Journal of Magnetism and Magnetic Materials 351 (2014) 25–28
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The effect of defects on the magnetic properties and spin polarization of Ti2FeAl Heusler alloy Qing-Long Fang a, Jian-Min Zhang a,n, Ke-Wei Xu b,c, Vincent Ji d a
College of Physics and Information Technology, Shaanxi Normal University, Xian 710062, Shaanxi, PR China State Key Laboratory for Mechanical Behavior of Materials, Xian Jiaotong University, Xian 710049, Shaanxi, PR China c College of Physics and Mechanical and Electronic Engineering, Xian University of Arts and Science, Xian 710065, Shaanxi, PR China d ICMMO/LEMHE, Université Paris-Sud 11, 91405 Orsay Cedex, France b
art ic l e i nf o
a b s t r a c t
Article history: Received 30 June 2013 Received in revised form 31 August 2013 Available online 27 September 2013
The effect of antisite, swap and vacancy defects on the magnetic properties and spin-polarization of the full-Heusler Ti2FeAl alloy with the Hg2CuTi-type structure is studied by using the first-principles calculations within density functional theory. The perfect Ti2FeAl Heusler alloy exhibits a ferromagnetic half-metallic behavior with the total magnetic moment of 1mΒ and indirect band gap of 0.543 eV. Among swap defect, only the total magnetic moment of the Ti2–Al swap defected is close to the perfect alloy. All defected structures destroy the half-metallicity and only AlTi1 and AlTi2 antisite and Fe vacancy defects maintain relatively high spin polarization. & 2013 Elsevier B.V. All rights reserved.
Keywords: Heusler alloy Defect Magnetic properties First-principles
1. Introduction Increased interest in the field of magnetoelectronics or spin electronics during the last decade has intensified research on the so-called half-metallic materials (HMM) which are metallic for one spin direction while at the same time semiconducting for the other spin direction and thus exhibit a complete spin polarization at the Fermi level and the realistic applications for spintronic devices [1–3]. This offers opportunities for a new generation of devices combining standard microelectronic with spin-dependent effects such as nonvolatile magnetic random access memories and magnetic sensors [4]. The gap in the half-metallic Heusler alloys is sensitive to several factors such as spin–orbit coupling, disorder effects, surface and interface effects, and the presence of defects [5–15]. It was demonstrated that in the presence of spin–orbit coupling (SOC), the spin polarization at the Fermi level EF is reduced; however, its value remains high. For weak SOC materials, the spin polarization is close to 100% [7]. Gercsi and Hono studied the effect of disorder on the half-metallicity of Co2FeSi alloy. They demonstrated that DO3-type disorder (the Co atoms were swapped by Fe atoms) decrease the total magnetic moment from 6.0 to 5.5mΒ and broaden the gap in the minority spin channel at Fermi level EF, whereas Co and Si atoms swap (A2 disorder) increase the magnetic moments lightly to 6.15mΒ, and no band gap in the minority-spin electron states exists [8]. Yu Feng et al. studied (001) surface of n
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Ti2CoAl alloy and shown that the half-metallicity was destroyed in five terminations [16]. The presence of defects in Heusler alloys has been found to affect their electronic and magnetic properties. It has been evidenced experimentally that a disorder up to 10% of the Mn atoms in Heusler alloys change places with elements from neighboring sublattices. Such a disorder may cause antisite defects because of similar atomic radii of the metal ions. These defects are suggested to be responsible for decreasing the spin-polarization and consequently destroying the halfmetallicity. Ravel et al. have shown, using Neutron diffraction and EXAFS measurements, that the disorder of Co2MnSi Heusler alloy is dominated by site-swapping between Co and Mn atoms [17]. They found that about 14% of Mn sites are occupied by Co and 5–7% of Co sites are occupied by Mn atoms. In addition, Co2MnGe has shown atomic disorder using anomalous X-ray diffraction, where about 12.7% of the Mn sublattices were occupied by Co, which was proposed to be the reason behind the destruction of half-metallicity [18]. Although the first-principles calculations revealed that the half-metallicity can be observed in Ti-based Heusler alloys with Hg2CuTi-type configuration [19–22], the evidences of high spinpolarization in spintronic devices are still questionable due to possible effect of defects in minority-spin gap, and information about Ti-based Heusler alloy defects are still scarce in previous theoretical and experimental studies to the best of our knowledge. Therefore, a systematic and comprehensive study of the defect effects could be of great benefit to the realistic meaning. In this paper, the effect of three classes of defects, namely the antisite, swap and vacancy defects on the magnetic properties and
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spin polarization of Ti2FeAl Heusler alloy is investigated. The antisite defects are created by the replacement of one kind of atom by another, which results in eight antisites. However, atomic swap defects are created by the interchange of two different atoms in the sublattices, which leads to five swaps, whereas, the vacancies are created by removing one kind of atoms (Ti1, Ti2, Fe or Al). The rest of the paper is arranged as follows: Section 2 includes the model and method of calculations. In Section 3, the formation energy, magnetic properties and spin polarization are discussed. Finally in Section 4, we summarize our results and conclusions.
k-point sampling is adopted for Brillouin zone integration, together with a Gaussian smearing broadening of 0.2 eV.
