- Email: [email protected]
A first-principle study of half-metallic ferrimagnetism in the CoFeTiSb quaternary Heusler compound
Journal of Magnetism and Magnetic Materials 354 (2014) 65–69
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
A first-principle study of half-metallic ferrimagnetism in the CoFeTiSb quaternary Heusler compound Saadi Berri a,n, D. Maouche b, M. Ibrir c, F. Zerarga a a
Department of Physics, Faculty of Sciences, University of Setif, Algeria Laboratory for Developing New Materials and their Characterizations, University of Setif, Algeria c Department of Physics, Faculty of Sciences, University of Msila, Algeria b
art ic l e i nf o
a b s t r a c t
Article history: Received 6 February 2013 Received in revised form 28 August 2013 Available online 6 November 2013
We have performed first-principle calculations of the structural, electronic and magnetic properties of CoFeTiSb quaternary Heusler compound, using full-potential linearized augmented plane wave (FPLAPW) scheme within the GGA. Features such as the lattice constant, the bulk modulus and its pressure derivative are reported. The electronic band structures and density of states of the CoFeTiSb quaternary compound show that the spin-up electrons are metallic, but the spin-down bands have a gap of 0.53 eV, resulting in stable half-metallic ferrimagnetic behavior with a magnetic moment of 2.00mB. Published by Elsevier B.V.
Keywords: Quaternary Heusler compound Spintronics FP-LAPW
1. Introduction Heusler compounds are ternary intermetallic compounds that have the general composition X2YZ. In this class, X and Y represent d-electron transition metals, and Z denotes an sp-electrons element [1]. In recent years, Heusler compounds have been extensively studied, motivated by their gained importance due to advancements in spintronics [2–6]. In contrast to half-metallic ferromagnets (HMFs) [7], only a few Heusler compounds (all of them with a rareearth metal at the Y position) have been successfully implemented as superconductors [8]. Pd2YSn is the Heusler compound with the highest critical temperature (4.9 K) [9]. The coexistence of antiferromagnetism and superconductivity, demonstrating the manifoldness of the Heusler family, was reported for Pd2YbSn [10] and Pd2ErSn [11]. Many of the Heusler compounds have been reported to be HMFs [12,13], and several Co2-based Heusler compounds have been used as electrodes in magnetic tunnel junctions [14,15]. Ni-based quaternary Heusler ferromagnets, NiFeMnGa and NiCoMnGa, with high spin polarization have been reported very recently [16]. Özdoğan [17] performed Ultrasoft pseudopotentials method to study the electronic structure, elastic and magnetic properties of NiCoCrGa quaternary Heusler compound. Alijani et al. [18] studied theoretically electronic structure of quaternary Heusler CoFeMnZ (Z¼ Al, Ga, Si, Ge) compounds. Generally, CoFeTiSb quaternary Heusler compound crystallize in the LiMgPdSn-type crystal structure. The resulting structure has
n
Corresponding author. Tel.: þ 213 95115576; fax: þ 213 36927210. E-mail address: [email protected] (S. Berri).
0304-8853/$ - see front matter Published by Elsevier B.V. http://dx.doi.org/10.1016/j.jmmm.2013.10.044
F4-3m symmetry with Wyckoff positions Co: 4b (3/4 3/4 3/4), Fe: 4c (1/4 1/4 1/4), Ti: 4d (1/2 1/2 1/2), Sb: 4a (0 0 0). The crystal structures of these compounds are shown in Fig. 1. In the present paper, the structural, electronic and magnetic properties of CoFeTiSb quaternary Heusler compound are reported.
Fig. 1. Crystal structure of quaternary Heusler compound.
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S. Berri et al. / Journal of Magnetism and Magnetic Materials 354 (2014) 65–69
Our main goal in this work is to evaluate examine the validity of the predictions of half metallicity for CoFeTiSb quaternary Heusler compound. The calculations are performed using ab initio full-potential linearized augmented plane wave (FP-LAPW) within the density functional theory DFT with the generalized gradient approximation GGA. Our paper is organized as follows. The theoretical background is presented in Section 2. Results and discussion are presented in Section 3. A summary of the results is given in Section 4.
