Structural stability, electronic and magnetic properties of

Structural stability, electronic and magnetic properties of (Ni1-xCox)2MnSn quaternary Heusler alloys. L. Seddik 1, S. Amari1,2,*, K. O. Obodo3, L. Beldi1, H. I. Faraoun4 and B. Bouhafs1 1

Laboratoire de Modélisation et Simulation en Sciences des Matériaux, Université Djillali Liabès de Sidi Bel-Abbès, Sidi Bel-Abbès, 22000, Algeria.

2

Faculty of Nature and Life Science, Hassiba Benbouali University of Chlef, 02000, Algeria.

3

Physics Department, University of South Africa, Pretoria, P O BoX 392, 0003, South Africa 4

LEPM-URMER, Université Abou Bekr Belkaid de Tlemcen, Tlemcen, 13000, Algeria.

Abstract In this study, we present the calculated structural , electronic and magnetic properties of mixed Heusler alloys (Ni1-xCox)2MnSn. Using ab-initio calculations with the full-potential augmented plane-wave method (FP-LAPW), we evaluated the various possible configurations of Ni and Co sites in the (Ni1-xCox)2MnSn crystallographic lattice. The lowest energy configuration is determined based on energetics considerations The calculated equilibrium lattice parameters and magnetic moments are in reasonable agreement with available experimental data. Of interest, we found that the change of total magnetic moment can be interpreted as a linear variation of the magnetic moment of manganese and cobalt atoms.

Keywords: Heusler alloys; Magnetism; Electronic band structure; Density functional theory.

∗ Corresponding

author: (S. Amari) [email protected]

1

1. Introduction Several studies have been carried out on Heusler alloys with emphasis on their structural properties and possible application.1-3 Heusler alloys generally crystallize in two cubic phase. The full-Heusler phase with chemical composition X2YZ crystallizes in the L21 structure (

) and consists of four sets of interpenetrating FCC lattice. The Wyckoff positions for the full-

Heusler phase: (0, 0, 0), (½, ½, ½), (¼, ¼, ¼) and (¾,¾,¾) are occupied by Z, Y, X and X’ respectively (See Fig. 1). The half-Heusler phase with chemical composition XYZ crystallizes in the C1b structure. The Half-Heusler structure is derived from the full Heusler structure by introducing vacancy in one of the two equivalent (X, X’) sites. In the Heusler structures, X is a transition metal, Z is a metal of main group III-V, and Y is a magnetically active transition metal such as manganese. The most widely studied Heusler alloys are the Ni2MnZ (where Z = Sn, Ge, Al, Ga, Sb)6-8 and Co2MnZ (where Z = Sn, Ga, Ge, Al, Si). 9-12 The latter is of interest because due to its magnetic character with resultant magnetic shape memory effect. This character is important in design of magnetic memory (MRAM) and hard disk for information storage in magnetic bits.

In our previous study,13 we determined the structural, electronic, magnetic and thermal properties of Co2MnZ (Z=Al, Ga) using the FP-LAPW method. Roy et al. 14 investigated the effect of Pt, Pd, Cu and Mn substitution at the Ni site in Ni2MnGa alloy system. They found that XXXX. Roy et al., 15 also studied the mechanical, electronic and magnetic properties of Ni2BC and Co2BC (B= Sc, Ti, V, Cr and Mn as well as Y, Zr, Nb, Mo and Tc; C= Ga and Sn) Heusler alloys. They showed that Ni-based materials are typically metallic in nature whereas, all the Co-based alloys exhibit a significant spin polarization at the Fermi level. Pugaczowa-Michalska16 investigated the effect of Ni-substitution on magnetic properties of Ni2MnGe alloy. The magnetic interactions in the ferromagnetic Heusler alloys X2MnY (X = Ni, Cu, Pd, Y = Al, Sn) alloys have been investigated by Kubo and Ishida using the combined orthogonalized plane wave-tight-binding (OPW-TB) method.17 The antiferromagnetic order

2

in the Ni2Mn(MnxSn1−x) Heusler alloy have been studied by Stager and Campbell using X-ray and neutron diffraction techniques. 18