3. Results and discussions We investigate the stability of the antisite, swap, and vacancy defects in Ti2FeAl Heusler alloy, which can be deduced from the value of the formation energy. The defect formation energy Ef is estimated as Ef ¼ Edef Eid ∑ni μi
2. Model and method of calculation See Fig. 1(1), in Hg2CuTi-type Ti-based Heusler alloy Ti2FeAl with F4 3m space group, the neighbor Ti atoms occupy A (0,0,0) and B (0.25,0.25,0.25), and the residual Fe enters C (0.5,0.5,0.5) and Al at D (0.75,0.75,0.75). Due to different surroundings of neighbor Ti atoms, in Ti2FeAl alloy there are two kinds of Ti atoms, namely A and B sites. After completely relaxing, we also obtain the optimized of the defect Ti2FeAl, as shown in Fig. 1(2)–(18). Comparing with the configurations of the perfect Ti2FeAl Heusler alloy, there is no change in the configurations of the antisite defect in Ti2FeAl Heusler alloy, while large changes are found in the mostly configurations of the swap and vacancy defects in Ti2FeAl Heusler alloy. It can be see that the atoms around the vacancy move toward the vacancy obviously in Ti1 and Al vacancies defects. In this paper, the calculations are performed using the Vienna ab initio simulation package (VASP) based on the density function theory (DFT) [23–26]. The electron–ionic core interaction is represented by the projector augmented wave (PAW) potentials [27] which are more accurate than the ultra-soft pseudopotentials. To treat electron exchange and correlation, the Perdew–Burke– Ernzerhof (PBE) [28] formulation of the generalized gradient approximation (GGA) is used. A conjugate-gradient algorithm is used to relax the ions into their ground states, and the energies and the forces on each ion are converged within 1.0 10 4 eV/ atom and 0.02 eV/Å, respectively. The cutoff energy for the planewaves is chosen to be 350 eV. A 6 6 6 Monkhorst-Pack grid for
ð1Þ
where Edef is the total energy of the supercell containing the defect and Eid is the total energy of the ideal Ti2FeAl full Heusler alloy (the two structures are modeled using the supercell of 32 atoms). The last term represents the energy difference added or removed. For the case of the antisite defects the number of atoms transferred (ni ¼ þ1 for the added atom and ni ¼ 1 for the removed atom) and μi is the chemical potential of these atoms in their stable bulk phases. However, for the case vacancy defected structure ni ¼ 1. This equation is simplified in the case of atomic swap defects to the following form: Ef ¼ Edef Eid
ð2Þ
This is due to the fact that the total number of atoms in the swap defected structure remains the same as that of the ideal case. Here the stable phases are considered hcp, fcc and fcc structures for bulk Ti, Fe and Al, respectively. Table 1 lists the formation energies of the various kinds of the defects. First we discuss the formation energies of the antisites, as listed in Table 1. It is noted that among the antisite defects, TiFe (Ef ¼ 0.376 eV), FeTi2 (Ef ¼0.300 eV) and AlFe (Ef ¼0.677 eV) show moderation energy, which suggests that these kinds defects are likely to be formed during Ti2FeAl growth. However, the rest of the antisite defects are found to be negative. Such negative values suggest the possibility of spontaneous formation of these kinds of the defects during the growth of Ti2FeAl alloy. Among the swap defected structures, we found that only the Ti1–Fe swap defected structure has negative value of the formation energy. Then, the absolute value of the formation energy for each
Fig. 1. Crystal structures of the perfect and defect Ti2FeAl Heusler alloys. (1) the perfect, (2) TiFe antisite, (3) TiAl antisite, (4)FeTi1 antisite, (5) FeTi2 antisite, (6) AlTi1 antisite, (7) AlTi2 antisite, (8) FeAl antisite, (9) AlFe antisite, (10) Ti1–Fe swap, (11) Ti2–Fe swap, (12) Ti1–Al swap (13) Ti2–Al swap, (14) Fe–Al swap, (15) Ti1 vacancy, (16) Ti2 vacancy, (17) Fe vacancy and (18) Al vacancy.
