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Robust ferromagnetism in Co2VIn Heusler alloy induced by swapping disorders
Journal Pre-proofs Robust ferromagnetism in Co2VIn Heusler alloy induced by swapping disorders Vineeta Shukla, Shiv Om Kumar PII: DOI: Reference:
S0304-8853(19)31525-2 https://doi.org/10.1016/j.jmmm.2019.166111 MAGMA 166111
To appear in:
Journal of Magnetism and Magnetic Materials
Received Date: Accepted Date:
24 April 2019 4 November 2019
Please cite this article as: V. Shukla, S.O. Kumar, Robust ferromagnetism in Co2VIn Heusler alloy induced by swapping disorders, Journal of Magnetism and Magnetic Materials (2019), doi: https://doi.org/10.1016/j.jmmm. 2019.166111
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© 2019 Published by Elsevier B.V.
Robust ferromagnetism in Co2 VIn Heusler alloy induced by swapping disorders Vineeta Shukla, Shiv Om Kumar Department of Physics, Indian Institute of Technology, Kharagpur 721302, India
Abstract As available in the literature, the physical properties of ternary intermetallic compounds (Heusler alloys) are highly influenced by atomic positions. Therefore, we studied the effect of antisite disorder or swapping X to Y position on the electrical and magnetic properties of the Co2 VIn Heusler alloy. We performed firstprinciples calculations using the full-potential linearized augmented plane wave (FP-LAPW) within wein2k. The compounds Co2 VIn and V2 CoIn were found to be stable in ferromagnetic state. It was observed that the swapping of C-V enhanced the magnetic moment two times larger than Co2 VIn alloy. Also, swapping Co-V diminished the half-metallic character of Co2 VIn and showed the traditional metallic behavior due to delocalization of valence electrons. Apart from swapping, 16.7% V inclusion in Co2 VIn alloy offers the more stable behavior than other systems, but suppress the magnetic moment in compare to Co2 VIn and V2 CoIn systems. Keywords: Heusler alloy, disorder, the density of states (DOS)
1. Introduction Due to multifunctional properties of Heusler Alloys, these alloys are always being a center of attraction for the researchers from the many decades. Their remarkable electronic structure establishes them to use in various spintronic devices such as spin-transfer torque and large magneto-resistance spin valves devices etc. Heusler Alloys are ternary intermetallic compounds which were first discovered by Heusler in 1903 [1]. They occur in the two forms: full-Heusler alloys and half-Heusler alloys which crystallize in L21 and Cb1 phases, respectively. For more convenient, these alloys are represented by X2 YZ and XYZ in which where X and Y are the transition metals (Co, Mn, V, Pd, etc.) and Z is an sp (Al, Si, Ge, etc.) element [2, 3, 4, 5]. It is noteworthy that atomic positions in Heusler alloys influence their physical properties, even, ∗ Corresponding ∗∗ E-mail
author: Shiv Om Kumar address: [email protected] (SO Kumar), [email protected] *(V Shukla))
Preprint submitted to Journal of Magnetism and Magnetic Materials
November 7, 2019
a slight disorder can alter the electronic structure and magnetic nature of these alloys. Thus, apart from L21 phase, full Heusler Alloys can be crystallized in disordered phases such as DO3 , B2, and A2 phases [6, 7, 8]. The arbitrary occupation of every site in the crystal lattice gives disordered A2 phase while in the B2 phase, Y and Z atoms randomly occupy their sites rather X remains in ordered position. On the other hand, the random distribution of X and Y or X and Z leads to the DO3 disorder. As we reported earlier that the presence of A2/B2 disorders destroys the half-metallicity of Co2 MnSi.75 Al.25 alloy. The disorder is an inherent property of any real material so it can be treated as an intrinsic disorder such as thermal antisites, binary swaps, and vacancies. Moreover, disorders become more important in the case of spin-based devices because these devices use the spin degrees of freedom. Disorders have their advantages and disadvantages [9]. It is well known that the spin polarization should be 100% in half-metallic materials. Nevertheless, 50%-70% polarization has been achieved experimentally because of disorders or swapping of elements in Heusler alloys [10]. Moreover, ordered L21 structures of some alloys shows the nonmagnetic state that limits the applications in shape memory effect alloys. In this regard, knowing of disorder or swapping may be helpful to design a new half ferromagnetic metal and shape memory effect alloys. So, it becomes important to investigate about these disorders. Among all type of Heusler alloy, Co-based alloys are of particular interest due to excellent Curie temperature limit, comparatively better magnetic moment and low Gilbert damping constant [11]. In this context, Co2 VZ where Z=Al, Ga Sn, and In are predicted to be half half-metallic [12, 13]. Among these alloys, Co2 VIn can be considered an excellent material because it is stable in L21 structure and possess spin polarization > 85% even calculated by the different computational methods. However, in our knowledge, the effect of disorder on this alloy could not be explored. Therefore, in the present work, we report the effect of antisite disorder or swapping of X to Y position in Co2 VIn Heusler alloy by first principle theory. We observed that swapping and antisite disorder diminishes the half-metallic character of Co2 VIn and showed the traditional metallic behavior due to delocalization of valence electrons. However, the disordered cubic structure of Co2 VIn alloys offer a more stable behavior than L21 systems but possess the minimum magnetic moment in compare to Co2 VIn and V2 CoIn system.