In this study, we systematically evaluated the structural, electronic and magnetic properties of quaternary (Ni1-xCox)2MnSn4,5 Heusler alloy using the full potential linearized augmented plane wave (FP- The manuscript is organized as follows: Section 2 gives a brief description of the method used in the calculations. Section 3 presents the results and discussion. In Section 4, we present the concluding remarks,

2. Computational details The electronic structure was calculated by means of the full potential linearized augmented plane wave (FP-LAPW) method as implemented in WIEN2k code.19 The exchange-correlation functional are described as implemented in the generalized gradient approximation (GGA-PBE).20 The cut-off parameters are RMT×KMAX = 8 for the plane waves and GMAX = 24 a.u-1 for the fourier expansion of potential in the interstitial region, where RMT is the smallest of the MT sphere radius and KMAX is the largest reciprocal lattice vector used in the plane wave expansion. The number of K-points used in the irreducible Brillouin zone (BZ) integration is 112. The muffin-tin sphere radii RMT used are 2.1 a.u. for both Ni and Co, 2.2 for Mn and Sn. The convergence criterion for the self-consistence calculation was set to charge convergence equal to 10-4.

3

3. Results and discussion 3.1. Structural properties The (Ni1-xCox)2MnSn compound is evaluated using a supercell structure (where x is 0, 0.125, 0.25, 0.375, 0.50, 0.625, 0.75, 0.875, 1). The super cell structure contains 16 atoms in the unit, which can be divided into 16 simple cubic sublattices. Eight of this units are occupied by Mn and Sn atoms ordered in a L21 structure, whereas Ni and Co atoms occupy the remaining eight sublattices. The Mn atoms and non-transition metal atoms occupy the following fixed positions (0, 0, 0), (0, ½, ½), (½, 0, ½), (½, ½, 0) for Sn atoms, (½, ½, ½), (½, 0, 0), (0, ½, 0), (0, 0, ½) for Mn atoms), whereas the transition metal Ni and Co atoms can be located at the (¼, ¼ , ¼), (¼, ¾, ¾), (¾, ¼, ¾), (¾,¾, ¼), (¾,¾,¾), (¾, ¼, ¼), (¼,¾, ¼), (¼,¼,¾) sites.

The possible x configuration of Ni and Co atoms concentration in the lattice were considered.. There is only one atomic configuration for concentrations x = 0, 0.125, 0.875 and 1. There are three atomic configurations for the concentration values x = 0.25, 0.75, 0.375 and 0.625. For the x = 0.5 concentration, there are six different configurations of Ni and Co atoms (the various possible occupations of Ni and Co sites in the crystallographic lattice are presented in Table 1.a, 2.a and 3.a). The calculated lattice parameters as shown in Table XXX are in reasonable agreement with experimental data.[reference]

, The minimum energy configurations are presented in Tables 1.b and 2.b. In the case of x = 0.5 (or the NiCoMnSn compound), we found that configurations (I, II, III, IV and VI) are energetically unfavorable, whereas, the V configuration is found to be energetically stable as presented in Table 3.b. Table 4 shows the calculated optimized equilibrium lattice constants, total energy and the magnetization compared to experimental data of (Ni1-

4

xCo x)2MnSn.

The results are in reasonable agreement with experimental studies.[REF] We

found that the lattice parameter of (Ni1-xCox)2MnSn decreases with increasing cobalt content.

3.2. Electronic properties To evaluated the electronic properties, we calculated the total density of states (DOS) and partial density of states (PDOS) of Ni2MnSn and Co2MnSn as presented in Fig. 2 and 3 respectively. From the calculated DOS, we observed that Co2MnSn crystal structure exhibits half-metallicity, while the Ni2MnSn crystal structure is metallic. The atom resolved DOS for the Ni2MnSn structure shows that the metallic character is attributed to the Sn atom with different level of asymmetry observed in the Ni, Mn and Sn atoms. The atom resolved DOS for the Co2MnSn structure shows that all the spin-up states are metallic for the different atom and a band gap is observed in the spin-down states as shown in Figure 3. Figure 4 and 5 shows the total and partial DOS of (Ni1-xCox)2MnSn. The total DOS as a function of Ni/Co concentration does not have a significant change in the over profile. The 3d states of Mn, Co and Ni atoms (see Figure 5) governs the electronic character of this compound around the Fermi level. Also, significant hybridization is observed amongst these transition metal atoms. The character for all the different concentration of Ni/Co is significantly different for the spin up and down states around the Fermi level. The DOS of various concentration shows significant contribution from the Mn 3d states. There is a large exchange splitting of the attributed to the Mn 3d states. The large exchange splitting results in large localized spin moment at the Mn site. The existence of this localized moments has been experimentally verified. 5 The contribution from the sp states are minimal hence not presented in the current investigation for the various atoms.