2. Method of calculations
Fig. 2. Volume optimization for the CoFeTiSb quaternary Heusler compound.
We have carried out first-principles calculations [19,20] with both full potential and linear augmented plane wave (FP-LAPW) method [21] as implemented in the WIEN2k code [22] within the density functional theory (DFT). The Perdew–Burke–Ernzerhof generalized gradient approximation GGA [23,24]. In the calculations reported here, we use a parameter RMTKmax ¼ 9, which determines matrix size (convergence), where Kmax is the plane wave cut-off and Rmt is the smallest of all atomic sphere radii. We have chosen the muffin-tin radii (MT) for Sb, Co, Fe and Ti to be 2.45, 2.4, 2.35 and 2.3 a.u. respectively. Within the spheres, the charge density and potential are expanded in terms of crystal harmonics up to angular momenta L¼ 10, and a plane wave expansion has been used in the interstitial region. The value of Gmax ¼ 14, where Gmax is defined as the magnitude of the largest vector in charge density Fourier expansion. The Monkorst–Pack special k-points were performed using 2000 special k-points in the Brillouin zone. The cut off energy, which defines the separation of valence and core states, was chosen as 6 Ry. We select the charge convergence as 0.0001e during selfconsistency cycles.
3. Results and discussion Table 1 Lattice constant a (Å), bulk modulus B (in GPa), pressure derivative of bulk modulus B′, total and partial magnetic moment (in μB) for CoFeTiSb quaternary Heusler compound. Compound
a
B
B'
mTi
mCo
mFe
mSb
mTotal
CoFeTiSb FM PM
6.08 6.11
175.18 127.82
4.52 4.29
0.16 –
1.05 –
1.20 –
0.09 –
2.00 –
We have calculated the total energy as a function of lattice constant of CoFeTiSb quaternary Heusler compound for both magnetic and non-magnetic configurations. The plots of calculated total energies versus reduced volume of CoFeTiSb quaternary Heusler compound is given in Fig. 2. The total energies versus changed volumes are fitted to the Murnaghan's equation of state [25] in order to determine the ground state properties, such as equilibrium lattice constant a, bulk modulus B and its pressure
Fig. 3. The band structures of the CoFeTiSb quaternary Heusler compound for the spin-up and spin-down electrons.
S. Berri et al. / Journal of Magnetism and Magnetic Materials 354 (2014) 65–69
67
Fig. 4. Spin-polarized total densities of states (DOS) and partial DOS.
derivative B′. The calculated structural parameters of CoFeTiSb quaternary Heusler compound are reported in Table 1. Until now, an experimental or theoretical lattice constant, the bulk modulus and its pressure derivative value has not been reported. We confirm the ferromagnetic state is more favorable than nonmagnetic one in energy. The calculated spin-polarized band structures of CoFeTiSb quaternary Heusler compound at the theoretical equilibrium lattice constant along high-symmetry directions of the first Brillouin zone are displayed in Fig. 3. The total and partial densities of states, in which the spin-up and spin-down sub-bands are plotted with black and red lines, respectively, are shown in Fig. 4. The Fermi level was set as 0 eV. In Fig. 3, it is clear that the majority-spin band is metallic, while the minority spin band shows a semiconducting gap around the Fermi level. In the minority-spin band, the valence band maximum (VBM) is located at 0.22 eV and the conduction band minimum (CBM) at 0.31 eV. The energy gap for spin-down electrons at around the Fermi level is 0.53 eV and close to the energy gap values for the Mn2CoSi compound [26]. This energy gap in the minority-spin band gap leads to 100% spin polarization at the Fermi level, resulting in the half-metallic behavior at equilibrium state. Fig. 4 shows the total density of states and partial density of as a function of energy for the CoFeTiSb quaternary Heusler compound at its equilibrium lattice constant. To illustrate the nature of the electronic band structures, we have plotted the partial density of states (DOS) of Ti-eg and t2g, Co-eg and t2g, Fe-eg and t2g, and Sb-s electrons for the spin-up and spin-down sub-bands, the figure indicates that band structures can be divided into three parts: at the energy region from: (1) 6.0 to 4.0 eV we find the contribution of Sb-s electrons, (2) 4.0 to 0.0 eV, which represents the contribution of Co t2g spin-up hybridized with Fe eg and t2g orbital, (the exchange-splitting between the spin-up and spin-down subbands of the Co eg and t2g and Fe eg and t2g states, which are the main contributor in the magnetic moment), and (3) 0.0 to 4.0 eV, Co eg in the minority spin hybridized with Ti eg and t2g states. The calculated total and atom-resolved magnetic moments of CoFeTiSb quaternary Heusler compound, are summarized in Table 1. The present study shows that the total magnetic moment
Fig. 5. The calculated total magnetic moment, the magnetic moments of the Co, Fe and Ti atoms as a function of lattice constant.
