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Anti-site-induced diluted magnetism in semiconductive CoFeTiAl alloy
Journal of Alloys and Compounds 657 (2016) 519e525
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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Anti-site-induced diluted magnetism in semiconductive CoFeTiAl alloy T.T. Lin a, b, X.F. Dai a, L.Y. Wang a, X.T. Wang a, X.F. Liu c, Y.T. Cui b, G.D. Liu a, b, * a
School of Material Sciences and Engineering, Hebei University of Technology, Tianjin, 300130, PR China School of Physics and Electronic Engineering, Chongqing Normal University, Chongqing, 400044, PR China c Department of Materials Science and Engineering, The University of Tennessee, Knoxville, TN37996, USA b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 7 July 2015 Received in revised form 11 October 2015 Accepted 16 October 2015 Available online 19 October 2015
The spin-polarized electronic band structure calculations are carried out to theoretically investigate the effect of anti-site disordering to the electronic band structure and magnetic properties of LiMgPdSb-type CoFeTiAl alloy. We found that the CoeTi and FeeTi antisite disordering can induce the diluted magnetism in CoFeTiAl alloy. Especially, the FeeTi antisite disordering can induce a 100% spin polarization at the Fermi level at a certain degree of anti-site disordering. The CoeFe antisite disordering is easy to occur in CoFeTiAl alloy but has little effect on the semiconductive characteristic and magnetic properties. The Co, Fe and Ti atoms at the anti-site contribute the magnetization in CoFeTiAl alloy. The diluted magnetism in CoFeTiAl alloy can be induced by the anti-site disordering instead of the introduction of magnetic dopant elements. © 2015 Elsevier B.V. All rights reserved.
Keywords: Heusler alloy Diluted magnetic semiconductor Anti-site Electronic band structure calculation
1. Introduction Heusler alloys have been intensively investigated in both experiment and theory because many attractive materials have been found in these alloys, like half-metal [1], shape memory alloy [2], topological insulator [3] and spin gapless semiconductor [4] etc. Especially, the half-metals are the most suitable materials to many spintronics devices, such as giant magnetoresistance (GMR), tunneling magnetoresistance (TMR) and spin-injecting devices etc. due to their 100% spin-polarization of conductive electrons. However, in practical applications, the lattice mismatch and the electronic mismatch usually lead to the destruction of high spin polarization [5e7]. For example, Bonell et al. [5] demonstrate the strong influence of mismatch dislocations and show that reducing their density strongly enhances the TMR. So, it is required to reduce the mismatch between the semiconductor/normal metal layer and the magnetic material layer as far as possible. The half-metals with Heusler structure are very mismatched to the current typical semiconductors in the lattice and the electronic structure. So, an important work is to search for highly-matched semiconductor and half-metallic materials with Heusler structure. In the past decades,
* Corresponding author. Building 8, 1st Road, DingZiGu Hongqiao Zone, Tianjin, PR China. Tel./fax: þ86 26564070. E-mail address: [email protected] (G.D. Liu). http://dx.doi.org/10.1016/j.jallcom.2015.10.131 0925-8388/© 2015 Elsevier B.V. All rights reserved.
dozens of highly spin-polarized materials have been found in Heusler alloys, but only a small number of semiconductors were reported. Up to now, the semiconductors with Heusler structure reported are CoTiSb, NiTiSn, CoNbSn [8], Fe2VAl [9], Fe2TiSn [10,11] and Fe2TiSi [12]. The work on these materials is mainly focused on the thermoelectricity and the diluted magnetic properties [13e25]. The ternary Heusler alloys have been investigated massively. Since Dai et al. [26] investigated the electronic structures, crystal structure and magnetic properties of the quaternary CoFeMnSi in 2009, the field of quaternary Heusler alloys has received great € an et al. [29] attraction by scientific researchers [27e32]. Ozdo g studied dozens of quaternary Heusler alloys and found some halfmetals, some spin-gapless semiconductors and some magnetic semiconductors. Zhang et al. [33] calculated the band gap and magnetism of CoFeTiZ (Z ¼ Si, Ge, Sn) alloy and showed that CoFeTiSi and CoFeTiGe alloys are both typically half-metallic ferrimagnets and CoFeTiSn is a quasi-half-metallic ferrimagnet. However, these quaternary Heusler alloys are mostly not synthesized in experiment. In 2011, Basit et al. [34] synthesized the quaternary CoFeTiAl (CFTA) alloy with LiMgPdSb-type structure and investigated the structure and the magnetic properties of CoFe1þXTi1XAl alloys in experiment. But the investigations on the detailed electronic structures and the effect of anti-site disordering on the electronic structure are absent. In this paper, we will focus on the CFTA and mainly investigate
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the effect of anti-site disordering on the electronic structure by first-principle calculations. A series of half-metallic diluted magnetic semiconductors generated by anti-site disordering will be predicted based on our calculated results. 2. Computational details The KorringaeKohneRostoker method combined with the coherent potential approximation and the local density approximation (KKR-CPA-LDA method) is a high-speed, high-precision and powerful method to carry out the first-principle calculations for disordered systems [35e39]. In this paper, the density of states (DOS) patterns and magnetic properties were calculated using the spin-polarized KKR-CPA-LDA method [40,41] for the CFTA alloys with various anti-site disordering. In the calculations, sixty k points in the irreducible Brillouin zone were adjusted to achieve selfconsistency. The convergence tolerance is 0.1 mRy for the total energy. The muffin-tin sphere radii of 2.3 a.u. were used for all the atoms. The density of states was achieved by the tetrahedral integration method [42]. The band structures of the perfectly ordered CFTA alloy were calculated by the CASTEP package [43,44]. 3. Results and discussion The LiMgPdSb-type CFTA structure model is shown in Fig. 1. The structure is composed of four face-centered-cubic sublattices interpenetrating along the space diagonal. In the Wyckoff coordinates, Co atoms occupy the A(0,0,0) site, Fe atoms occupy the C(1/2,1/2,1/2) site, Ti atoms occupy the B(1/4,1/4,1/4) site and Al atoms occupy the D(3/4,3/4,3/4) site. We use “x% (0 < x 15) CoeFe anti-site” to represent the exchange of x% of Co at A sites and x% of Fe at C sites. The same expression is also applied to CoeTi and FeeTi anti-site disordering. The abbreviations of C-FAD, C-TAD and F-TAD represent the CoeFe, CoeTi and FeeTi anti-site disordering, respectively. The equilibrium lattice parameter of the LiMgPdSbtype CFTA alloys with different anti-site disordering is firstly calculated by minimizing the total energy using KKR-CPA method. The ordered CFTA alloy is considered by 0% anti-site disordering. The equilibrium lattice parameter of the ordered CFTA alloy is 5.84 Å, which is slightly less than 5.85 Å obtained from the X-ray diffraction patterns measured at room temperature [34]. It is reasonable to attribute the slight difference between the theoretical and the experimental result to the measurement error or
