Intermetallics 33 (2013) 33e37
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The effect of defects on the electronic and magnetic properties of the Co2VSn full Heusler alloy: Ab-initio calculations N.T. Mahmoud a, J.M. Khalifeh a, *, B.A. Hamad a, A.A. Mousa b a b
Physics Department, The University of Jordan, 11942-Amman, Jordan Civil Engineering Department, Middle East University, P.O. Box 42, 11610-Amman, Jordan
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 August 2012 Received in revised form 12 September 2012 Accepted 13 September 2012 Available online 8 November 2012
Density Functional Theory (DFT) calculations are performed using full potential linearized augmented plane wave (FP-LAPW) method to investigate the effect of defects on the electronic and magnetic properties of Co2VSn full Heusler alloy. The formation energies are calculated for antisite, swap and vacancy defects. The Vsn antisite, V, Co and Sn vacancies have relatively low formation energies with high probability to occur. The half metallicity is maintained in all structures with band gaps smaller than that of the perfect alloy except for CoSn, SnCo antisite and CoeSn swap, which exhibit a metallic behavior. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: A. Ternary alloy systems B. Electronic structure of metals and alloys D. Defects: point defects E. Ab-initio calculations
1. Introduction Heusler alloys are the center of interest since 1903 , when Heusler reported that ferromagnetic alloys could be made from nonferromagnetic constituents, Cu, Mn, and main group elements such as Al and Sn. The ferromagnetic properties of these alloys were related to the chemical ordering and concentration of Mn atoms. In general, there are two types of Heusler systems, the ﬁrst type has the L21 structure, which consists of four fcc sublattices . These alloys are referred to as full Heusler alloys, which are ternary compounds with 2:1:1 stoichiometry and a chemical formula X2YZ (space group 225:Fm3 m). The X and Y are transition metals and Z is a main group metal, in some cases Y is replaced by a rare earth element. The X atoms are located at A(0.25,0.25,0.25) and C(0.5,0.5,0.5). The Y and Z atoms are located at B(0.75,0.75,0.75) and D(0,0,0), respectively , see Fig. 1(a). The other type is C1b structure where one of the four sublattices is unoccupied (A site), with chemical formula XYZ, see Fig. 1(b). The most important feature of some Heusler alloy is the halfmetallic ferromagnetism (HMF), which means that the conduction electrons are 100% spin-polarized e due to the gap at the Fermi
* Corresponding author. E-mail address: [email protected]
(J.M. Khalifeh). 0966-9795/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.intermet.2012.09.012
level, EF, in the minority spin channel e and the ﬁnite density of states at EF for the majority spin channel . So Half-metals are hybrids between normal metals and semiconductors. The majorityspin band is crossed by the Fermi level as in a normal metal while the Fermi level falls within a gap in the minority-spin band as in semiconductors leading to a perfect 100% spin-polarization . The spin polarization is likely to be reduced due to the occurrence of atomic defects such as stoichiometric atomic swaps and nonstoichiometric antisites . The SlaterePauling curve [7,8] is a simple way to study the interrelation between the valence electron concentration and the magnetic moments for ferromagnetic alloys. It is well known that Heusler compounds follow the SlaterePauling rule for predicting their total spin magnetic moment (Mt) [9e11] that scales linearly with the number of valence electrons (Nv); Mt ¼ Nv 24 for fullHeusler alloys and Mt ¼ Nv 18 for half-Heusler alloys [3,12]. Iron-based alloys such as Fe2YSi (Y]Cr, Mn, Fe, Co,Ni) have also been investigated experimentally and theoretically . However, only Fe2MnSi and Fe2CrSi were found to be half metallic and ferromagnetic with appreciable total magnetic moments, in agreement with the Slater Pauling rule . The effect of defects on the electronic and magnetic structure were investigated for Fe2MnSi Heusler alloy . The formation energies were calculated for antisite, swap, and vacancy defects. Three defects, namely MnFe and MnSi antisite as well as FeeMn swap defects were predicted to occur spontaneously as they have negative