5

If Co concentration is increased, there are low significant changes in the electronic structure. One in the increase on magnetic moment could be a reason of change of Co and Mn magnetic moment (see Fig. 4). The other is the change of the position of the Fermi level in this way we noticed an emergence of a gap in the case of Co 2MnSn alloy. Due to the increase of Mn-Co and Co-Co interactions. Counter to the other alloys, when the minority Mn-bands hybridize very little with Ni-bands. 3.3. Magnetic properties The total magnetic moment of the (Ni1-xCox)2MnSn Heusler alloys and magnetic moment per atom are shown in Figure 6. Figure 6a compares our results with recent experimental[REF] and theoretical results.[REF] The increase in the Co concentration results in significant increase in the total magnetic moment of (Ni1-xCox)2MnSn. Figure 6b does not make sense. Our calculations show that the values of the saturation magnetization calculated on the quaternary alloys increase to 5.21 B when four Co and two Ni atoms are in the (Ni1xCo x)2MnSn

lattice (See Table 4). The increased magnetic moment for Ni0.75Co1.25MnSn,

Ni0.5Co1.5MnSn and Ni0.25Co1.75MnSni is different from those reported in Ref. 4. This is attributed to the position of the cobalt and nickel atoms in the cell (see Fig. 1). This calculations show that there is a small decrease of Mn spin moment, this reduction is attributed to strong hybridization between Mn 3d states and Ga sp states. The dependence of the local magnetic moment on the Co atoms depends on the location of the cobalt atom in the cell, and also on the increase Co-Ni interactions, which it’s clearly seen from the Figure 4. The Sn atoms give the lowest contribution to the total magnetic moment (-0.05, -0.07 B). 4. Conclusion In summary, using full-potential augmented-plane-wave method, we performed firstprinciples calculations of the total energy, density of states and magnetic moment of Co- and Mn-based Heusler alloys with varying composition (Ni1-xCox)2MnSn. The calculated 6

structural and magnetic properties are in reasonable agreement with experimental data. We found that the presence and location of the Co/Ni atoms determine the overall magnetic moment of (Ni1-xCox)2MnSn alloys. We found that Ni2MnSn and Co2MnSn are metallic and half-metallic respectively. On the other hand the total magnetic moment is determined by Mn atoms but its local magnetic moment can be increased due to strong hybridization between Mn-Co and Co-Ni bands. We also observe a very small negative contribution from Sn atoms (-0.05, -0.07 B) to the total magnetic moment.

Acknowledgements B.B acknowledges the Algerian Academy of Sciences and Technology (AAST) and the Abdus-Salam International Center for Theoretical Physics (ICTP, Trieste, Italy). K.O.O thanks Moritz Braun and the University of South Africa for financial support.