2. Computational details We employed self-consistent full-potential linearized augmented plane wave (FP-LAPW) method comprises generalized gradient approximation within wien2k code [14, 15]. In this method, non-overlapping muffin-tin (MT) spheres are distributed in space that is separated by an interstitial region. We choose muffin-tin (MT) spheres radii of Co, V and In as 2.37, 2.31 and 2.37, respectively. The energy threshold 2
between the core and the valence states and k points were set to 6.5 Rydberg (Ry) and 1000, respectively. In case of Co2 VIn alloy Co, V and Intake place at Wyckoff coordinates Co1 (0.75, 0.75, 0.75), Co2 (0.25, 0.25, 0.25), V (0, 0, 0) and In (0.5, 0.5, 0.5) respectively, as shown in Fig. 1 [11]. After the swapping V takes the place of Co while In remains in the same position. Both compounds were optimized by using Hellmann-Feynman forces on atoms. Disorders were obtained by making 2*2*2 supercell in which 16.7% Co atoms were replaced by V. In the above calculation, Co(3d7 4s2 ), V(3d3 4s2 ) and In(5s2 5p1 ) are taken as valence electrons. The convergences of energy in SCF iteration was set to 1×10−4 Ry.
Figure 1: Schematic representation of the swapping of Co to V in Co2 VIn Heusler alloy.
3. Results and discussion To see the stable phases of Co2 VIn alloy before and after antisite disorder and swapping of Co-V, we performed volume optimization which gives the minimum energy for a number of volumes of Co2 VIn and V2 CoIn as shown in Fig. 2. The equilibrium energy (E0 ), lattice parameter (a0 ), bulk modulus (B) and its first derivative (B’) were obtained from the empirical Birch Murnaghan’ equation of states. The above equation is given by following expression[16]
ET ot (V ) = E0 +
V0 B VB V0 −1 ∗ + 1− − 1) V V
B 0 (B 0
(1)
Where E0 , B and B’ refer to equilibrium energy, bulk modulus and its first derivative at equilibrium volume V0 .
The structural properties of Co2 VIn and V2 CoIn were estimated in nonmagnetic and ferromagnetic 3
Figure 2: Total energy optimization as the function of volume for nonmagnetic and ferromagnetic phases for (a) Co2 VIn and (b) V2 CoIn and (c) ferromagnetic phase of disordered Co2 VIn Heusler alloys.
Table 1: Optimized parameters for Co2 VIn, V2 CoIn and disordered Co2 VIn Heusler alloys in stable phases.
Material Co2 VIn 16.7% V in Co2 VIn V2 CoIn
lattice constant (˚ A) 6.010 6.062 6.203
enthalpy (Ry) -17328.059 -67353.1938 - 16223.909
B (GPa) 176.767 166.1418 149.912
B’ (GPa) 5.217 5.207 5.281
states. Fig. 2 (a, b) show ferromagnetic state is more stable than the nonmagnetic state for both compounds. The equilibrium lattice parameters are listed in table 1. Apart from L21 structure of Co2 VIn and V2 CoIn, disordered Co2 VIn structure shows more stable configuration in cubic phase. Furthermore, disordered Co2 VIn and V2 CoIn have the larger lattice constant value in compare to Co2 VIn. It is anticipated that a larger atomic radius of V than Co is responsible for increasing the lattice constant values. Also, it is found that bulk modulus decreases after the swapping of Co-V elements as well as in 16.7% V inclusion in Co2 VIn. It can be understood by considering the EN values of Co, and V. The V atom has less electronegativity than that of Co atom. Thus, the 16.7% of V inclusion with Co atom in disordered Co2 VIn Heusler alloy, the average binding force of chemical bonds decreases. As a result, the bulk modulus of disordered Co2 VIn Heusler alloy decreases. Meanwhile, Co atoms are swapped by V atoms then average binding force decreases 4
more sharply that reduce the bulk modulus of V2 CoIn in compare to ordered Co2 VIn and disordered Co2 VIn Heusler alloys. After this, we calculated density of states (DOS) from the optimized structures. For the
Figure 3: (a) Total DOS (b) partial DOS of Co, (c) partial DOS of V and (d) partial DOS of In of Co2 VIn Heusler alloy.
better understanding of swapping disorder on Co2 VIn, initially we need to discuss electronic structure of Co2 VIn alloy. The calculated total and partial DOS of Co2 VIn structure are shown in Fig. 3 (a, b, c, d). For Co2 VIn alloy, the majority spin direction shows metallic behavior while minority spin direction consist of almost zero states around the Fermi level which indicates the semi-metallic behavior as repoted elsewhere. Even through 100% spin polarization can be achieved by using different approximation method of calculations including GGA+U, PBE+GGA+U etc, as reported in literature [13].