for CoFeTiSb quaternary Heusler compound is 2.00mB. The total magnetic moment of this compound is an integer value which is exactly according the Slater–Pauling rule for a half-metal [27], mtot ¼Nv-24, where mtot is the total spin magnetic moment per
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S. Berri et al. / Journal of Magnetism and Magnetic Materials 354 (2014) 65–69
formula unit of the system and Nv is the total number of valence electrons accumulated in the system. The Fe and Co atoms have a positive magnetic moments compared to Ti. The large exchange splitting of the Fe-3d and Co-3d states leads to a large magnetic moment at the Ti atoms. The magnetic moment of the titanium atom is different for knowledge. For example, in the semiconductor Fe2TiSn, the magnetic moment of Ti atoms is 0mB [28], while in the half metallic full-Heusler is 0.46mB for Fe2TiSb [28], and 0.526mB for Mn2TiGe [29]. In Fig. 5 we present detailed information on the atomic and total magnetic moments as a function of lattice constant. The calculated total magnetic moment is 2.00mB within all range of the lattice parameter. The calculated magnetic moments of the Fe atoms increase with increase in lattice constant, while the magnetic moment of the Ti atoms decreases, and the magnetic moment of Co atoms slightly increase with lattice constant. In Fig. 6, the TDOS of CoFeTiSb at different lattice constants are presented. In minority spin, with lattice expanding, a clear change of the Fermi level position is observed. All this retains a high spin polarization ratio of CoFeTiSb within the range studied 5.74–6.42 Å.
In order to understand the nature of chemical bonding, we display, in Fig. 7 the contours of charge densities in (110) plane for CoFeTiSb compound. From Fig. 7, we can see that the near spherical charge distribution around the Sb atoms site are negligible and as a result the Sb atoms are fairly isolated, indicating that the bonding Sb–Fe and Sb– Co, are expected to be of some ionic character. On the other hand, the Fe and Co atoms hybridization with Ti atom (see Fig. 4), and Co atoms hybridized with Ti atoms for minority spin, occur with an interaction between the Fe and Co with Ti atom, indicating that a covalent interaction occurs between Fe and Co with Ti atoms. The bonding character may be described as a mixture of covalent and ionic character.
4. Conclusion For the CoFeTiSb quaternary Heusler compound, the electronic structure and magnetic properties have been calculated using the first principles full-potential linearized augmented plane waves (FPLAPW) method. The spin-polarization calculations showed that the CoFeTiSb
Fig. 6. (Color online). Total TDOS for the CoFeTiSb quaternary Heusler compound as a function of the lattice constant, spin-up (black line) and spin-down (red line).
Fig. 7. Charge density distribution in the plane (110) of CoFeTiSb quaternary Heusler compound.