References 1. G. E. Bacon, J.S. Plant, J. Phys. F: Met. Phys. 1, 524 (1971). 7

2. J. Dubowik, I. Gościańska, A. Szlaferek, Y. V. Kudryavtsev, Mat. Sci. Poland 25 (2007) 583. 3. I. Galanakis, Ph. Mavropoulos, P. H. Dederichs, J. Phys. D Appl. Phys. 39, 765 (2006). 4. M. Pugaczowa-Michalska, J. Magn. Magn. Mater. 185, 35 (1998). 5. E. Uhl, J. Solid State Chem. 43, 354 (1982). 6. A. T. Zayak and P. Entel, J. Magn. Magn. Mater. 290-291, 874 (2005). 7. S. Ağduk and G. Gökoğlu, J. Alloys Compd. 511, 9 (2012). 8. J. Li, Z. Zhang, Y. Sun, J. Zhang, G. Zhou, H. Luo, G. Liu, Physica B: Condensed Matter 409, 35 (2013). 9. P. J. Webster, J. Phys. Chem. Solids 32, 1221 (1971). 10. E. Valerio, C. Grigorescu, S.A. Manea, F. Guinneton, W.R. Branford, M. Autric, Appl. Surf. Sci. 247, 151 (2005). 11. S. Picozzi and A. Continenza, Phys. Rev. B 66, 094421 (2002). 12. Y. Kurtulus, R. Dronskowski, G. D. Samolyuk, and V. P. Antropov, Phys. Rev. B 71, 014425 (2005). 13. R. Mebsout, S. Amari, S. Méçabih, B. Abbar, B. Bouhafs, Int. J. Thermophys. 34, 507 (2013). 14. T. Roy, M. E. Gruner, P. Entel, A. Chakrabarti , J. Alloys Compd. 632, 822 (2015). 15. T. Roy, D. Pandey, A. Chakrabarti, Phys. Rev. B 93, 184102 (2016). 16. M. Pugaczowa-Michalska, Comput. Mater. Sci. 50, 15 (2010). 17. Y. Kubo, S. Ishida, J. Magn. Magn. Mater. 31–34, 47 (1983). 18. C. V. Stager, C. C. M. Campbell, Can. J. Phys. 56, 674 (1978). 19. P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, J. Luitz, An Augmented Plane Wave Plus Local Orbitals Program for Calculating Crystal Properties, (Vienna University of Technology, Austria, 2012). 20. J. P. Perdew, S. Burke and M. Ernzehof, Phys. Rev. Lett. 77, 3865 (1996). 8

21. M. Asato, M. Ohkubo, T. Hoshino, F. Nakamura, N. Fujima and H. Tatsuoka, Mater. Trans. 49, 1760 (2008). 22. F. Heusler, W. Stark, and E. Haupt, Verh. der Phys. Ges. 5, 219 (1903).

Figure captions: Fig. 1: Drawing of crystal structure of the Heusler crystal structure of Ni2MnSn.

9

Fig. 2: The calculated total and partial spin-polarized densities of states of Ni2MnSn. The vertical dashed line indicates the Fermi level. The positive and negative values of DOS, hold for spin-up and spin-down states, respectively. Fig. 3: The calculated total and partial spin-polarized densities of states of Co 2MnSn. The vertical dashed line indicates the Fermi level. The positive and negative values of DOS, hold for spin-up and spin-down states, respectively. Fig. 4: The calculated total spin-polarized densities of states of (Ni1-xCox)2MnSn alloys. The vertical dashed line indicates the Fermi level. The positive and negative values of DOS, hold for spin-up and spin-down states, respectively. Fig. 5: The calculated partial spin-polarized densities of states of (Ni1-xCox)2MnSn alloys. The vertical dashed line indicates the Fermi level. The positive and negative values of DOS, hold for spin-up and spin-down states, respectively. Fig. 6: The dependence of the (a) total and (b) local magnetic moments on the concentration x for (Ni1-xCox)2MnSn. Experimental and theoretical magnetic moment values are taken from Refs. 4 and 5.

Table Captions:

10

Table 1:

(a)

The various possible site

occupancy configurations

for

x=0.25.

Configurations for x=0.75 are obtained by replacement of Ni atoms by Co atoms- and vice versa for both systems. (b) The relative total energy ΔEi = Ei -E0 (mRy/atom) of the configuration specified in Table 1.a.

Table 2: (a) The various possible site occupancy configurations for x=0.375. Configurations for x=0.625 are obtained by replacement of Ni atoms by Co atoms and vice-versa for both systems. (b) The relative total energy ΔEi = Ei -E0 (mRy/atom) of the configuration specified in Table 2.a.

Table 3: (a) The various possible site occupancy configurations for x=0.5. (b) The relative total energy ΔEi = Ei - E0 (mRy/atom) of the configuration specified in Table 3.a.