The p electrons of
In atoms lead to DOS around 5 eV. These p electrons hybridize with p and d state of transition metal atoms. The extent of p-d hybridization can be described in term of the degree of occupation [17]. The d states are wide on the energy scale and extend from -4 eV to +2 eV due to the strong hybridization between the 3d states. From -4 eV to +2 eV energy scale is occupied by the d states, resulting from the 5
Figure 4: (a) Total DOS (b) partial DOS of V, (c) partial DOS of Co and (d) partial DOS of In of V2 CoIn Heusler alloy.
strong hybridization between the 3d states (Co and V). It is well established that the d-d band gap usually results from the strong interactions between the d states of the X and Y atoms of X2 YZ Heusler alloys. The formation of the bonding and anti-bonding peaks take place due to co-valent hybridization between these states that determine the position of the Fermi level. The nearest neighbors of Co are V (4 atoms), and In (4 atoms), its DOS consists of some two peaks in spin up and down states. Similarly, V, which is surrounded by eight nearest Co atoms, also shows two-peak which are well known as bonding and anti-bonding peak. These peaks are detached by Fermi energy level in DOS. These peaks are outcome of eg -t2g splitting [18] Fig. 4 (a) represents the total DOS of V2 CoIn for swapping of Co to V. It is visible from the Fig 5 (a) that swapping Co-V disorder alters the electronic structure of the swapped compound, i.e., V2 CoIn. Interestingly, swapping of Co-V does not only disrupt the bandgap in minority band but also enhances the magnetic moments by two times. In total DOS plot, other states appear around Fermi level in the minority-spin band. It is anticipated that these new states are created due to the decolonization of the 6
Table 2: Calculated spin magnetic moments in µB /f.u. for the Co2 VIn
Material Co2 VIn Co2 VIn V2 CoIn Disordered Co2 VIn
mX 2.182 2.3736 2.3118 1.031
mY 0.074 -.15223 1.41186 .07784
mZ 0.078 -.01889 .00986 -.003385
mvoid -.16755 .26707 -.226335
mtotal 2.031 2.03 4.00 0.87
half metallic yes nearly no no
method GGA+U GGA GGA GGA
reference [13] present present present
Figure 5: Band structure of Co2 VIn (a) in spin up and (b)in spin down states.
valence electron in 3d atoms that hybridize with In 5p atoms, as depicted in Fig. 4 (b, c, d). While the PDOS plot of V (Fig. 4 (b)) indicates that swapping of V to Co influence considerably to PDOS. Its spin up PDOS expands while its spin-down PDOS have the negligible effect of swapping. On other hands, PDOS of Co shrinks for the spin-up state and expands for the spin downstate that reverses its moment sign. Thus, major contribution occurs from the V atom, which is accompanied by Co atoms. Moreover, the robust magnetic moment of V2 CoIn is mainly caused by the parallel alignment of V and Co spins which contribute the positive spin moment in comparison with Co2 VIn in which anti-parallel alignment of spin Co and V reduces the spin moment. The total magnetic moment was found to be 2.0349 µB /f.u. and 4.0006 µB /f.u. for Co2 VIn and V2 CoIn, respectively. Fig. 5 (a,b) indicates the spin resolved (spin up and spin down) band structures of Co2 VIn Heusler alloy. The spin down band structure shows nearly half metallic characteristic which is consistent with the total DOS, as shown in Fig. 3(a). Nevertheless, the different methods such as GGA+U, LDA+U etc. show 7
Figure 6: Band structure of V2 CoIn (a) in spin up and (b) in spin down states.