N.T. Mahmoud et al. / Intermetallics 33 (2013) 33e37
2. Calculation method The calculations were performed using DFT  based on FPLAPW method , as implemented in WIEN2K package . The electronic exchange-correlation potential is described with the generalized gradient approximation (GGA) . The ideal structure has closed packed L21 cubic structure with a space group Fm3 m(255) structure, which consists of four interpenetrated facecentered cubic (FCC) sublattices. The Co atoms are placed at (0.25,0.25,0.25) and (0.75,0.75,0.75) .The V and Sn atoms are located at (0,0,0) and (0.5,0.5,0.5) respectively. The calculations are performed using (2 2 2) super cell with 32 atoms per unit cell. The basis set parameters are: a 16 Ryd cut off energy for the plane waves in the interstitial region between the mufﬁn tins and 169 Ryd for the potential. The wave function expansion inside the mufﬁn tins are taken up to lmax ¼ 10 and the potential expansion up to lmax ¼ 4. The core energy cut off is taken as 6.0 Ryd. The Mufﬁn tin radius (RMT) is set to RMT ¼ 2.45 a.u. for all atoms. The k-point sampling in the irreducible part of the Brillouin Zone (BZ) is performed using (8 8 8) Monkhorst-pack grid. All structures are fully relaxed until the forces on the atoms are less than 2 m Ry/a.u. The convergence of the self consistent calculations are taken with respect to total charge of the system with a tolerance of 0.0001 electron charge. The lattice constant is obtained by optimizing the structure using Murnghan equation of state , which is found to be 6.022 A. The calculated density of states (DOS) are performed using the tetrahedron method with Bl chlcorrections . 3. Results and discussion
Fig. 1. (a) Crystalline structures of full Heusler alloys; L21 structure. (b) Crystalline structures of half Hesluer alloys; C1b structure.
formation energies, whereas, Mn and Si vacancies, FeeSi swap, and FeMn antisite defects were found to be unlikely to occur . However, the rest of the (FeSi, MnSi, and SiFe) antisites, MneSi swap, and Fe vacancy defects have relatively low formation energies that suggest higher probabilities to occur. The band gaps of the defected structures are found to be smaller than the ideal structure with almost zero values in the cases of FeSi antisite and FeeSi swap defects. The structure with Fe vacancy defect, however, exhibits almost the same energy gap as that of the ideal structure. The magnetic structure was also affected by the presence of defects except for FeeMn and MneSi swap defects that show the same total magnetic moment of 3 mB/f.u. as the ideal structure . In addition, Fe2CrSi full Heusler alloy has been studied and it was found that the perfect structure is a half-metallic ferromagnetic with a band gap of 0.6 eV. When the defects were introduced, the FeSi and CrSi antisite as well as FeeSi and CreSi defects destroyed the half metallicity, however the remaining antisite, swap and vacancy defects retained the half metallicity with band gaps lower than the perfect case . Cobalt-based alloys such as Co2MnZ (Z ¼ Si,Ge,Sn),Co2CrZ (Z ¼ Al,Ga) and Co2FeSi [10,11,17e21] are found to be half metallic alloys. These alloys are promising for spintronic applications due to their high total magnetic moments and Curie temperatures. In this work, we report electronic and magnetic properties of perfect Co2VSn Heusler alloy and the defected structures (antisite, vacancy and swap). The rest of the paper is organized as follows: Section 2 is devoted to the method of calculation; Section 3 focuses on the results and discussion, and Section 4 deals with the concluding remarks.