thermal expansion. In addition, our calculated results indicate that the equilibrium lattice parameters are almost the same as for the ordered case for all the CFTA alloys with different anti-site disordering. So, the lattice parameter of 5.84 Å is used to calculate the DOS patterns, band structures and magnetic properties for all the CFTA alloys with different anti-site disordering. In order to observe clearly the electronic properties, the CASTEP code is firstly used to calculate the band structures of the ordered LiPbMgSn-type CFTA alloy since the KKR-CPA method does not work to give the band structure. The achieved band structures are shown in Fig. 2(a). It is clear that the ordered LiPbMgSn-type CFTA alloy is a semiconductor with a direct band gap of about 0.2 eV. Fig. 2(b) shows the total DOS (TDOS) patterns calculated by CASTEP and KKR-CPA method, respectively. It can be seen that these two TDOS patterns are quite consistent in the shape and the distribution of DOS. The only difference is that the band gap width achieved by KKR-CPA method is smaller than that by CASTEP. Although these two theoretical methods are slightly different in the prediction of the band gap width, the calculated results by both these methods indicate that the ordered CFTA alloy is a semiconductor. Fig. 3 shows the curves of the total energy versus the degree of anti-site disordering for the CFTA alloy with C-FAD, C-TAD and FTAD. It can be seen that the total energy increases linearly with the increasing x for the CFTA alloy with F-TAD and C-TAD. The incremental intensity is 3 meV and 4.2 meV per 1%. For the C-FAD case, the total energy nonlinearly and monotonously increases with the increasing x. The incremental intensity is less than 0.12 meV per 1% in the whole calculation range, which is far less than that generated by the C-TAD and F-TAD. At the same time, the total energies of the CFTA alloys with the CoeFe anti-site disordering are quite close to that of the ordered CFTA alloy and always lower than those with the CoeTi and FeeTi anti-site disordering. These are all signs that the CoeFe anti-site disordering is easy to occur and the CoeTi anti-site disordering should rarely occur in the CFTA alloy. The electronic structures of the CFTA alloys with 1e15% CFAD are calculated. Several typical DOS patterns are shown in Fig. 4(a). From Fig. 4(a), it can be seen that all the CFTA alloys with CoeFe anti CFAD are in a nonmagnetic ground state. The DOS and the band gap near the Fermi level is hardly affected by the CFAD. More clearly, the difference of total DOS between the ordered CFTA alloy and the CFTA alloys with the CFAD are shown in Fig. 4(b). It can be seen that the difference of total DOS is almost zero in the range of 0.2 eV near the Fermi level. So, it is clear that the CFAD has no influence on the semiconductive characteristic of the ordered CFTA matrix. Since all the DOS patterns of the CFTA alloys with 1e15% CFAD are quite
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Fig. 1. Crystal structure of LiMgPdSb-type CoFeTiAl alloy. Co atoms occupy the A(0,0,0) site, Fe atoms occupy the C(1/2,1/2,1/2) site, Ti atoms occupy the B(1/4,1/4,1/4) site and Al atoms occupy the D(3/4,3/4,3/4) site.
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Fig. 2. (a) Band structure achieved by the CASTEP code, (b) the total DOS (TDOS) patterns achieved by the CASTEP code and (c) the TDOS patterns achieved by the KKRCPA method for the ordered LiPbMgSn-type CoTiFeAl alloy.
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The degree of anti-site disordering (x%) Fig. 3. The curves of the total energy versus the degree of anti-site disordering for the CoFeTiAl alloy with CoeFe, CoeTi and FeeTi anti-site disordering. The x represents to exchange x% of the atom number at a sublattice site and those at another sublattice site. The total energy of the ordered CoFeTiAl alloy was set as the zero point of Y axis.
similar, the PDOS of CFTA alloy with 5% CFAD is taken as a representative to illustrate the effect of anti-site atoms as shown in Fig. 4(c). From Fig. 4(c), it can be seen that although the DOS of Co and Fe atoms at the anti-site are different from the Co and Fe atom at the normal site, they still have no spin splitting. The main difference between the anti-site and the normal atoms is the distribution of DOS in the energy. For the Co atom at the anti-site, the DOS is more concentrated in the range of 1 ~ 3 eV and the
Fig. 5. The TDOS patterns of CoFeTiAl alloys with 1%, 3%, 7%, 10% and 15% FeeTi antisite disordering (achieved by the KKR-CPA method).
highest peak of DOS occurs at about 1.2 eV which is closer to the Fermi level than 2.0 eV where the highest peak of DOS of the normal Co atom occurs. For the Fe atom at the anti-site, the DOS is more dispersed in the range of 0.2 ~ 2.8 eV and the highest peak of DOS occurs at about 0.4 eV which is closer to the Fermi level than 0.9 eV where the highest peak of DOS of the normal Fe atom occurs. More importantly, it should be noted that both the Co and
Fig. 4. (a) The calculated TDOS plots by the KKR-CPA method for CoFeTiAl alloy with 1%, 5% and 10% CoeFe anti-site disordering. (b) The difference curves of TDOS (The TDOS of the CoFeTiAl alloys with anti-site disordering minus the TDOS of the ordered CoFeTiAl alloy). (c) The calculated total DOS and PDOS plots by the KKR-CPA method for CoTiFeAl alloy with 5% CoeFe anti-site disordering.
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Fe atoms at the anti-site do not generate any impurity band in the band gap of the matrix. So, the semiconductive band gap is kept in the CFTA alloys with the CFAD. Further, we can conclude that although the CFAD is easy to occur in CFTA alloy due to the small driving energy, it does neither destroy the semiconductivity nor contribute to the magnetization. So, the CFAD has little influence on carrier concentration and spin-polarization. Fig. 5 shows the total DOS patterns of CFTA alloys with the different degree of the F-TAD. From Fig. 5, it can be seen that the CFTA alloys show a half-metallicity and the spin polarization is up to 100% at the Fermi level when the degree of the F-TAD is lower than 2% or between 4% and 10% (x 2 or 4 x 10). Specifically, the Fermi level lies in a band gap in spin-down channel and has a metallic intersection with the energy bands in spin-up channel. In addition, it can be found that the DOS at the Fermi level increases with the increasing degree of the F-TAD, which implies that we can adjust the concentration of the conductive electron with 100% spin
polarization by changing the degree of the F-TAD. However, when the degree of the F-TAD is between 2% and 4% or higher than 10% (2 < x < 4 or 10 < x), the band gap at the Fermi level in spin-down channel is filled in by some impurity bands. In such a situation, the CFTA alloys become ordinary metals and the spin polarization at the Fermi level also becomes very low. In order to find out why the electronic structures at the Fermi level are different in the different disordering degree, the PDOS patterns are shown in Fig. 6 for the CFTA alloys with 1%, 3%, 7% and 15% F-TAD. It can be seen that both Fe and Ti atoms at the anti-site have a large spin splitting for all the CFTA alloys and the Fe and Ti atoms at the normal site are still in nonmagnetic state. Further, it can also be seen that the Fe and Ti atoms at the anti-site generate the impurity bands in the band gap of the matrix. The performance of the impurity bands in DOS patterns is just that a peak of DOS occurs in the band gap. So, the more Fe and Ti atoms at the anti-site, the higher peak of DOS in the band gap. More carefully, let us
Fig. 6. The PDOS patterns of CoFeTiAl alloys with (a) 1%, (b) 3%, (c) 7%, (d) 15% FeeTi anti-site disordering (achieved by the KKR-CPA method).