perfect half metallicity of the Co2 VIn alloy. It is reported that GGA method suppresses the band gap in compare to other adavanced methods such as mbj-GGA [11]. Fig. 6 (a,b) shows the band structure in spin up and down states of V2 CoIn Heusler alloy. The overlapping of valence and conduction band for for both type of spin states at X-point in band structure of V2 CoIn Heusler alloy indicates the metallic nature of V2 CoIn alloy. Fig. 7 (a) represents the total DOS of disordered Co2 VIn for by replacing 16.7% Co by V. It can be seen from the Fig 7 (a) that antisite disorder also alters the electronic structure Co2 VIn significantly similar to V2 CoIn as the result of delocalization of electrons. Even though the presence of a little amount of antisites V in Co2 VIn elevated DOS around the Fermi level. PDOS plot of Co (Fig. 7 (b)) shows that 16.7% inclusion of V in place of Co-leads the more spin-down states over the spin-up states. As a result, the moment has a big contraction. Nevertheless, PDOS of V expands in both spin up and down direction, aligning the overall spin of V anti-parallel Co. In this case, the total magnetic moment decreases in disordered Co2 VIn. The total magnetic moment was found to be 0.8718 µB /f.u. Decolonization of valence electron can be understood in term of electronegativity (EN). EN is the tendency of a bonded atom to attract the shared electrons while the delocalization degree of valence electrons significantly influences the DOS peaks [19]. The elements Co and V possess EN and atomic radii 1.88, 1.63 and 200 pm, 205 pm, respectively. Since EN of V is smaller 8
Figure 7: (a) Total DOS (b) partial DOS of Co, (c) partial DOS of V and (d) partial DOS of In of 16.7 % V Co2 VIn Heusler alloy.
than that of Co, the attractive ability decreases when V atom increases in compare to Co atom in alloying of Co, V with In. Moreover, the strong interaction between the 3d atoms and In 5p electrons leads to the increased delocalization degree of valence electrons. Therefore, decrement in attractive ability and increment in delocalization degree generates other states around the Fermi level, which, is accountable for the metallic behavior of disordered and swapped Co-V Heusler alloy [20].
4. Conclusion In brief, the physical properties of ternary intermetallic compounds (Heusler alloys) are highly influenced by atomic positions. Therefore, we studied the effect of swapping X to Y position on the electrical and magnetic properties of the Co2 VIn Heusler alloy. We performed first-principles calculations using the fullpotential linearized augmented plane wave (FP-LAPW) within wein2k. Both compounds Co2 VIn, V2 CoIn, and disordered Co2 VIn were found to be stable in ferromagnetic state. It was seen that the swapping of 9
Co-V enhanced the magnetic moment two times larger than Co2 VIn alloy, but the presence of disorder in Co2 VIn decreases the magnetic moment in compare to Co2 VIn and V2 CoIn. Also, swapping Co-V and disorder diminished the half-metallic character of Co2 VIn and showed the traditional metallic behavior due to delocalization of valence electrons.
5. Acknowledgments V. Shukla is grateful to MHRD, India, for financial support and IIT Kharagpur for providing research facilities in this work. V. Shukla is also thankful to her supervisor Dr. S. K. Srivastava for providing a conducive environment for research work.
6. Author Contributions The work was equally contributed by S. O. Kumar and V.Shukla. References [1] F. Heusler, ”U about magnetic manganese alloys, Negotiations of the German Physical Society 5 (1903) 219. [2] R. Paudel, J. Zhu, Structural, electronic, magnetic, elastic, and thermal properties of co-based equiatomic quaternary heusler alloys, Journal of Magnetism and Magnetic Materials 453 (2018) 10–16. [3] R. Paudel, J. Zhu, Investigation of half-metallicity and magnetism of bulk and (111)-surfaces of fe2mnp full heusler alloy, Vacuum 164 (2019) 336–342. [4] J. Ma, J. He, D. Mazumdar, K. Munira, S. Keshavarz, T. Lovorn, C. Wolverton, A. W. Ghosh, W. H. Butler, Computational investigation of inverse heusler compounds for spintronics applications, Physical Review B 98 (9) (2018) 094410. [5] F. Faid, M. Elchikh, S. Bahlouli, K. Kaddar, Strong correlation effect in ferrimagnetic half-metallic v 2 coal and v 2 coga heusler compounds, Journal of Superconductivity and Novel Magnetism (2018) 1–10. [6] V. Khovailo, T. Takagi, A. Vasilev, H. Miki, M. Matsumoto, R. Kainuma, On order–disorder (l21 b2) phase transition in ni2+ xmn1xga heusler alloys, physica status solidi (a) 183 (2) (2001) R1–R3. [7] Y. Han, A. Bouhemadou, R. Khenata, Z. Cheng, T. Yang, X. Wang, Prediction of possible martensitic transformations in all-d-metal zinc-based heusler alloys from first-principles, Journal of Magnetism and Magnetic Materials 471 (2019) 49–55. [8] Y. Han, M. Wu, M. Kuang, T. Yang, X. Chen, X. Wang, All-d-metal equiatomic quaternary heusler hypothetical alloys zncdtmn (t= fe, ru, os, rh, ir, ni, pd, pt): A first-principle investigation of electronic structures, magnetism, and possible martensitic transformations, Results in Physics 11 (2018) 1134–1141. [9] Y. Ma, Z. Ni, H. Luo, H. Liu, F. Meng, E. Liu, W. Wang, G. Wu, Site preference, electronic structure and possible martensitic transformation in heusler alloys ni2coz (z= al, ga, in, si, ge, sn, sb), Intermetallics 81 (2017) 1–8. [10] J. Enamullah, K. Suresh, A. Alam, Half-metallic co-based quaternary heusler alloys for spintronics: Defect-and pressureinduced transitions and properties, Physical Review B 94 (18). [11] S. O. Kumar, V. Shukla, S. K. Srivastava, Ferromagnetic behavior of si substituted co2mnal. 25si. 75 full heusler alloy, Materials Letters 225 (2018) 134–137.