S. Berri et al. / Journal of Magnetism and Magnetic Materials 354 (2014) 65–69
quaternary Heusler compound is a half-metallic ferrimagnet with a magnetic moment of 2.00mB within the entire range of lattice constant. Therefore, the CoFeTiSb quaternary Heusler compound is a promising material for future spintronic applications. References [1] P.J. Webster, K.R.A. Ziebeck, in: H.P.J. Wijn (Ed.), Magnetic Alloy and Compounds of d-Elements with Main Group Elements Landolt-Bö rnstein New Series Group III, vol 19c, Springer, Berlin, 1988, p. 75; K.R.A. Ziebeck, K-U. Neuman, in: H.P.J. Wijn (Ed.), Magnetic Properties of Metals Landolt-Bö rnstein New Series Group III, vol 32, Springer, Berlin, 2001, p. 64. [2] S.A. Wolf, D.D. Awschalom, R.A. Buhrman, J.M. Daughton, S. von Molnar, M.L. Roukes, A.Y. Chtchelkanova, D.M. Treger, Science 294 (2001) 1488. [3] G.A. Prinz, Science 282 (1998) 1660. [4] Y. Ohno, D.K. Young, B. Beshoten, F. Matsukura, H. Ohno, D.D. Awschalom, Nature 402 (1999) 790. [5] T. Dietl, H. Ohno, F. Matsukura, J. Cibert, D. Ferrand, Science 287 (2000) 1019. [6] J.H. Park, E. Voscovo, H.J. Kim, C. Kwon, R. Ramesh, T. Venkatesh, Nature 392 (1998) 794. [7] R.A. de Groot, F.M. Mueller, P.G.V. Engen, K.H.J. Buschow, Phys. Rev. Lett. 50 (1983) 2024. [8] M. Ishikawa, J.L. Jorda, A. Junod, in: W. Buckel, W. Weber (Eds.), Superconductivity in d- and f-Band Metals, Kernforschungszentrum Karlsruhe, Germany, 1982. [9] J.H. Wernick, G.W. Hull, J.E. Bernardini, J.V. Waszczak, Mater. Lett. 2 (1983) 90. [10] H.A. Kierstead, B.D. Dunlap, S.K. Malik, A.M. Umarji, G.K. Shenoy, Phys. Rev. B 32 (1985) 135.
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[11] R.N. Shelton, L.S. Hausermann-Berg, M.J. Johnson, P. Klavins, H.D. Yang, Phys. Rev. B 34 (1986) 199. [12] H.C. Kandpal, G.H. Fecher, C. Felser, J. Phys. D: Appl. Phys. 40 (2007) 1507. [13] C. Felser, G.H. Fecher, B. Balke, Angew. Chem. Int. Ed. 46 (2007) 668. [14] T. Marukame, T. Ishikawa, S. Hakamata, K. Matsuda, T. Uemura, M. Yamamoto, Appl. Phys. Lett. 90 (2007) 012508. [15] N. Tezuka, N. Ikeda, S. Sugimoto, K. Inomata, Appl. Phys. Lett. 89 (2006) 252508. [16] V. Alijani, J. Winterlik, G.H. Fecher, S.S. Naghavi, C. Felser, Phys. Rev. B 83 (2011) 184428. [17] G. Özdoğan, Solid State Sci. 14 (2012) 1273–1276. [18] V. Alijani, S. Ouardi, G.H. Fecher, J. Winterlik, S.S. Naghavi, X. Kozina, G. Tryganyuk, C. Felser, E. Ikenaga, Y. Yamashita, S. Ueda, K. Kobayashi, Phys. Rev. B 84 (2011) 224416. [19] P. Hohenberg, W. Kohn, Phys. Rev. B 136 (1964) 864. [20] W. Kohn, L.J. Sham, Phys. Rev. A 140 (1965) 1133. [21] J.C. Slater, Adv. Quant. Chem. 1 (1964) 5564. [22] P. Blaha, K. Schwarz, G.K.H. Madsen, D. Kvasnicka, J. Luitz, WIEN2K, an Augmented Plane Wave þLocal orbitals Program for Calculating Crystal Properties, Karlheinz Schwarz, Technische Universität, Wien, Austria, 2001, ISBN:3-9501031-1-2. [23] J.P. Perdew, K. Burke, Y. Wang, Phys. Rev. B 54 (1996) 16533. [24] J.P. Perdew, S. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [25] F.D. Murnaghan, Proc. Natl. Acad. Sci. USA 30 (1944) 244. [26] N. Xing, H. Li, J. Dong, R. Long, Ch. Zhang, Comput. Mater. Sci. 42 (2008) 600–605. [27] J.C. Slater, J. Phys. Chem. 41 (1964) 3199. [28] H. Luo, G. Liu, F. Meng, J. Li, E. Liu, G. Wu, J. Magn. Magn. Mater. 324 (2012) 3295. [29] H. Zenasni, H.I. Faraoun, C. Esling, J. Magn. Magn. Mater. 333 (2013) 162–168.