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Fig. 7. The curves of total and local atomic magnetic moments versus the degree of the FeeTi anti-site disordering. The red solid circles represent the ferromagnetic zone and the blue solid circles represent the ferrimagnetic zone. The solid lines represent the linear fitting. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
observe the PDOS of Fe and Ti at the anti-site, respectively. It can be found that both Fe and Ti atoms show a 100% spin polarization at the Fermi level in all the CFTA alloys. The Fermi level always lies in a band gap in the “minority-spin” channel and has a metallic intersection with the bands in the “majority-spin” channel for the Fe and Ti atoms at the anti-site. Further, it should be noted that the “majority-spin” channel is the spin-up channel for both the Fe and Ti atoms at the anti-site in the CFTA alloys with 1% and 7% F-TAD. So, the spin polarization of the CFTA alloys with 1% and 7% F-TAD is still up to 100% at the Fermi level. But in CFTA alloys with 3% and 15% FTAD, the “majority-spin” channel is the spin-up channel for the Fe atom and the spin-down channel for the Ti atom. From the magnetic point of view, the magnetic moment of Ti is parallel to that of Fe (ferromagnetic coupling) in CFTA alloys with 1% and 7% F-TAD but the magnetic moment of Ti is antiparallel to that of Fe
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(antiferromagnetic coupling) in the CFTA alloys with 3% and 15% FTAD. In other words, the magnetic coupling interaction has an oscillating variation with the increasing degree of FeeTi anti-site disordering in the CFTA alloys. In CFTA alloys with the F-TAD, the magnetic situation is similar to the conventional diluted magnetic semiconductor and the only difference is that the magnetic carriers are the Fe and Ti atoms at the anti-site in CFTA alloy and the introduced magnetic dopant atoms in the conventional diluted semiconductor. The oscillating variation of the magnetic coupling interaction has also been observed in many conventional diluted magnetic semiconductors and is usually explained by the RudermaneKitteleKasuyaeYosida (RKKY) model [45,46]. In addition, it should be noted that it is the antiferromagnetic exchange interaction between Fe and Ti atoms that leads to some DOS in the majority-spin channel of the Ti atom filling in the band gap of the spin-down channel for the CFTA alloys with 3% and 15% F-TAD. So, the spin polarization at the Fermi level is not 100% anymore for the CFTA alloys with 3% and 15% F-TAD. Fig. 7 shows the relationships of total and local atomic magnetic moments versus the degree of the F-TAD. Each curve is divided into two parts to discuss. One part is ferromagnetic zone (ferromagnetic coupling occurs between Fe and Ti, represented by red solid circle) and the other one is ferrimagnetic zone (antiferromagnetic coupling occurs between Fe and Ti, represented by blue solid circle). The solid lines represent the linear fitting. From Fig. 7, it can be seen that the total magnetic moment linearly increases with the increasing degree of the F-TAD both in ferromagnetic and ferrimagnetic zone. The incremental rate of total magnetic moment in ferromagnetic state is higher than that in ferrimagnetic zone. The magnetic moment of Fe (Ti) linearly decreases from 3.8 (0.96) to 3.71 (0.88) mB when the degree of the F-TAD increases from 1% to 10% in ferromagnetic zone. In ferrimagnetic zone, the magnetic moment of Fe (Ti) linearly decreases from 3.78 (0.85) to 3.68 (0.63) mB when the degree of the F-TAD increases from 3% to 15%. So, it is clear that the increase of the total magnetic moment is derived from the increase in the number of the anti-site atoms instead of the local atomic magnetic moments. In addition, it should be noted that at the inflection point from the ferromagnetic
Fig. 8. (a) The calculated TDOS plots by the KKR-CPA method for CoFeTiAl alloy with 1%, 5%, 10% and 15% CoeTi anti-site disordering. (b) The calculated PDOS plots by the KKR-CPA method for CoFeTiAl alloy with 5% CoeTi anti-site disordering.
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to ferrimagnetic zone, all the local atomic magnetic moments have an abrupt change. The magnetic moment of Fe atom in ferrimagnetic zone is larger than that in ferromagnetic zone but the situation is opposite for Ti atom. The abrupt change in local atomic magnetic moment leads to the abrupt change in the total magnetic moment. Fig. 8(a) shows the TDOS patterns of CFTA with the different degree of C-TAD. From these TDOS patterns, we can see that all the cases are similar in the shape and effect of the C-TAD when the content of CoeTi antisite is in the 1%e15% range. The DOS at the Fermi level increases with the increasing degree of the C-TAD. For all the CFTA alloys with the different degree of the C-TAD, the TDOS is asymmetric in the spin-up and the spin-down channel, which indicates that the material is in magnetic ground state. However, it is different from the cases with the F-TAD, the CFTA alloys with the C-TAD show a low spin polarization at the Fermi level. In spin-up channel, the band gap of the matrix was filled in by a small and flat peak of DOS as well as the band gap is kept in spin-down channel. However, the Fermi level does not fall within the band gap in the spin-down channel anymore. So, the CFTA alloys with the C-TAD are not the half-metallic materials with a 100% conduction electron spin polarization. In order to make the origin of DOS at the Fermi level clear, as a typical case, the PDOS patterns of the CFTA alloy with 5% CoeTi C-TAD are shown in Fig. 8(b). It is clear that the DOS in the band gap of the matrix mainly originates from the Co and Ti atoms at the anti-site and partly the Fe atom of the matrix in the spin-up channel. In the spin-down channel, the Fermi level shifts towards the higher energy away from the band gap and has an intersection with a high DOS peak of the anti-site Ti and Co atoms, which makes the CFTA alloys with the C-TAD have a low spin-polarization at the Fermi level. In addition, from the PDOS patterns, it can be found that the Co atom at the anti-site has a large spin splitting and a magnetic moment of 2.98 mB. The Ti atom at the anti-site has a small spin splitting and a magnetic moment of 0.19 mB. It should be noted that the magnetic moment of Ti atom is antiparallel to that of Co atom and the material is in ferrimagnetic state. In fact, our calculated results show that the magnetic moment of the Ti atom is antiparallel to that of Co atom in all the CFTA alloys with 1%e15% C-TAD. Fig. 9 shows the curves of total and local atomic magnetic moments versus the degree of C-TAD. From Fig. 9, it can be seen that