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[12] H. C. Kandpal, G. H. Fecher, C. Felser, Calculated electronic and magnetic properties of the half-metallic, transition metal based heusler compounds, Journal of Physics D: Applied Physics 40 (6) (2007) 1507. [13] M. Zipporah, P. Rohit, M. Robinson, M. Julius, S. Ralph, K. Arti, First-principle investigation of structural, electronic and magnetic properties of co2vin and covin heusler compounds, AIP Advances 7 (5) (2017) 055705. [14] P. Blaha, K. Schwarz, G. K. Madsen, D. Kvasnicka, J. Luitz, wien2k, An augmented plane wave+ local orbitals program for calculating crystal properties. [15] J. P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Physical review letters 77 (18) (1996) 3865. [16] S. O. Kumar, V. Shukla, S. K. Srivastava, Role of electronegativity on the bulk modulus, magnetic moment and band gap of co2mnal based heusler alloys, Journal of Science: Advanced Materials and Devices 4 (2019) 158–162. [17] H. Luo, H. Zhang, J. Chen, G. Wu, X. Dai, X. Zhu, C. Jiang, H. Xu, Disorder enhanced magnetic moment in fe 2 cral ribbons, Functional Materials Letters 1 (02) (2008) 115–120. [18] I. Galanakis, P. Dederichs, N. Papanikolaou, Slater-pauling behavior and origin of the half-metallicity of the full-heusler alloys, Physical Review B 66 (17) (2002) 174429. [19] K. Li, C. Kang, D. Xue, Electronegativity calculation of bulk modulus and band gap of ternary zno-based alloys, Materials Research Bulletin 47 (10) (2012) 2902–2905. [20] C. Felser, A. Hirohata, Heusler alloys, Springer, 2015.
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S0304-8853(19)31525-2 https://doi.org/10.1016/j.jmmm.2019.166111 MAGMA 166111
To appear in:
Journal of Magnetism and Magnetic Materials
Received Date: Accepted Date:
24 April 2019 4 November 2019
Please cite this article as: V. Shukla, S.O. Kumar, Robust ferromagnetism in Co2VIn Heusler alloy induced by swapping disorders, Journal of Magnetism and Magnetic Materials (2019), doi: https://doi.org/10.1016/j.jmmm. 2019.166111
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2019 Published by Elsevier B.V.
Robust ferromagnetism in Co2 VIn Heusler alloy induced by swapping disorders Vineeta Shukla, Shiv Om Kumar Department of Physics, Indian Institute of Technology, Kharagpur 721302, India
Abstract As available in the literature, the physical properties of ternary intermetallic compounds (Heusler alloys) are highly influenced by atomic positions. Therefore, we studied the effect of antisite disorder or swapping X to Y position on the electrical and magnetic properties of the Co2 VIn Heusler alloy. We performed firstprinciples calculations using the full-potential linearized augmented plane wave (FP-LAPW) within wein2k. The compounds Co2 VIn and V2 CoIn were found to be stable in ferromagnetic state. It was observed that the swapping of C-V enhanced the magnetic moment two times larger than Co2 VIn alloy. Also, swapping Co-V diminished the half-metallic character of Co2 VIn and showed the traditional metallic behavior due to delocalization of valence electrons. Apart from swapping, 16.7% V inclusion in Co2 VIn alloy offers the more stable behavior than other systems, but suppress the magnetic moment in compare to Co2 VIn and V2 CoIn systems. Keywords: Heusler alloy, disorder, the density of states (DOS)
1. Introduction Due to multifunctional properties of Heusler Alloys, these alloys are always being a center of attraction for the researchers from the many decades. Their remarkable electronic structure establishes them to use in various spintronic devices such as spin-transfer torque and large magneto-resistance spin valves devices etc. Heusler Alloys are ternary intermetallic compounds which were first discovered by Heusler in 1903 [1]. They occur in the two forms: full-Heusler alloys and half-Heusler alloys which crystallize in L21 and Cb1 phases, respectively. For more convenient, these alloys are represented by X2 YZ and XYZ in which where X and Y are the transition metals (Co, Mn, V, Pd, etc.) and Z is an sp (Al, Si, Ge, etc.) element [2, 3, 4, 5]. It is noteworthy that atomic positions in Heusler alloys influence their physical properties, even, ∗ Corresponding ∗∗ E-mail
author: Shiv Om Kumar address: [email protected] (SO Kumar), [email protected] *(V Shukla))
Preprint submitted to Journal of Magnetism and Magnetic Materials
November 7, 2019