Q.-L. Fang et al. / Journal of Magnetism and Magnetic Materials 351 (2014) 25–28
Table 1 Formation energies Ef (eV) of the defective Ti2FeAl. System Antisite TiFe TiAl FeTi1 FeTi2 AlTi1 AlTi2 FeAl AlFe Swap Ti1–Fe Ti2–Fe Ti1–Al Ti2–Al Fe–Al Vacancy Ti1 Ti2 Fe Al
27
Table 2 Magnetic moments (mΒ) of perfect and defect Ti2FeAl supercell (2 2 2), Xd refers to defect atoms.
Ef (eV) Total
System
Ti1
Ti2
Fe
Al
Xd
Prefect Ti2FeAl
0.831
0.563
0.917
0.025
–
8.000
0.424
1.211
0.003
TiFe ¼ 0.439
0.912
TiAl
0.483, 0.335 0.861
0.741
0.025
TiAl ¼ 0.459
0.235 0.321 0.002 0.450 0.249
FeTi1
0.560
0.473, 0.568 0.226
0.011
FeTi1 ¼ 0.229
4.178
FeTi2
0.570
0.547
0.084, 1.487 1.227
FeTi2 ¼ 2.214
3.753
AlTi1
0.612
0.284
0.029, 0.019 0.008
AlTi1 ¼0.029
5.517
0.640 0.507 2.857 0.544
AlTi2
0.639
0.391
AlTi2 ¼0.032
6.067
FeAl
0.560
1.329
FeAl ¼ 1.548
1.678
AlFe
0.975, 0.735
0.539, 0.553 0.700
0.024, 0.005 0.027
0.961
0.028
AlFe ¼ 0.002
12.809
0.311, 0.351 0.431
0.046, 2.056 1.210
0.007
0.425
0.501, 0.198 0.292
Ti ¼ 0.276, Fe¼0.002 Ti ¼ 0.193, Fe¼ 1.263 Ti ¼ 0.339, Al ¼ 0.023 Ti ¼ 0.323, Al ¼ 0.022 Fe¼ 1.232, Al ¼ 0.014
0.376 0.387 0.800 0.300 0.720 0.516 0.128 0.677
Antisite TiFe
Swap Ti1–Fe
swap defected structure is less than 0.5 eV. The different situation for vacancy defects, we found that Fe vacancy defect has the highest formation energy among all of the defects. However, for Ti1, Ti2 and Al vacancy defects the absolute value of the formation energy for each vacancy defected structure is slightly larger than 0.5 eV. Perfect Ti2FeAl alloy is one of the stable ferromagnets with a total magnetic moment of 1mΒ/f.u. that is mainly contributed by Ti and Fe atoms. As listed in Table 2, the local magnetic moments of Ti1, Ti2 and Fe are 0.831, 0.563 and 0.917mΒ, respectively. While the magnetic moment of Al atom is too small (0.025mΒ) and can be neglectable. It is clear that the alloy has a half-metallicity because it has an integral total magnetic moment M t , which agrees with the Slater–Pauling rule that is described by the following relation [29,30]:
Ti2 Fe
M t ¼ N v 18
Al
where Nv is the number of valence electrons per cell. The local magnetic moments vary due to the presence of defects in the system. The 2 2 2 super cell of the ideal alloy exhibits a total magnetic moment of 8mΒ/cell (8(1mΒ/f.u.)). However, the magnetic moments are different for all the defected structures. Among swap defect, only the total magnetic moment of the Ti2–Al swap defected is close to the perfect alloy. In addition, TiAl and AlFe antisites and Fe vacancy defects all exhibit larger values than that of the perfect alloy. The increase of the total magnetic moments from the ideal value can be related to different reasons. The reason of the raise of the total magnetic moment in TiAl antisite defected structure is due to the increase of the local magnetic moment of Ti antisite atom at the D site, as well as in AlFe antisite defected structure is due to the positive value of Al antisite atom at the C site. However, it is due to the absence of one Fe atom in the case of Fe vacancy defected structure. The residuals exhibit smaller total magnetic moments than the ideal structures. The reason for the decrease in total magnetic moment due to the decreasing local magnetic moment of the atom at A or B site or the increasing absolute value of the atom at C site. While the Ti2 and Al vacancy defects exhibit antiferromagnetic behavior and the local magnetic moment of each atom is very small. The perfect Ti2FeAl Heusler alloy is half-metallic ferromagnet with an indirect band gap along Γ–Χ symmetry line in the spindown channel (see Fig. 2), which leads to a spin polarization of 100% at the Fermi level. The band structure exhibits the gap width of 0.543 eV for the perfect Ti2FeAl Heusler alloy, which is slightly larger than 0.5 eV obtained by Yang et al. [31] due to the different
Ti1–Al