the total magnetic moment linearly increases with the increasing degree of the C-TAD. The magnetic moment of Co linearly decreases from 3.01 to 2.92 mB but the magnetic moment of Ti linearly increases from 0.16 to 0.25 mB when the degree of C-TAD increases from 1% to 15%. So, it is clear that the change of local atomic moments is to reduce the total magnetic moment with the increasing degree of C-TAD. The increase of the total magnetic moment is derived from the increase in the number of the anti-site atoms instead of the local atomic magnetic moments which is similar to FTAD. 4. Conclusions We predict that the ordered LiMgPdSb-type CFTA alloy is a nonmagnetic semiconductor with a direct band gap. The C-FAD has no effect on the semiconductive characteristics and the magnetic properties. Without any magnetic dopant element, only the F-TAD and C-TAD can generate the spin splitting of Fe, Co and Ti at the anti-site and make them become magnetic atoms in CFTA alloy. The CFTA alloys with the F-TAD and C-TAD are the diluted magnetic semiconductors. Especially, the CFTA alloys with the F-TAD have a half-metallicity with 100% spin polarization of conductive electrons. Since the magnetic atoms come from the anti-site disordering instead of the introduction of the additional elements, the diluted magnetic CFTA alloy with the anti-site disordering is highly matched to the ordered semiconductive CFTA alloy in both the lattice parameter and the electronic structure, which is quite advantageous to the practical application. Nonequilibrium heat treatment or preparation methods, such as quenching and melt-spin method, are usually able to induce the occurrence of anti-site disordering. The driving force of C-TAD and F-TAD is far less than the C-TAD. So, it is possible to induce the CFAD and F-TAD and simultaneously to avoid the C-TAD. Fortunately, the C-FAD has no effect on the semiconductive characteristics and magnetic properties and the F-TAD generates a 100% spin polarization of conductive electrons and a large magnetic moment. We predict that the CFTA alloys with the C-FAD and F-TAD can be achieved in experiment and are a series of diluted magnetic semiconductors with a 100% spin polarization. Acknowledgments This work was supported by National Natural Science Foundation of China (Grant No. 51271071), the Basic and Frontier Research Project of Chongqing City (No. cstc2013jjB50001), Chongqing City Funds for Distinguished Young Scientists (No. cstc2014jcyjjq50003). One of the authors (G.D. Liu) acknowledges the financial support from Hebei Province Program for Top Young Talents. References
Fig. 9. The curves of total and local atomic magnetic moments versus the degree of the CoeTi anti-site disordering. The red solid circles represent the calculated data. The solid lines represent the linear fitting. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
[1] R.A. de Groot, F.M. Mueller, P.G. van Engen, K.H.J. Buschow, Phys. Rev. Lett. 50 (1983) 2024. [2] K. Ullakko, J.K. Huang, C. Kantner, R.C. O'Handley, V.V. Kokorin, Appl. Phys. Lett. 69 (1996) 1966e1968. [3] S. Chadov, X.L. Qi, J. Kübler, G.H. Fecher, C. Felser, S.C. Zhang, Nat. Mater. 9 (2010) 541. [4] S. Ouardi, G.H. Fecher, C. Felser, J. Kübler, Phys. Rev. Lett. 110 (2013) 100401. [5] F. Bonell, S. Andrieu, C. Tiusan, F. Montaigne, E. Snoeck, B. Belhadji, L. Calmels, vre, A. Taleb-Ibrahimi, Phys. Rev. B 82 (2010) 092405. F. Bertran, P.L. Fe [6] H. Liu, Y. Honda, K. Matsuda, M. Arita, T. Uemura, M. Yamamoto, Jpn. J. Appl. Phys. 51 (2012) 093004. [7] T. Scheike, H. Sukegawa, T. Furubayashi, Z. Wen, K. Inomata, T. Ohkubo, K. Hono, S. Mitani, Appl. Phys. Lett. 105 (2014) 242407. [8] J. Tobola, J. Pierre, S. Kaprzyk, R.V. Skolozdra, M.A. Kouacou, J. Phys. Condens. Matter 10 (1998) 1013. [9] Y. Nishino, M. Kato, S. Asano, K. Soda, M. Hayasaki, U. Mizutani, Phys. Rev. Lett. 79 (1997) 1909.
T.T. Lin et al. / Journal of Alloys and Compounds 657 (2016) 519e525 [10] A. Slebarski, M.B. Maple, E.J. Freeman, C. Sirvent, D. Tworuszka, M. Orzechowska, A. Wrona, A. Jezierski, S. Chiuzbaian, M. Neumann, Phys. Rev. B 62 (2000) 3296. [11] S.V. Dordevic, D.N. Basov, A. Slebarski, M.B. Maple, L. Degiorgi, Phys. Rev. B 66 (2002) 075122. [12] S. Yabuuchi, M. Okamoto, A. Nishide, Y. Kurosaki, J. Hayakawa, Appl. Phys. Exp. 6 (2013) 025504. [13] C. Venkatesh, V. Srinivas, V.V. Rao, S.K. Srivastava, P.S. Babu, J. Alloys Compd. 577 (2013) 417. [14] C. Venkatesh, S.K. Srivastava, V.V. Rao, Physica B 448 (2014) 237e243. [15] M. Mikami, K. Kobayashi, T. Kawada, K. Kubo, N. Uchiyama, Jpn. J. Appl. Phys. 47 (2008) 1512. [16] M. Mikami, K. Kobayashi, T. Kawada, K. Kubo, N. Uchiyama, J. Electron. Mater. 38 (2009) 1121. [17] Y. Nishino, H. Kato, M. Kato, U. Mizutani, Phys. Rev. B 63 (2001) 233303. [18] M. Vasundhara, V. Srinivas, V.V. Rao, Phys. Rev. B 77 (2008) 224415. [19] Y. Nishino, S. Deguchi, U. Mizutani, Phys. Rev. B 74 (2006) 115115. [20] C.S. Lue, C.F. Chen, J.Y. Lin, Y.T. Yu, Y.K. Kuo, Phys. Rev. B 75 (2007) 064204. [21] K. Soda, S. Harada, M. Kato, S. Yagi, Y. Sandaiji, Y. Nishino, IOP Conf. Ser. Mater. Sci. Eng. 18 (2011) 142004. [22] M. Vasundhara, V. Srinivas, V.V. Rao, T.V.C. Rao, IEEE Trans. Magn. 42 (2006) 3105e3107. [23] T. Graf, C. Felser, S.S.P. Parkin, Prog. Solid State Chem. 39 (2011) 1. [24] F. Casper, T. Graf, S. Chadov, B. Balke, C. Felser, Semicond. Sci. Technol. 27 (2012) 063001. [25] K. Bartholome, B. Balke, D. Zuckermann, J. Electron. Mater. 43 (2014) 1775. [26] X. Dai, G. Liu, G.H. Fecher, C. Felser, Y. Li, H. Liu, J. Appl. Phys. 105 (2009) 07E901. € an, E. S¸as¸ıog lu, Appl. Phys. Lett. 103 (2013) 142404. [27] I. Galanakis, K. Ozdo g
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[28] G.Y. Gao, Lei Hu, K.L. Yao, Bo Luo, N. Liu, J. Alloys Compd. 551 (2013) 539. € an, E. S¸as¸ıog lu, I. Galanakis, J. Appl. Phys. 113 (2013) 193903. [29] K. Ozdo g [30] G.Z. Xu, E.K. Liu, Y. Du, G.J. Li, G.D. Liu, W.H. Wang, G.H. Wu, Eur. Phys. Lett. 102 (2013) 17007. [31] S. Berri, D. Maouche, M. Ibrir, F. Zerarga, J. Magn. Magn. Mater. 354 (2014) 65. [32] L. Xiong, L. Yi, G.Y. Gao, J. Magn. Magn. Mater. 360 (2014) 98. [33] Y.J. Zhang, Z.H. Liu, G.T. Li, X.Q. Ma, G.D. Liu, J. Alloys Compd. 616 (2014) 449e453. [34] L. Basit, G.H. Fecher, S. Chadov, B. Balke, C. Felser, Eur. J. Inorg. Chem. (2011) 3950e3954. [35] H. Katayama, K. Terakura, J. Kanamori, Solid State Commun. 29 (5) (1979) 431e434. [36] S. Blugel, H. Akai, R. Zeller, P.H. Dederichs, Phys. Rev. B 35 (7) (1987) 3271e3283. [37] S. Kaprzyk, A. Bansil, Phys. Rev. B 42 (12) (1990) 7358. [38] H. Akai, Hyperfine Interact. 68 (1) (1992) 3e14. [39] M. Ogura, H. Akai, Appl. Phys. Lett. 91 (25) (2007) 253118. [40] H. Akai, see http://sham.phys.sci.osaka-u.ac.jp/kkr for program's code of KKRCPA-LDA. [41] H. Akai, Phys. Rev. Lett. 81 (1998) 3002. [42] P.E. Blochl, O. Jepsen, O.K. Andersen, Phys. Rev. B 49 (23) (1994) 16223e16233. [43] M.C. Payne, M.P. Teter, D.C. Allan, T.A. Arias, J.D. Joannopoolous, Rev. Mod. Phys. 64 (1992) 1065. [44] M.D. Segall, P.L.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, M.C. Payne, J. Phys. Condens. Matter 14 (2002) 2717. [45] C. Zener, Phys. Rev. 81 (1951) 440. [46] T. Dietl, et al., Science 287 (2000) 1019.