a slight disorder can alter the electronic structure and magnetic nature of these alloys. Thus, apart from L21 phase, full Heusler Alloys can be crystallized in disordered phases such as DO3 , B2, and A2 phases [6, 7, 8]. The arbitrary occupation of every site in the crystal lattice gives disordered A2 phase while in the B2 phase, Y and Z atoms randomly occupy their sites rather X remains in ordered position. On the other hand, the random distribution of X and Y or X and Z leads to the DO3 disorder. As we reported earlier that the presence of A2/B2 disorders destroys the half-metallicity of Co2 MnSi.75 Al.25 alloy. The disorder is an inherent property of any real material so it can be treated as an intrinsic disorder such as thermal antisites, binary swaps, and vacancies. Moreover, disorders become more important in the case of spin-based devices because these devices use the spin degrees of freedom. Disorders have their advantages and disadvantages [9]. It is well known that the spin polarization should be 100% in half-metallic materials. Nevertheless, 50%-70% polarization has been achieved experimentally because of disorders or swapping of elements in Heusler alloys [10]. Moreover, ordered L21 structures of some alloys shows the nonmagnetic state that limits the applications in shape memory effect alloys. In this regard, knowing of disorder or swapping may be helpful to design a new half ferromagnetic metal and shape memory effect alloys. So, it becomes important to investigate about these disorders. Among all type of Heusler alloy, Co-based alloys are of particular interest due to excellent Curie temperature limit, comparatively better magnetic moment and low Gilbert damping constant [11]. In this context, Co2 VZ where Z=Al, Ga Sn, and In are predicted to be half half-metallic [12, 13]. Among these alloys, Co2 VIn can be considered an excellent material because it is stable in L21 structure and possess spin polarization > 85% even calculated by the different computational methods. However, in our knowledge, the effect of disorder on this alloy could not be explored. Therefore, in the present work, we report the effect of antisite disorder or swapping of X to Y position in Co2 VIn Heusler alloy by first principle theory. We observed that swapping and antisite disorder diminishes the half-metallic character of Co2 VIn and showed the traditional metallic behavior due to delocalization of valence electrons. However, the disordered cubic structure of Co2 VIn alloys offer a more stable behavior than L21 systems but possess the minimum magnetic moment in compare to Co2 VIn and V2 CoIn system.
2. Computational details We employed self-consistent full-potential linearized augmented plane wave (FP-LAPW) method comprises generalized gradient approximation within wien2k code [14, 15]. In this method, non-overlapping muffin-tin (MT) spheres are distributed in space that is separated by an interstitial region. We choose muffin-tin (MT) spheres radii of Co, V and In as 2.37, 2.31 and 2.37, respectively. The energy threshold 2
between the core and the valence states and k points were set to 6.5 Rydberg (Ry) and 1000, respectively. In case of Co2 VIn alloy Co, V and Intake place at Wyckoff coordinates Co1 (0.75, 0.75, 0.75), Co2 (0.25, 0.25, 0.25), V (0, 0, 0) and In (0.5, 0.5, 0.5) respectively, as shown in Fig. 1 [11]. After the swapping V takes the place of Co while In remains in the same position. Both compounds were optimized by using Hellmann-Feynman forces on atoms. Disorders were obtained by making 2*2*2 supercell in which 16.7% Co atoms were replaced by V. In the above calculation, Co(3d7 4s2 ), V(3d3 4s2 ) and In(5s2 5p1 ) are taken as valence electrons. The convergences of energy in SCF iteration was set to 1×10−4 Ry.
Figure 1: Schematic representation of the swapping of Co to V in Co2 VIn Heusler alloy.
3. Results and discussion To see the stable phases of Co2 VIn alloy before and after antisite disorder and swapping of Co-V, we performed volume optimization which gives the minimum energy for a number of volumes of Co2 VIn and V2 CoIn as shown in Fig. 2. The equilibrium energy (E0 ), lattice parameter (a0 ), bulk modulus (B) and its first derivative (B’) were obtained from the empirical Birch Murnaghan’ equation of states. The above equation is given by following expression[16]
ET ot (V ) = E0 +
V0 B VB V0 −1 ∗ + 1− − 1) V V
B 0 (B 0
(1)
Where E0 , B and B’ refer to equilibrium energy, bulk modulus and its first derivative at equilibrium volume V0 .