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
A first-principle study of half-metallic ferrimagnetism in the CoFeTiSb quaternary Heusler compound Saadi Berri a,n, D. Maouche b, M. Ibrir c, F. Zerarga a a
Department of Physics, Faculty of Sciences, University of Setif, Algeria Laboratory for Developing New Materials and their Characterizations, University of Setif, Algeria c Department of Physics, Faculty of Sciences, University of Msila, Algeria b
art ic l e i nf o
a b s t r a c t
Article history: Received 6 February 2013 Received in revised form 28 August 2013 Available online 6 November 2013
We have performed first-principle calculations of the structural, electronic and magnetic properties of CoFeTiSb quaternary Heusler compound, using full-potential linearized augmented plane wave (FPLAPW) scheme within the GGA. Features such as the lattice constant, the bulk modulus and its pressure derivative are reported. The electronic band structures and density of states of the CoFeTiSb quaternary compound show that the spin-up electrons are metallic, but the spin-down bands have a gap of 0.53 eV, resulting in stable half-metallic ferrimagnetic behavior with a magnetic moment of 2.00mB. Published by Elsevier B.V.
Keywords: Quaternary Heusler compound Spintronics FP-LAPW
1. Introduction Heusler compounds are ternary intermetallic compounds that have the general composition X2YZ. In this class, X and Y represent d-electron transition metals, and Z denotes an sp-electrons element [1]. In recent years, Heusler compounds have been extensively studied, motivated by their gained importance due to advancements in spintronics [2–6]. In contrast to half-metallic ferromagnets (HMFs) [7], only a few Heusler compounds (all of them with a rareearth metal at the Y position) have been successfully implemented as superconductors [8]. Pd2YSn is the Heusler compound with the highest critical temperature (4.9 K) [9]. The coexistence of antiferromagnetism and superconductivity, demonstrating the manifoldness of the Heusler family, was reported for Pd2YbSn [10] and Pd2ErSn [11]. Many of the Heusler compounds have been reported to be HMFs [12,13], and several Co2-based Heusler compounds have been used as electrodes in magnetic tunnel junctions [14,15]. Ni-based quaternary Heusler ferromagnets, NiFeMnGa and NiCoMnGa, with high spin polarization have been reported very recently [16]. Özdoğan [17] performed Ultrasoft pseudopotentials method to study the electronic structure, elastic and magnetic properties of NiCoCrGa quaternary Heusler compound. Alijani et al. [18] studied theoretically electronic structure of quaternary Heusler CoFeMnZ (Z¼ Al, Ga, Si, Ge) compounds. Generally, CoFeTiSb quaternary Heusler compound crystallize in the LiMgPdSn-type crystal structure. The resulting structure has
n
Corresponding author. Tel.: þ 213 95115576; fax: þ 213 36927210. E-mail address: [email protected] (S. Berri).
0304-8853/$ - see front matter Published by Elsevier B.V. http://dx.doi.org/10.1016/j.jmmm.2013.10.044
F4-3m symmetry with Wyckoff positions Co: 4b (3/4 3/4 3/4), Fe: 4c (1/4 1/4 1/4), Ti: 4d (1/2 1/2 1/2), Sb: 4a (0 0 0). The crystal structures of these compounds are shown in Fig. 1. In the present paper, the structural, electronic and magnetic properties of CoFeTiSb quaternary Heusler compound are reported.
Fig. 1. Crystal structure of quaternary Heusler compound.