In this work we investigate the electronic, magnetic and energetic properties of the perfect and defected structures of Co2VSn alloy. We performed calculations for three kinds of defects, namely, antisite (one atom replaces the other), swap (two atoms exchange their sites), and vacancy (one atom is removed). 3.1. Energetics The stability of the perfect Co2VSn Heusler alloy is investigated by calculating the formation energy using the formula:
Ef ¼ Etot
where, ni is the number of atoms for each constituent, mi is the chemical potential of the ith element in its stable bulk phase (Co, V and Sn are in hcp, bcc and diamond phases, respectively). We found that the formation energy of Co2VSn structure is 0.225 eV. The defect formation energy is estimated as:
Ef ¼ Edef Eper
where Edef is the total energy of the super cell containing the defect, Eper is the total energy of the full Heusler alloy using the same super cell with 32 atoms, nj is the number of atoms transferred to or from the chemical reservoir, and mj is the chemical potential of theses transferred, exchanged or removed atoms in their stable bulk phases, see Table 1. We found negative values of formation energy for Vsn antisite (Ef ¼ 1.132 eV), Co vacancy (Ef ¼ 0.168 eV), V vacancy (Ef ¼ 0.117 eV), defects. Such negative values suggest the possibility of spontaneous formation of these kinds of defects during the growth of Co2VSn. However, Sn-vacancy (Ef ¼ 1.514 eV) and VeSn swap (Ef ¼ 0.134 eV) shows moderate formation energy, which suggests that these kinds of defects are likely to be formed during Co2VSn growth. However, the rest of swap and vacancy
N.T. Mahmoud et al. / Intermetallics 33 (2013) 33e37
Table 1 Formation energy, Ef (eV),of the defected Co2VSn. System
defects are found to exhibit slightly higher formation energies. Therefore, although their occurrence can certainly not be excluded, these defects are expected to have a relatively small density.
magnetic moment is mainly dominated by the Co atom (see Table 2), the local magnetic moments of Co, V and Sn are 1.1, 0.87 and 0.015 mB, respectively. The total and local magnetic moments vary by introducing defects as mentioned previously (see Table 2). Only three structures maintain the same total magnetic moment as the perfect alloy, namely CoSn, CoV antisite as well as VeSn swap defected structures. The decrease of the total magnetic moments from the perfect one can be related to different reasons. In the vacancy defects the main reason of the reduction in the total magnetic moment is due to the absence of one atom either Co or V. In VCo antisite defects, the reduction of the magnetic moment is due to the replacement of Co atom by V, which exhibits a magnetic moment of 0.668 mB that is coupled antiferromagnetically with its ﬁrst nearest neighbors (V atom). However, in the case of SnV antisite, the reduction of the
3.2. Magnetic moments In this subsection, we discuss the magnetic properties of the system, focusing in particular on the defect-induced changes on the local magnetism. Perfect Co2VSn alloy is ferromagnetic with a total magnetic moment of 24 mB/cell in the (2 2 2) super cell (8 3 mB/f.u.). The total magnetic moment in our calculations agrees with previous calculations using GGA , whereas it disagrees with those using LSDA þ U . However, both calculations report higher total magnetic moments than the experimental values, which may be related to the B2-like disorder . The Table 2 Magmatic moment (in units of mB) of perfect and defected Co2VSnsupercell (2 2 2). System Perfect (super) Antisites
Co2VSn CoSn CoV SnV SnCo
V Sn Swap
1.1 1.123, 1.250 1.068, 1.140 1.081, 1.038 1.016, 1.099, 0.924, 1.081, 1.295 1.033, 1.179 1.038, 1.000 1.010, 1.040, 1.201 0.911, 0.921, 1.072 1.104, 0.968 1.031, 0.995 1.1017, 1.053, 1.029, 1.089, 1.071 1.030, 1.21, 1.064 1.044 1.182, 1.198, 1.089 1.040, 0.895, 1.047 1.43 1.11, 1.18, 0.961
0.87 0.591, 0.513 0.758, 0.828 0.913, 0.975 0.823, 1.061
0.015 0.306, 0.301 0.022, 0.015 0.018 0.011 0.017 0.015
e CoSn: 1.782
0.808, 0.815 0.599, 0.012
0.015 0.012 0.014
0.461, 0.768 0.551, 0.493 0.722, 0.631 0.448
0.022 0.016 0.013 0.011 0.006, 0.009, 0.01
Cov: 1.36 VCo: 0.534
0.696, 0.919, 1.032, 0.777
0.012 0.016 0.013
SnCo: 0.048 CoSn: 1.719
0.86, 0.826 1.088
0.016 0.013 0.020
VSn: 0.992 SnV: 0.020
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Fig. 3. Band structure of the minority spin channel of VSn antisite defected structure. Fig. 2. Band structure and TDOS of the minority spin channel of the ideal Co2VSn Heusler alloy.