The structural properties of Co2 VIn and V2 CoIn were estimated in nonmagnetic and ferromagnetic 3
Figure 2: Total energy optimization as the function of volume for nonmagnetic and ferromagnetic phases for (a) Co2 VIn and (b) V2 CoIn and (c) ferromagnetic phase of disordered Co2 VIn Heusler alloys.
Table 1: Optimized parameters for Co2 VIn, V2 CoIn and disordered Co2 VIn Heusler alloys in stable phases.
Material Co2 VIn 16.7% V in Co2 VIn V2 CoIn
lattice constant (˚ A) 6.010 6.062 6.203
enthalpy (Ry) -17328.059 -67353.1938 - 16223.909
B (GPa) 176.767 166.1418 149.912
B’ (GPa) 5.217 5.207 5.281
states. Fig. 2 (a, b) show ferromagnetic state is more stable than the nonmagnetic state for both compounds. The equilibrium lattice parameters are listed in table 1. Apart from L21 structure of Co2 VIn and V2 CoIn, disordered Co2 VIn structure shows more stable configuration in cubic phase. Furthermore, disordered Co2 VIn and V2 CoIn have the larger lattice constant value in compare to Co2 VIn. It is anticipated that a larger atomic radius of V than Co is responsible for increasing the lattice constant values. Also, it is found that bulk modulus decreases after the swapping of Co-V elements as well as in 16.7% V inclusion in Co2 VIn. It can be understood by considering the EN values of Co, and V. The V atom has less electronegativity than that of Co atom. Thus, the 16.7% of V inclusion with Co atom in disordered Co2 VIn Heusler alloy, the average binding force of chemical bonds decreases. As a result, the bulk modulus of disordered Co2 VIn Heusler alloy decreases. Meanwhile, Co atoms are swapped by V atoms then average binding force decreases 4
more sharply that reduce the bulk modulus of V2 CoIn in compare to ordered Co2 VIn and disordered Co2 VIn Heusler alloys. After this, we calculated density of states (DOS) from the optimized structures. For the
Figure 3: (a) Total DOS (b) partial DOS of Co, (c) partial DOS of V and (d) partial DOS of In of Co2 VIn Heusler alloy.
better understanding of swapping disorder on Co2 VIn, initially we need to discuss electronic structure of Co2 VIn alloy. The calculated total and partial DOS of Co2 VIn structure are shown in Fig. 3 (a, b, c, d). For Co2 VIn alloy, the majority spin direction shows metallic behavior while minority spin direction consist of almost zero states around the Fermi level which indicates the semi-metallic behavior as repoted elsewhere. Even through 100% spin polarization can be achieved by using different approximation method of calculations including GGA+U, PBE+GGA+U etc, as reported in literature [13].
The p electrons of
In atoms lead to DOS around 5 eV. These p electrons hybridize with p and d state of transition metal atoms. The extent of p-d hybridization can be described in term of the degree of occupation [17]. The d states are wide on the energy scale and extend from -4 eV to +2 eV due to the strong hybridization between the 3d states. From -4 eV to +2 eV energy scale is occupied by the d states, resulting from the 5
Figure 4: (a) Total DOS (b) partial DOS of V, (c) partial DOS of Co and (d) partial DOS of In of V2 CoIn Heusler alloy.
strong hybridization between the 3d states (Co and V). It is well established that the d-d band gap usually results from the strong interactions between the d states of the X and Y atoms of X2 YZ Heusler alloys. The formation of the bonding and anti-bonding peaks take place due to co-valent hybridization between these states that determine the position of the Fermi level. The nearest neighbors of Co are V (4 atoms), and In (4 atoms), its DOS consists of some two peaks in spin up and down states. Similarly, V, which is surrounded by eight nearest Co atoms, also shows two-peak which are well known as bonding and anti-bonding peak. These peaks are detached by Fermi energy level in DOS. These peaks are outcome of eg -t2g splitting [18] Fig. 4 (a) represents the total DOS of V2 CoIn for swapping of Co to V. It is visible from the Fig 5 (a) that swapping Co-V disorder alters the electronic structure of the swapped compound, i.e., V2 CoIn. Interestingly, swapping of Co-V does not only disrupt the bandgap in minority band but also enhances the magnetic moments by two times. In total DOS plot, other states appear around Fermi level in the minority-spin band. It is anticipated that these new states are created due to the decolonization of the 6
Table 2: Calculated spin magnetic moments in µB /f.u. for the Co2 VIn
Material Co2 VIn Co2 VIn V2 CoIn Disordered Co2 VIn
mX 2.182 2.3736 2.3118 1.031
mY 0.074 -.15223 1.41186 .07784
mZ 0.078 -.01889 .00986 -.003385
mvoid -.16755 .26707 -.226335
mtotal 2.031 2.03 4.00 0.87
half metallic yes nearly no no
method GGA+U GGA GGA GGA
reference [13] present present present
Figure 5: Band structure of Co2 VIn (a) in spin up and (b)in spin down states.