66
S. Berri et al. / Journal of Magnetism and Magnetic Materials 354 (2014) 65–69
Our main goal in this work is to evaluate examine the validity of the predictions of half metallicity for CoFeTiSb quaternary Heusler compound. The calculations are performed using ab initio full-potential linearized augmented plane wave (FP-LAPW) within the density functional theory DFT with the generalized gradient approximation GGA. Our paper is organized as follows. The theoretical background is presented in Section 2. Results and discussion are presented in Section 3. A summary of the results is given in Section 4.
2. Method of calculations
Fig. 2. Volume optimization for the CoFeTiSb quaternary Heusler compound.
We have carried out first-principles calculations [19,20] with both full potential and linear augmented plane wave (FP-LAPW) method [21] as implemented in the WIEN2k code [22] within the density functional theory (DFT). The Perdew–Burke–Ernzerhof generalized gradient approximation GGA [23,24]. In the calculations reported here, we use a parameter RMTKmax ¼ 9, which determines matrix size (convergence), where Kmax is the plane wave cut-off and Rmt is the smallest of all atomic sphere radii. We have chosen the muffin-tin radii (MT) for Sb, Co, Fe and Ti to be 2.45, 2.4, 2.35 and 2.3 a.u. respectively. Within the spheres, the charge density and potential are expanded in terms of crystal harmonics up to angular momenta L¼ 10, and a plane wave expansion has been used in the interstitial region. The value of Gmax ¼ 14, where Gmax is defined as the magnitude of the largest vector in charge density Fourier expansion. The Monkorst–Pack special k-points were performed using 2000 special k-points in the Brillouin zone. The cut off energy, which defines the separation of valence and core states, was chosen as 6 Ry. We select the charge convergence as 0.0001e during selfconsistency cycles.
3. Results and discussion Table 1 Lattice constant a (Å), bulk modulus B (in GPa), pressure derivative of bulk modulus B′, total and partial magnetic moment (in μB) for CoFeTiSb quaternary Heusler compound. Compound
a
B
B'
mTi
mCo
mFe
mSb
mTotal
CoFeTiSb FM PM
6.08 6.11
175.18 127.82
4.52 4.29
0.16 –
1.05 –
1.20 –
0.09 –
2.00 –
We have calculated the total energy as a function of lattice constant of CoFeTiSb quaternary Heusler compound for both magnetic and non-magnetic configurations. The plots of calculated total energies versus reduced volume of CoFeTiSb quaternary Heusler compound is given in Fig. 2. The total energies versus changed volumes are fitted to the Murnaghan's equation of state [25] in order to determine the ground state properties, such as equilibrium lattice constant a, bulk modulus B and its pressure
Fig. 3. The band structures of the CoFeTiSb quaternary Heusler compound for the spin-up and spin-down electrons.
S. Berri et al. / Journal of Magnetism and Magnetic Materials 354 (2014) 65–69
67
Fig. 4. Spin-polarized total densities of states (DOS) and partial DOS.
