using thefirst-principles
full-potential linearized augmented plane waves (FPLAPW)
method At the equilibrium lattice constant, our calculations
pre-dict that Co2TaAl is half-metallic ferromagnet (HMF) with a
mag-netic moment of 2mB/fu and HMflip 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
agree-ment with experiagree-ment data Therefore, the Co2TaAl Heusler
com-pound is a candidate material for future spintronic applications
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