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Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom
Anti-site-induced diluted magnetism in semiconductive CoFeTiAl alloy T.T. Lin a, b, X.F. Dai a, L.Y. Wang a, X.T. Wang a, X.F. Liu c, Y.T. Cui b, G.D. Liu a, b, * a
School of Material Sciences and Engineering, Hebei University of Technology, Tianjin, 300130, PR China School of Physics and Electronic Engineering, Chongqing Normal University, Chongqing, 400044, PR China c Department of Materials Science and Engineering, The University of Tennessee, Knoxville, TN37996, USA b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 7 July 2015 Received in revised form 11 October 2015 Accepted 16 October 2015 Available online 19 October 2015
The spin-polarized electronic band structure calculations are carried out to theoretically investigate the effect of anti-site disordering to the electronic band structure and magnetic properties of LiMgPdSb-type CoFeTiAl alloy. We found that the CoeTi and FeeTi antisite disordering can induce the diluted magnetism in CoFeTiAl alloy. Especially, the FeeTi antisite disordering can induce a 100% spin polarization at the Fermi level at a certain degree of anti-site disordering. The CoeFe antisite disordering is easy to occur in CoFeTiAl alloy but has little effect on the semiconductive characteristic and magnetic properties. The Co, Fe and Ti atoms at the anti-site contribute the magnetization in CoFeTiAl alloy. The diluted magnetism in CoFeTiAl alloy can be induced by the anti-site disordering instead of the introduction of magnetic dopant elements. © 2015 Elsevier B.V. All rights reserved.
Keywords: Heusler alloy Diluted magnetic semiconductor Anti-site Electronic band structure calculation
1. Introduction Heusler alloys have been intensively investigated in both experiment and theory because many attractive materials have been found in these alloys, like half-metal [1], shape memory alloy [2], topological insulator [3] and spin gapless semiconductor [4] etc. Especially, the half-metals are the most suitable materials to many spintronics devices, such as giant magnetoresistance (GMR), tunneling magnetoresistance (TMR) and spin-injecting devices etc. due to their 100% spin-polarization of conductive electrons. However, in practical applications, the lattice mismatch and the electronic mismatch usually lead to the destruction of high spin polarization [5e7]. For example, Bonell et al. [5] demonstrate the strong influence of mismatch dislocations and show that reducing their density strongly enhances the TMR. So, it is required to reduce the mismatch between the semiconductor/normal metal layer and the magnetic material layer as far as possible. The half-metals with Heusler structure are very mismatched to the current typical semiconductors in the lattice and the electronic structure. So, an important work is to search for highly-matched semiconductor and half-metallic materials with Heusler structure. In the past decades,
* Corresponding author. Building 8, 1st Road, DingZiGu Hongqiao Zone, Tianjin, PR China. Tel./fax: þ86 26564070. E-mail address: [email protected] (G.D. Liu). http://dx.doi.org/10.1016/j.jallcom.2015.10.131 0925-8388/© 2015 Elsevier B.V. All rights reserved.
dozens of highly spin-polarized materials have been found in Heusler alloys, but only a small number of semiconductors were reported. Up to now, the semiconductors with Heusler structure reported are CoTiSb, NiTiSn, CoNbSn [8], Fe2VAl [9], Fe2TiSn [10,11] and Fe2TiSi [12]. The work on these materials is mainly focused on the thermoelectricity and the diluted magnetic properties [13e25]. The ternary Heusler alloys have been investigated massively. Since Dai et al. [26] investigated the electronic structures, crystal structure and magnetic properties of the quaternary CoFeMnSi in 2009, the field of quaternary Heusler alloys has received great € an et al. [29] attraction by scientific researchers [27e32]. Ozdo g studied dozens of quaternary Heusler alloys and found some halfmetals, some spin-gapless semiconductors and some magnetic semiconductors. Zhang et al. [33] calculated the band gap and magnetism of CoFeTiZ (Z ¼ Si, Ge, Sn) alloy and showed that CoFeTiSi and CoFeTiGe alloys are both typically half-metallic ferrimagnets and CoFeTiSn is a quasi-half-metallic ferrimagnet. However, these quaternary Heusler alloys are mostly not synthesized in experiment. In 2011, Basit et al. [34] synthesized the quaternary CoFeTiAl (CFTA) alloy with LiMgPdSb-type structure and investigated the structure and the magnetic properties of CoFe1þXTi1XAl alloys in experiment. But the investigations on the detailed electronic structures and the effect of anti-site disordering on the electronic structure are absent. In this paper, we will focus on the CFTA and mainly investigate
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the effect of anti-site disordering on the electronic structure by first-principle calculations. A series of half-metallic diluted magnetic semiconductors generated by anti-site disordering will be predicted based on our calculated results. 2. Computational details The KorringaeKohneRostoker method combined with the coherent potential approximation and the local density approximation (KKR-CPA-LDA method) is a high-speed, high-precision and powerful method to carry out the first-principle calculations for disordered systems [35e39]. In this paper, the density of states (DOS) patterns and magnetic properties were calculated using the spin-polarized KKR-CPA-LDA method [40,41] for the CFTA alloys with various anti-site disordering. In the calculations, sixty k points in the irreducible Brillouin zone were adjusted to achieve selfconsistency. The convergence tolerance is 0.1 mRy for the total energy. The muffin-tin sphere radii of 2.3 a.u. were used for all the atoms. The density of states was achieved by the tetrahedral integration method [42]. The band structures of the perfectly ordered CFTA alloy were calculated by the CASTEP package [43,44]. 3. Results and discussion The LiMgPdSb-type CFTA structure model is shown in Fig. 1. The structure is composed of four face-centered-cubic sublattices interpenetrating along the space diagonal. In the Wyckoff coordinates, Co atoms occupy the A(0,0,0) site, Fe atoms occupy the C(1/2,1/2,1/2) site, Ti atoms occupy the B(1/4,1/4,1/4) site and Al atoms occupy the D(3/4,3/4,3/4) site. We use “x% (0 < x 15) CoeFe anti-site” to represent the exchange of x% of Co at A sites and x% of Fe at C sites. The same expression is also applied to CoeTi and FeeTi anti-site disordering. The abbreviations of C-FAD, C-TAD and F-TAD represent the CoeFe, CoeTi and FeeTi anti-site disordering, respectively. The equilibrium lattice parameter of the LiMgPdSbtype CFTA alloys with different anti-site disordering is firstly calculated by minimizing the total energy using KKR-CPA method. The ordered CFTA alloy is considered by 0% anti-site disordering. The equilibrium lattice parameter of the ordered CFTA alloy is 5.84 Å, which is slightly less than 5.85 Å obtained from the X-ray diffraction patterns measured at room temperature [34]. It is reasonable to attribute the slight difference between the theoretical and the experimental result to the measurement error or