derivative B′. The calculated structural parameters of CoFeTiSb quaternary Heusler compound are reported in Table 1. Until now, an experimental or theoretical lattice constant, the bulk modulus and its pressure derivative value has not been reported. We confirm the ferromagnetic state is more favorable than nonmagnetic one in energy. The calculated spin-polarized band structures of CoFeTiSb quaternary Heusler compound at the theoretical equilibrium lattice constant along high-symmetry directions of the first Brillouin zone are displayed in Fig. 3. The total and partial densities of states, in which the spin-up and spin-down sub-bands are plotted with black and red lines, respectively, are shown in Fig. 4. The Fermi level was set as 0 eV. In Fig. 3, it is clear that the majority-spin band is metallic, while the minority spin band shows a semiconducting gap around the Fermi level. In the minority-spin band, the valence band maximum (VBM) is located at 0.22 eV and the conduction band minimum (CBM) at 0.31 eV. The energy gap for spin-down electrons at around the Fermi level is 0.53 eV and close to the energy gap values for the Mn2CoSi compound [26]. This energy gap in the minority-spin band gap leads to 100% spin polarization at the Fermi level, resulting in the half-metallic behavior at equilibrium state. Fig. 4 shows the total density of states and partial density of as a function of energy for the CoFeTiSb quaternary Heusler compound at its equilibrium lattice constant. To illustrate the nature of the electronic band structures, we have plotted the partial density of states (DOS) of Ti-eg and t2g, Co-eg and t2g, Fe-eg and t2g, and Sb-s electrons for the spin-up and spin-down sub-bands, the figure indicates that band structures can be divided into three parts: at the energy region from: (1) 6.0 to 4.0 eV we find the contribution of Sb-s electrons, (2) 4.0 to 0.0 eV, which represents the contribution of Co t2g spin-up hybridized with Fe eg and t2g orbital, (the exchange-splitting between the spin-up and spin-down subbands of the Co eg and t2g and Fe eg and t2g states, which are the main contributor in the magnetic moment), and (3) 0.0 to 4.0 eV, Co eg in the minority spin hybridized with Ti eg and t2g states. The calculated total and atom-resolved magnetic moments of CoFeTiSb quaternary Heusler compound, are summarized in Table 1. The present study shows that the total magnetic moment
Fig. 5. The calculated total magnetic moment, the magnetic moments of the Co, Fe and Ti atoms as a function of lattice constant.
for CoFeTiSb quaternary Heusler compound is 2.00mB. The total magnetic moment of this compound is an integer value which is exactly according the Slater–Pauling rule for a half-metal [27], mtot ¼Nv-24, where mtot is the total spin magnetic moment per
68
S. Berri et al. / Journal of Magnetism and Magnetic Materials 354 (2014) 65–69
formula unit of the system and Nv is the total number of valence electrons accumulated in the system. The Fe and Co atoms have a positive magnetic moments compared to Ti. The large exchange splitting of the Fe-3d and Co-3d states leads to a large magnetic moment at the Ti atoms. The magnetic moment of the titanium atom is different for knowledge. For example, in the semiconductor Fe2TiSn, the magnetic moment of Ti atoms is 0mB [28], while in the half metallic full-Heusler is 0.46mB for Fe2TiSb [28], and 0.526mB for Mn2TiGe [29]. In Fig. 5 we present detailed information on the atomic and total magnetic moments as a function of lattice constant. The calculated total magnetic moment is 2.00mB within all range of the lattice parameter. The calculated magnetic moments of the Fe atoms increase with increase in lattice constant, while the magnetic moment of the Ti atoms decreases, and the magnetic moment of Co atoms slightly increase with lattice constant. In Fig. 6, the TDOS of CoFeTiSb at different lattice constants are presented. In minority spin, with lattice expanding, a clear change of the Fermi level position is observed. All this retains a high spin polarization ratio of CoFeTiSb within the range studied 5.74–6.42 Å.
In order to understand the nature of chemical bonding, we display, in Fig. 7 the contours of charge densities in (110) plane for CoFeTiSb compound. From Fig. 7, we can see that the near spherical charge distribution around the Sb atoms site are negligible and as a result the Sb atoms are fairly isolated, indicating that the bonding Sb–Fe and Sb– Co, are expected to be of some ionic character. On the other hand, the Fe and Co atoms hybridization with Ti atom (see Fig. 4), and Co atoms hybridized with Ti atoms for minority spin, occur with an interaction between the Fe and Co with Ti atom, indicating that a covalent interaction occurs between Fe and Co with Ti atoms. The bonding character may be described as a mixture of covalent and ionic character.
4. Conclusion For the CoFeTiSb quaternary Heusler compound, the electronic structure and magnetic properties have been calculated using the first principles full-potential linearized augmented plane waves (FPLAPW) method. The spin-polarization calculations showed that the CoFeTiSb
Fig. 6. (Color online). Total TDOS for the CoFeTiSb quaternary Heusler compound as a function of the lattice constant, spin-up (black line) and spin-down (red line).
Fig. 7. Charge density distribution in the plane (110) of CoFeTiSb quaternary Heusler compound.
S. Berri et al. / Journal of Magnetism and Magnetic Materials 354 (2014) 65–69
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