Table 4: The calculated lattice constants a (in Å), total magnetic moment µtot (in µB/Cell) per cell and the local magnetic moments µMn, µCo, µNi (in µB/atom) of Mn, Co, and Ni atoms, respectively, of the (Ni1-xCox)2MnSn alloys, and compared to experimental and other theoretical works when available. .

Table 1.a Site

I

II

III

(1/4, 1/4, 1/4) (1)

Ni

Ni

Ni

(1/4, 3/4, 3/4) (2)

Ni

Ni

Ni

11

(3/4, 1/4, 3/4) (3)

Ni

Ni

Ni

(3/4, 3/4, 1/4) (4)

Ni

Co

Ni

(3/4, 3/4, 3/4) (5)

Ni

Co

Co

(3/4, 1/4, 1/4) (6)

Co

Ni

Co

(1/4, 3/4, 1/4) (7)

Co

Ni

Ni

(1/4, 1/4, 3/4) (8)

Ni

Ni

Ni

Table 1.b Composition

ΔEI

ΔEII

ΔEIII

0.75

Ni0.5Co1.5MnSn

6.0

7.25

0

0.25

Ni1.5Co0.5MnSn

8.25

7.6

0.5(-)

Table 2.a Site

I

II

III

(1/4, 1/4, 1/4) (1)

Ni

Ni

Ni

(1/4, 3/4, 3/4) (2)

Ni

Ni

Co

12

(3/4, 1/4, 3/4) (3)

Ni

Ni

Ni

(3/4, 3/4, 1/4) (4)

Co

Co

Co

(3/4, 3/4, 3/4) (5)

Co

Ni

Ni

(3/4, 1/4, 1/4) (6)

Co

Co

Co

(1/4, 3/4, 1/4) (7)

Ni

Co

Ni

(1/4, 1/4, 3/4) (8)

Ni

Ni

Ni

Table 2.b Composition

ΔEI

ΔEII

ΔEIII

0.625

Ni0.75Co1.25MnSn

7.0

14.0

0

0.375

Ni1.25Co0.75MnSn

6.6

15.5

0

Table 3.a Site

I

II

III

(1/4, 1/4, 1/4) (1)

Ni

Ni

Ni

(1/4, 3/4, 3/4) (2)

Co

Co

Ni

13

(3/4, 1/4, 3/4) (3)

Ni

Ni

Ni

(3/4, 3/4, 1/4) (4)

Co

Ni

Co

(3/4, 3/4, 3/4) (5)

Co

Co

Co

(3/4, 1/4, 1/4) (6)

Ni

Co

Co

(1/4, 3/4, 1/4) (7)

Co

Co

Co

(1/4, 1/4, 3/4) (8)

Ni

Ni

Ni

Table 3.b Composition 0.5

NiCoMnSn

ΔEI

ΔEII

ΔEIII

ΔEIV

ΔEV

ΔEVI

14.35

6.0

13.6

8.0

0.6

30.5

Table 4 Total

a

Mn

Co

Ni

Our calc.

Exp. Ref. 5

Our calc.

Other calc. Ref. 4

Exp. Ref. 5

Our calc.

Ni2MnSn

6.054

6.052

4.00

4.063

3.98

3.38

-

0.23

Ni1.75Co0.25MnSn

6.050

6.046

4.10

4.09

-

3.33

1.28

0.28

Ni1.5Co0.5MnSn

6.046

6.040

4.51

4.26

4.28

3.33

1.26

0.28

Ni1.25Co0.75MnSn

6.041

6.033

4.60

4.41

-

3.27

1.23

0.32

NiCoMnSn

6.032

6.027

4.91

4.51

4.55

3.26

1.22

0.33

Ni0.75Co1.25MnSn

6.024

6.020

5.11

4.70

-

3.22

1.20

0.39

Ni0.5Co1.5MnSn

6.012

6.013

5.20

4.86

4.89

3.16

1.16

0.43

Ni0.25Co1.75MnSn

5.999

6.007

5.21

4.99

-

3.13

1.10

0.51

Co2MnSn

5.985

5.999

5.09

5.02

5.02

3.00

1.05

-

Fig. 1

14

Fig. 2 15

Fig. 3

16

Fig. 4

17

Fig. 5

18

Fig. 6

19

20