thermal expansion. In addition, our calculated results indicate that the equilibrium lattice parameters are almost the same as for the ordered case for all the CFTA alloys with different anti-site disordering. So, the lattice parameter of 5.84 Å is used to calculate the DOS patterns, band structures and magnetic properties for all the CFTA alloys with different anti-site disordering. In order to observe clearly the electronic properties, the CASTEP code is firstly used to calculate the band structures of the ordered LiPbMgSn-type CFTA alloy since the KKR-CPA method does not work to give the band structure. The achieved band structures are shown in Fig. 2(a). It is clear that the ordered LiPbMgSn-type CFTA alloy is a semiconductor with a direct band gap of about 0.2 eV. Fig. 2(b) shows the total DOS (TDOS) patterns calculated by CASTEP and KKR-CPA method, respectively. It can be seen that these two TDOS patterns are quite consistent in the shape and the distribution of DOS. The only difference is that the band gap width achieved by KKR-CPA method is smaller than that by CASTEP. Although these two theoretical methods are slightly different in the prediction of the band gap width, the calculated results by both these methods indicate that the ordered CFTA alloy is a semiconductor. Fig. 3 shows the curves of the total energy versus the degree of anti-site disordering for the CFTA alloy with C-FAD, C-TAD and FTAD. It can be seen that the total energy increases linearly with the increasing x for the CFTA alloy with F-TAD and C-TAD. The incremental intensity is 3 meV and 4.2 meV per 1%. For the C-FAD case, the total energy nonlinearly and monotonously increases with the increasing x. The incremental intensity is less than 0.12 meV per 1% in the whole calculation range, which is far less than that generated by the C-TAD and F-TAD. At the same time, the total energies of the CFTA alloys with the CoeFe anti-site disordering are quite close to that of the ordered CFTA alloy and always lower than those with the CoeTi and FeeTi anti-site disordering. These are all signs that the CoeFe anti-site disordering is easy to occur and the CoeTi anti-site disordering should rarely occur in the CFTA alloy. The electronic structures of the CFTA alloys with 1e15% CFAD are calculated. Several typical DOS patterns are shown in Fig. 4(a). From Fig. 4(a), it can be seen that all the CFTA alloys with CoeFe anti CFAD are in a nonmagnetic ground state. The DOS and the band gap near the Fermi level is hardly affected by the CFAD. More clearly, the difference of total DOS between the ordered CFTA alloy and the CFTA alloys with the CFAD are shown in Fig. 4(b). It can be seen that the difference of total DOS is almost zero in the range of 0.2 eV near the Fermi level. So, it is clear that the CFAD has no influence on the semiconductive characteristic of the ordered CFTA matrix. Since all the DOS patterns of the CFTA alloys with 1e15% CFAD are quite
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Fig. 1. Crystal structure of LiMgPdSb-type CoFeTiAl alloy. Co atoms occupy the A(0,0,0) site, Fe atoms occupy the C(1/2,1/2,1/2) site, Ti atoms occupy the B(1/4,1/4,1/4) site and Al atoms occupy the D(3/4,3/4,3/4) site.
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Fig. 2. (a) Band structure achieved by the CASTEP code, (b) the total DOS (TDOS) patterns achieved by the CASTEP code and (c) the TDOS patterns achieved by the KKRCPA method for the ordered LiPbMgSn-type CoTiFeAl alloy.
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The degree of anti-site disordering (x%) Fig. 3. The curves of the total energy versus the degree of anti-site disordering for the CoFeTiAl alloy with CoeFe, CoeTi and FeeTi anti-site disordering. The x represents to exchange x% of the atom number at a sublattice site and those at another sublattice site. The total energy of the ordered CoFeTiAl alloy was set as the zero point of Y axis.
similar, the PDOS of CFTA alloy with 5% CFAD is taken as a representative to illustrate the effect of anti-site atoms as shown in Fig. 4(c). From Fig. 4(c), it can be seen that although the DOS of Co and Fe atoms at the anti-site are different from the Co and Fe atom at the normal site, they still have no spin splitting. The main difference between the anti-site and the normal atoms is the distribution of DOS in the energy. For the Co atom at the anti-site, the DOS is more concentrated in the range of 1 ~ 3 eV and the
Fig. 5. The TDOS patterns of CoFeTiAl alloys with 1%, 3%, 7%, 10% and 15% FeeTi antisite disordering (achieved by the KKR-CPA method).
highest peak of DOS occurs at about 1.2 eV which is closer to the Fermi level than 2.0 eV where the highest peak of DOS of the normal Co atom occurs. For the Fe atom at the anti-site, the DOS is more dispersed in the range of 0.2 ~ 2.8 eV and the highest peak of DOS occurs at about 0.4 eV which is closer to the Fermi level than 0.9 eV where the highest peak of DOS of the normal Fe atom occurs. More importantly, it should be noted that both the Co and
Fig. 4. (a) The calculated TDOS plots by the KKR-CPA method for CoFeTiAl alloy with 1%, 5% and 10% CoeFe anti-site disordering. (b) The difference curves of TDOS (The TDOS of the CoFeTiAl alloys with anti-site disordering minus the TDOS of the ordered CoFeTiAl alloy). (c) The calculated total DOS and PDOS plots by the KKR-CPA method for CoTiFeAl alloy with 5% CoeFe anti-site disordering.
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Fe atoms at the anti-site do not generate any impurity band in the band gap of the matrix. So, the semiconductive band gap is kept in the CFTA alloys with the CFAD. Further, we can conclude that although the CFAD is easy to occur in CFTA alloy due to the small driving energy, it does neither destroy the semiconductivity nor contribute to the magnetization. So, the CFAD has little influence on carrier concentration and spin-polarization. Fig. 5 shows the total DOS patterns of CFTA alloys with the different degree of the F-TAD. From Fig. 5, it can be seen that the CFTA alloys show a half-metallicity and the spin polarization is up to 100% at the Fermi level when the degree of the F-TAD is lower than 2% or between 4% and 10% (x 2 or 4 x 10). Specifically, the Fermi level lies in a band gap in spin-down channel and has a metallic intersection with the energy bands in spin-up channel. In addition, it can be found that the DOS at the Fermi level increases with the increasing degree of the F-TAD, which implies that we can adjust the concentration of the conductive electron with 100% spin
polarization by changing the degree of the F-TAD. However, when the degree of the F-TAD is between 2% and 4% or higher than 10% (2 < x < 4 or 10 < x), the band gap at the Fermi level in spin-down channel is filled in by some impurity bands. In such a situation, the CFTA alloys become ordinary metals and the spin polarization at the Fermi level also becomes very low. In order to find out why the electronic structures at the Fermi level are different in the different disordering degree, the PDOS patterns are shown in Fig. 6 for the CFTA alloys with 1%, 3%, 7% and 15% F-TAD. It can be seen that both Fe and Ti atoms at the anti-site have a large spin splitting for all the CFTA alloys and the Fe and Ti atoms at the normal site are still in nonmagnetic state. Further, it can also be seen that the Fe and Ti atoms at the anti-site generate the impurity bands in the band gap of the matrix. The performance of the impurity bands in DOS patterns is just that a peak of DOS occurs in the band gap. So, the more Fe and Ti atoms at the anti-site, the higher peak of DOS in the band gap. More carefully, let us
Fig. 6. The PDOS patterns of CoFeTiAl alloys with (a) 1%, (b) 3%, (c) 7%, (d) 15% FeeTi anti-site disordering (achieved by the KKR-CPA method).