magnetic moment is due to the absence of V atom replaced by Sn atom. On the other hand, the increase in the total magnetic moment of VSn antisite defected structure is due to the increase of the local magnetic moment of V atom (0.87 mB) at the D site instead of 0.0145 mB for Sn. The increase of the total magnetic moment in the case of CoeSn-swap defect is due to the increase of the local magnetic moment of the swapped Co atom. This is due to the magnetic nature of Co element.
cases is related to the fact that when Co atoms occupy Sn sites they become second nearest neighbors to V atoms, which decreases the ded covalent hybridization. Therefore, the antisite Co atom induces a spin down state in the gap at the Fermi level, see Fig. 4(a) and (b). This behavior is strongly correlated with the high formation energies of these defects. The remaining antisite cases, namely CoV, SnV and VCo have band gaps smaller than that of the perfect alloy, whereas, Vsn defected structure exhibits a larger value. Regarding the vacancy defected structures, they all possess half metallicity with band gaps smaller than the perfect case, see Table 3. In the swap defects, both CoeV and VeSn defected structures are half metallic with band gaps of 0.22 and 0.63 eV, respectively. However,
3.3. Band gap and density of states The half metallic behavior manifests itself in a band gap of one of the spin densities, where the Fermi level falls inside that gap . The gap plays an important role in studying the half metallic and magnetic properties. The origin of the band gap has been related to the covalent hybridization between the lower d bands of the high valent transition metal (Co atom) with the higher d band of the lower-valent transition metal (V atom) . The perfect Co2VSn structure shows an indirect band gap along GeX symmetry line in the minority spin channel of 0.56 eV with 100% spin polarization at the Fermi level, see Fig. 2. However, the defected structures show direct band gaps at G high symmetry point, see Fig. 3 for VSn antisite defected structure (as an example). Table 3 summarizes the values of these band gaps. In the case of the antisite defected structures we found that the half metallicity is maintained for all the considered cases except those of CoSn and SnCo antisite defects. The reason of the band gap absence in these
Table 3 Band gaps (in units of eV) in the minority spin channels and spin polarizations of perfect and defected Co2VSn structures. System Perfect (super) Antisites
Co2VSn CoSn CoV SnV SnCo Vsn VCo Co V Sn CoeV CoeSn VeSn
Band gap (eV)
0.56 0.00 0.33 0.45 0.00 0.66 0.35 0.49 0.23 0.40 0.22 0.00 0.63
100.0 74.8 100.0 100.0 65.6 100.0 100.0 100.0 100.0 100.0 100.0 54.5 100.0
Yes No Yes Yes No Yes Yes Yes Yes Yes Yes No Yes
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LAPW method and GGA functional. The perfect structure is totally spin polarized at the Fermi level with a band gap of 0.56 eV. The formation energies for Vsn antisite, V, Co and Sn vacancies are relatively low, whereas the rest defected structures have high values. The half metallicity is maintained in all defected structures except for CoSn and SnCo antisites as well as CoeSn swap defects, which exhibits a metallic behavior. This exceptional property would make Co2VSn HMF an ideal candidate for spin injection devices to be used in spin electronics.
Acknowledgment The authors acknowledge the generous support of the scientiﬁc research support fund (SRF) from the Ministry of Higher Education and Research in Jordan.
References     Fig. 4. TDOS of (a) CoSn, (b) SnCo antisite defected structures.
              
Fig. 5. TDOS of the CoeSn swap defected structure.
the half metallicity is absent in the case of CoeSn swap defect (see Fig. 5), which is due to the nature of Co atom, where its ﬁrst nearest neighbors are Co rather than V and Al. 4. Conclusion We investigated the electronic and magnetic properties of perfect and defected Co2VSn alloy using DFT calculations within FP-
         
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