valence electron in 3d atoms that hybridize with In 5p atoms, as depicted in Fig. 4 (b, c, d). While the PDOS plot of V (Fig. 4 (b)) indicates that swapping of V to Co influence considerably to PDOS. Its spin up PDOS expands while its spin-down PDOS have the negligible effect of swapping. On other hands, PDOS of Co shrinks for the spin-up state and expands for the spin downstate that reverses its moment sign. Thus, major contribution occurs from the V atom, which is accompanied by Co atoms. Moreover, the robust magnetic moment of V2 CoIn is mainly caused by the parallel alignment of V and Co spins which contribute the positive spin moment in comparison with Co2 VIn in which anti-parallel alignment of spin Co and V reduces the spin moment. The total magnetic moment was found to be 2.0349 µB /f.u. and 4.0006 µB /f.u. for Co2 VIn and V2 CoIn, respectively. Fig. 5 (a,b) indicates the spin resolved (spin up and spin down) band structures of Co2 VIn Heusler alloy. The spin down band structure shows nearly half metallic characteristic which is consistent with the total DOS, as shown in Fig. 3(a). Nevertheless, the different methods such as GGA+U, LDA+U etc. show 7
Figure 6: Band structure of V2 CoIn (a) in spin up and (b) in spin down states.
perfect half metallicity of the Co2 VIn alloy. It is reported that GGA method suppresses the band gap in compare to other adavanced methods such as mbj-GGA [11]. Fig. 6 (a,b) shows the band structure in spin up and down states of V2 CoIn Heusler alloy. The overlapping of valence and conduction band for for both type of spin states at X-point in band structure of V2 CoIn Heusler alloy indicates the metallic nature of V2 CoIn alloy. Fig. 7 (a) represents the total DOS of disordered Co2 VIn for by replacing 16.7% Co by V. It can be seen from the Fig 7 (a) that antisite disorder also alters the electronic structure Co2 VIn significantly similar to V2 CoIn as the result of delocalization of electrons. Even though the presence of a little amount of antisites V in Co2 VIn elevated DOS around the Fermi level. PDOS plot of Co (Fig. 7 (b)) shows that 16.7% inclusion of V in place of Co-leads the more spin-down states over the spin-up states. As a result, the moment has a big contraction. Nevertheless, PDOS of V expands in both spin up and down direction, aligning the overall spin of V anti-parallel Co. In this case, the total magnetic moment decreases in disordered Co2 VIn. The total magnetic moment was found to be 0.8718 µB /f.u. Decolonization of valence electron can be understood in term of electronegativity (EN). EN is the tendency of a bonded atom to attract the shared electrons while the delocalization degree of valence electrons significantly influences the DOS peaks [19]. The elements Co and V possess EN and atomic radii 1.88, 1.63 and 200 pm, 205 pm, respectively. Since EN of V is smaller 8
Figure 7: (a) Total DOS (b) partial DOS of Co, (c) partial DOS of V and (d) partial DOS of In of 16.7 % V Co2 VIn Heusler alloy.
than that of Co, the attractive ability decreases when V atom increases in compare to Co atom in alloying of Co, V with In. Moreover, the strong interaction between the 3d atoms and In 5p electrons leads to the increased delocalization degree of valence electrons. Therefore, decrement in attractive ability and increment in delocalization degree generates other states around the Fermi level, which, is accountable for the metallic behavior of disordered and swapped Co-V Heusler alloy [20].
4. Conclusion In brief, the physical properties of ternary intermetallic compounds (Heusler alloys) are highly influenced by atomic positions. Therefore, we studied the effect of swapping X to Y position on the electrical and magnetic properties of the Co2 VIn Heusler alloy. We performed first-principles calculations using the fullpotential linearized augmented plane wave (FP-LAPW) within wein2k. Both compounds Co2 VIn, V2 CoIn, and disordered Co2 VIn were found to be stable in ferromagnetic state. It was seen that the swapping of 9
Co-V enhanced the magnetic moment two times larger than Co2 VIn alloy, but the presence of disorder in Co2 VIn decreases the magnetic moment in compare to Co2 VIn and V2 CoIn. Also, swapping Co-V and disorder diminished the half-metallic character of Co2 VIn and showed the traditional metallic behavior due to delocalization of valence electrons.
5. Acknowledgments V. Shukla is grateful to MHRD, India, for financial support and IIT Kharagpur for providing research facilities in this work. V. Shukla is also thankful to her supervisor Dr. S. K. Srivastava for providing a conducive environment for research work.
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