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Fig. 7. The curves of total and local atomic magnetic moments versus the degree of the FeeTi anti-site disordering. The red solid circles represent the ferromagnetic zone and the blue solid circles represent the ferrimagnetic zone. The solid lines represent the linear fitting. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
observe the PDOS of Fe and Ti at the anti-site, respectively. It can be found that both Fe and Ti atoms show a 100% spin polarization at the Fermi level in all the CFTA alloys. The Fermi level always lies in a band gap in the “minority-spin” channel and has a metallic intersection with the bands in the “majority-spin” channel for the Fe and Ti atoms at the anti-site. Further, it should be noted that the “majority-spin” channel is the spin-up channel for both the Fe and Ti atoms at the anti-site in the CFTA alloys with 1% and 7% F-TAD. So, the spin polarization of the CFTA alloys with 1% and 7% F-TAD is still up to 100% at the Fermi level. But in CFTA alloys with 3% and 15% FTAD, the “majority-spin” channel is the spin-up channel for the Fe atom and the spin-down channel for the Ti atom. From the magnetic point of view, the magnetic moment of Ti is parallel to that of Fe (ferromagnetic coupling) in CFTA alloys with 1% and 7% F-TAD but the magnetic moment of Ti is antiparallel to that of Fe
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(antiferromagnetic coupling) in the CFTA alloys with 3% and 15% FTAD. In other words, the magnetic coupling interaction has an oscillating variation with the increasing degree of FeeTi anti-site disordering in the CFTA alloys. In CFTA alloys with the F-TAD, the magnetic situation is similar to the conventional diluted magnetic semiconductor and the only difference is that the magnetic carriers are the Fe and Ti atoms at the anti-site in CFTA alloy and the introduced magnetic dopant atoms in the conventional diluted semiconductor. The oscillating variation of the magnetic coupling interaction has also been observed in many conventional diluted magnetic semiconductors and is usually explained by the RudermaneKitteleKasuyaeYosida (RKKY) model [45,46]. In addition, it should be noted that it is the antiferromagnetic exchange interaction between Fe and Ti atoms that leads to some DOS in the majority-spin channel of the Ti atom filling in the band gap of the spin-down channel for the CFTA alloys with 3% and 15% F-TAD. So, the spin polarization at the Fermi level is not 100% anymore for the CFTA alloys with 3% and 15% F-TAD. Fig. 7 shows the relationships of total and local atomic magnetic moments versus the degree of the F-TAD. Each curve is divided into two parts to discuss. One part is ferromagnetic zone (ferromagnetic coupling occurs between Fe and Ti, represented by red solid circle) and the other one is ferrimagnetic zone (antiferromagnetic coupling occurs between Fe and Ti, represented by blue solid circle). The solid lines represent the linear fitting. From Fig. 7, it can be seen that the total magnetic moment linearly increases with the increasing degree of the F-TAD both in ferromagnetic and ferrimagnetic zone. The incremental rate of total magnetic moment in ferromagnetic state is higher than that in ferrimagnetic zone. The magnetic moment of Fe (Ti) linearly decreases from 3.8 (0.96) to 3.71 (0.88) mB when the degree of the F-TAD increases from 1% to 10% in ferromagnetic zone. In ferrimagnetic zone, the magnetic moment of Fe (Ti) linearly decreases from 3.78 (0.85) to 3.68 (0.63) mB when the degree of the F-TAD increases from 3% to 15%. So, it is clear that the increase of the total magnetic moment is derived from the increase in the number of the anti-site atoms instead of the local atomic magnetic moments. In addition, it should be noted that at the inflection point from the ferromagnetic
Fig. 8. (a) The calculated TDOS plots by the KKR-CPA method for CoFeTiAl alloy with 1%, 5%, 10% and 15% CoeTi anti-site disordering. (b) The calculated PDOS plots by the KKR-CPA method for CoFeTiAl alloy with 5% CoeTi anti-site disordering.
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to ferrimagnetic zone, all the local atomic magnetic moments have an abrupt change. The magnetic moment of Fe atom in ferrimagnetic zone is larger than that in ferromagnetic zone but the situation is opposite for Ti atom. The abrupt change in local atomic magnetic moment leads to the abrupt change in the total magnetic moment. Fig. 8(a) shows the TDOS patterns of CFTA with the different degree of C-TAD. From these TDOS patterns, we can see that all the cases are similar in the shape and effect of the C-TAD when the content of CoeTi antisite is in the 1%e15% range. The DOS at the Fermi level increases with the increasing degree of the C-TAD. For all the CFTA alloys with the different degree of the C-TAD, the TDOS is asymmetric in the spin-up and the spin-down channel, which indicates that the material is in magnetic ground state. However, it is different from the cases with the F-TAD, the CFTA alloys with the C-TAD show a low spin polarization at the Fermi level. In spin-up channel, the band gap of the matrix was filled in by a small and flat peak of DOS as well as the band gap is kept in spin-down channel. However, the Fermi level does not fall within the band gap in the spin-down channel anymore. So, the CFTA alloys with the C-TAD are not the half-metallic materials with a 100% conduction electron spin polarization. In order to make the origin of DOS at the Fermi level clear, as a typical case, the PDOS patterns of the CFTA alloy with 5% CoeTi C-TAD are shown in Fig. 8(b). It is clear that the DOS in the band gap of the matrix mainly originates from the Co and Ti atoms at the anti-site and partly the Fe atom of the matrix in the spin-up channel. In the spin-down channel, the Fermi level shifts towards the higher energy away from the band gap and has an intersection with a high DOS peak of the anti-site Ti and Co atoms, which makes the CFTA alloys with the C-TAD have a low spin-polarization at the Fermi level. In addition, from the PDOS patterns, it can be found that the Co atom at the anti-site has a large spin splitting and a magnetic moment of 2.98 mB. The Ti atom at the anti-site has a small spin splitting and a magnetic moment of 0.19 mB. It should be noted that the magnetic moment of Ti atom is antiparallel to that of Co atom and the material is in ferrimagnetic state. In fact, our calculated results show that the magnetic moment of the Ti atom is antiparallel to that of Co atom in all the CFTA alloys with 1%e15% C-TAD. Fig. 9 shows the curves of total and local atomic magnetic moments versus the degree of C-TAD. From Fig. 9, it can be seen that
the total magnetic moment linearly increases with the increasing degree of the C-TAD. The magnetic moment of Co linearly decreases from 3.01 to 2.92 mB but the magnetic moment of Ti linearly increases from 0.16 to 0.25 mB when the degree of C-TAD increases from 1% to 15%. So, it is clear that the change of local atomic moments is to reduce the total magnetic moment with the increasing degree of C-TAD. The increase of the total magnetic moment is derived from the increase in the number of the anti-site atoms instead of the local atomic magnetic moments which is similar to FTAD. 4. Conclusions We predict that the ordered LiMgPdSb-type CFTA alloy is a nonmagnetic semiconductor with a direct band gap. The C-FAD has no effect on the semiconductive characteristics and the magnetic properties. Without any magnetic dopant element, only the F-TAD and C-TAD can generate the spin splitting of Fe, Co and Ti at the anti-site and make them become magnetic atoms in CFTA alloy. The CFTA alloys with the F-TAD and C-TAD are the diluted magnetic semiconductors. Especially, the CFTA alloys with the F-TAD have a half-metallicity with 100% spin polarization of conductive electrons. Since the magnetic atoms come from the anti-site disordering instead of the introduction of the additional elements, the diluted magnetic CFTA alloy with the anti-site disordering is highly matched to the ordered semiconductive CFTA alloy in both the lattice parameter and the electronic structure, which is quite advantageous to the practical application. Nonequilibrium heat treatment or preparation methods, such as quenching and melt-spin method, are usually able to induce the occurrence of anti-site disordering. The driving force of C-TAD and F-TAD is far less than the C-TAD. So, it is possible to induce the CFAD and F-TAD and simultaneously to avoid the C-TAD. Fortunately, the C-FAD has no effect on the semiconductive characteristics and magnetic properties and the F-TAD generates a 100% spin polarization of conductive electrons and a large magnetic moment. We predict that the CFTA alloys with the C-FAD and F-TAD can be achieved in experiment and are a series of diluted magnetic semiconductors with a 100% spin polarization. Acknowledgments This work was supported by National Natural Science Foundation of China (Grant No. 51271071), the Basic and Frontier Research Project of Chongqing City (No. cstc2013jjB50001), Chongqing City Funds for Distinguished Young Scientists (No. cstc2014jcyjjq50003). One of the authors (G.D. Liu) acknowledges the financial support from Hebei Province Program for Top Young Talents. References
Fig. 9. The curves of total and local atomic magnetic moments versus the degree of the CoeTi anti-site disordering. The red solid circles represent the calculated data. The solid lines represent the linear fitting. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
[1] R.A. de Groot, F.M. Mueller, P.G. van Engen, K.H.J. Buschow, Phys. Rev. Lett. 50 (1983) 2024. [2] K. Ullakko, J.K. Huang, C. Kantner, R.C. O'Handley, V.V. Kokorin, Appl. Phys. Lett. 69 (1996) 1966e1968. [3] S. Chadov, X.L. Qi, J. Kübler, G.H. Fecher, C. Felser, S.C. Zhang, Nat. Mater. 9 (2010) 541. [4] S. Ouardi, G.H. Fecher, C. Felser, J. Kübler, Phys. Rev. Lett. 110 (2013) 100401. [5] F. Bonell, S. Andrieu, C. Tiusan, F. Montaigne, E. Snoeck, B. Belhadji, L. Calmels, vre, A. Taleb-Ibrahimi, Phys. Rev. B 82 (2010) 092405. F. Bertran, P.L. Fe [6] H. Liu, Y. Honda, K. Matsuda, M. Arita, T. Uemura, M. Yamamoto, Jpn. J. Appl. Phys. 51 (2012) 093004. [7] T. Scheike, H. Sukegawa, T. Furubayashi, Z. Wen, K. Inomata, T. Ohkubo, K. Hono, S. Mitani, Appl. Phys. Lett. 105 (2014) 242407. [8] J. Tobola, J. Pierre, S. Kaprzyk, R.V. Skolozdra, M.A. Kouacou, J. Phys. Condens. Matter 10 (1998) 1013. [9] Y. Nishino, M. Kato, S. Asano, K. Soda, M. Hayasaki, U. Mizutani, Phys. Rev. Lett. 79 (1997) 1909.