0.443, 0.203 0.626
Ti2–Al
0.621
Fe–Al
0.720, 0.725
0.221, 0.287 0.278, 0.346 0.702, 0.575
0.172
0.122
0.001 0.853, 0.992 0.015
0.001 0.868
Vacancy Ti1
0.007, 0.003
spin-up
4
1.154
0.024, 0.004 0.006 0.021, 0.007 0.029
3.843 6.472 7.820 6.135
1.246, 0.062 0.003 1.373
0.005
–
0.216
0.000 0.017
– –
0.000 11.933
0.004
0.001
–
0.000
Ti2FeAl
spin-down
2
Energy (eV)
ð3Þ
Ti2–Fe
0.160
0.234, 0.704 0.496
10.38
0
-2
-4
-6
W
L Λ Γ
Δ
Χ Ζ WK W
L Λ Γ
Δ
Χ ΖW K
Fig. 2. The band structure of spin-up (left panel) and spin-down (light panel) channels for perfect Ti2FeAl alloy. The Fermi level is set at zero energy and indicated by red solid line. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
calculated method used. The spin polarization P is defined as P¼
DF↑ ðtotÞ DF↓ ðtotÞ DF↑ ðtotÞ þ DF↓ ðtotÞ
ð4Þ
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Q.-L. Fang et al. / Journal of Magnetism and Magnetic Materials 351 (2014) 25–28
4. Conclusions
Table 3 Spin polarization P of perfect and defective Ti2FeAl structures. System
The effect of antisite, swap and vacancy defects on the magnetic properties and spin polarization of the full-Heusler Ti2FeAl alloy with the Hg2CuTi-type structure have been studied by using the firstprinciples projector augmented wave (PAW) potential within the generalized gradient approximation (GGA). The following conclusions are obtained
P (%)
Perfect Ti2FeAl Antisite TiFe TiAl FeTi1 FeTi2 AlTi1 AlTi2 FeAl AlFe
100 17.48 66.50 53.85 50.32 79.62 88.42 60.48 40.24
Swap Ti1–Fe Ti2–Fe Ti1–Al Ti2–Al Fe–Al
9.34 2.41 47.23 44.32 51.43
Vacancy Ti1 Ti2 Fe Al
17.97 0.00 83.20 0.00
EF
EF
Acknowledgments The authors would like to acknowledge the National Natural Science Foundation of China (Grant nos. 51071098, 11104175, 11214216) and the State Key Development for Basic Research of China (Grant no. 2010CB631002) for providing financial support for this research.
EF
Ti1-Al swap
Ti2-Fe swap
15 Ti1-Fe swap
(1) The perfect Ti2FeAl Heusler alloy exhibits a ferromagnetic halfmetallic behavior with the total magnetic moment of 1mΒ and indirect band gap of 0.543 eV. (2) The formation energies of the mostly defected structures are relatively low, except for Fe vacancy defected structure. (3) Among swap defect, only the total magnetic moment of the Ti2–Al swap defected is close to the perfect alloy. (4) All defected structures destroy the half-metallicity and only AlTi1 and AlTi2 antisite and Fe vacancy defects maintain relatively high spin polarization.
DOS (eV/electrons)
0
References
-15 15 Ti2-Al swap
Fe-Al swap
Ti1 vacancy
Fe vacancy
Al vacancy
0 -15 15 Ti2 vacancy 0 -15 -6
-3
0
3
-6
-3 0 Energy (eV)
3
-6
-3
0
3
Fig. 3. Total density of states (TDOS) of the Ti2FeAl Heusler alloy with swap and vacancy defects. Black line (red line) denotes spin-up (spin-down) channel. The Fermi level is set at zero energy and indicated by vertical green line. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
where DF↑ ðtotÞ and DF↓ ðtotÞ are the spin-up and spin-down densities of states (DOS) at the Fermi level. The values of the spin polarization P are affected by the presence of the defects, as listed in Table 3. From this table, one can see that the half-metallicity is destructed and the spin polarization of 100% has not been detected. Most of the defected structures exhibit low spin-polarizations, while the high spin polarizations maintain in AlTi1 and AlTi2 antisite and Fe vacancy defects. Fig. 3 shows the Total density of states (TDOS) of the Ti2FeAl Heusler alloy with swap and vacancy defects. In detail, for Ti2 and Al vacancies, the electronic structures are identical for both spin channels. While for Fe vacancy, the value of the spin-up DOS is far larger than that of the spin-down DOS at the Fermi level. The electronic structures are almost completely symmetric for the rest of the defects.
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