T.T. Lin et al. / Journal of Alloys and Compounds 657 (2016) 519e525 [10] A. Slebarski, M.B. Maple, E.J. Freeman, C. Sirvent, D. Tworuszka, M. Orzechowska, A. Wrona, A. Jezierski, S. Chiuzbaian, M. Neumann, Phys. Rev. B 62 (2000) 3296. [11] S.V. Dordevic, D.N. Basov, A. Slebarski, M.B. Maple, L. Degiorgi, Phys. Rev. B 66 (2002) 075122. [12] S. Yabuuchi, M. Okamoto, A. Nishide, Y. Kurosaki, J. Hayakawa, Appl. Phys. Exp. 6 (2013) 025504. [13] C. Venkatesh, V. Srinivas, V.V. Rao, S.K. Srivastava, P.S. Babu, J. Alloys Compd. 577 (2013) 417. [14] C. Venkatesh, S.K. Srivastava, V.V. Rao, Physica B 448 (2014) 237e243. [15] M. Mikami, K. Kobayashi, T. Kawada, K. Kubo, N. Uchiyama, Jpn. J. Appl. Phys. 47 (2008) 1512. [16] M. Mikami, K. Kobayashi, T. Kawada, K. Kubo, N. Uchiyama, J. Electron. Mater. 38 (2009) 1121. [17] Y. Nishino, H. Kato, M. Kato, U. Mizutani, Phys. Rev. B 63 (2001) 233303. [18] M. Vasundhara, V. Srinivas, V.V. Rao, Phys. Rev. B 77 (2008) 224415. [19] Y. Nishino, S. Deguchi, U. Mizutani, Phys. Rev. B 74 (2006) 115115. [20] C.S. Lue, C.F. Chen, J.Y. Lin, Y.T. Yu, Y.K. Kuo, Phys. Rev. B 75 (2007) 064204. [21] K. Soda, S. Harada, M. Kato, S. Yagi, Y. Sandaiji, Y. Nishino, IOP Conf. Ser. Mater. Sci. Eng. 18 (2011) 142004. [22] M. Vasundhara, V. Srinivas, V.V. Rao, T.V.C. Rao, IEEE Trans. Magn. 42 (2006) 3105e3107. [23] T. Graf, C. Felser, S.S.P. Parkin, Prog. Solid State Chem. 39 (2011) 1. [24] F. Casper, T. Graf, S. Chadov, B. Balke, C. Felser, Semicond. Sci. Technol. 27 (2012) 063001. [25] K. Bartholome, B. Balke, D. Zuckermann, J. Electron. Mater. 43 (2014) 1775. [26] X. Dai, G. Liu, G.H. Fecher, C. Felser, Y. Li, H. Liu, J. Appl. Phys. 105 (2009) 07E901. € an, E. S¸as¸ıog lu, Appl. Phys. Lett. 103 (2013) 142404. [27] I. Galanakis, K. Ozdo g
525
[28] G.Y. Gao, Lei Hu, K.L. Yao, Bo Luo, N. Liu, J. Alloys Compd. 551 (2013) 539. € an, E. S¸as¸ıog lu, I. Galanakis, J. Appl. Phys. 113 (2013) 193903. [29] K. Ozdo g [30] G.Z. Xu, E.K. Liu, Y. Du, G.J. Li, G.D. Liu, W.H. Wang, G.H. Wu, Eur. Phys. Lett. 102 (2013) 17007. [31] S. Berri, D. Maouche, M. Ibrir, F. Zerarga, J. Magn. Magn. Mater. 354 (2014) 65. [32] L. Xiong, L. Yi, G.Y. Gao, J. Magn. Magn. Mater. 360 (2014) 98. [33] Y.J. Zhang, Z.H. Liu, G.T. Li, X.Q. Ma, G.D. Liu, J. Alloys Compd. 616 (2014) 449e453. [34] L. Basit, G.H. Fecher, S. Chadov, B. Balke, C. Felser, Eur. J. Inorg. Chem. (2011) 3950e3954. [35] H. Katayama, K. Terakura, J. Kanamori, Solid State Commun. 29 (5) (1979) 431e434. [36] S. Blugel, H. Akai, R. Zeller, P.H. Dederichs, Phys. Rev. B 35 (7) (1987) 3271e3283. [37] S. Kaprzyk, A. Bansil, Phys. Rev. B 42 (12) (1990) 7358. [38] H. Akai, Hyperfine Interact. 68 (1) (1992) 3e14. [39] M. Ogura, H. Akai, Appl. Phys. Lett. 91 (25) (2007) 253118. [40] H. Akai, see http://sham.phys.sci.osaka-u.ac.jp/kkr for program's code of KKRCPA-LDA. [41] H. Akai, Phys. Rev. Lett. 81 (1998) 3002. [42] P.E. Blochl, O. Jepsen, O.K. Andersen, Phys. Rev. B 49 (23) (1994) 16223e16233. [43] M.C. Payne, M.P. Teter, D.C. Allan, T.A. Arias, J.D. Joannopoolous, Rev. Mod. Phys. 64 (1992) 1065. [44] M.D. Segall, P.L.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, M.C. Payne, J. Phys. Condens. Matter 14 (2002) 2717. [45] C. Zener, Phys. Rev. 81 (1951) 440. [46] T. Dietl, et al., Science 287 (2000) 1019.