Induced spin polarization in Fe2VAl by substitution of Co at Fe site

Computational Materials Science 108 (2015) 56–61

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Induced spin polarization in Fe2VAl by substitution of Co at Fe site Vivek Kumar Jain, Vishal Jain, N. Lakshmi ⇑, Aarti R. Chandra, K. Venugopalan Department of Physics, Mohanlal Sukhadia University, Udaipur, 313001 Rajasthan, India

a r t i c l e

i n f o

Article history: Received 24 November 2014 Received in revised form 6 May 2015 Accepted 3 June 2015

Keywords: Electronic structure calculation Heusler alloy Semi metallic Half-metallicity Magnetic moment

a b s t r a c t The effects on electronic structure properties by Co substitution in Fe2VAl Heusler alloy have been determined by means of first principle calculations using generalized gradient approximation and calculated equilibrium lattice constants and magnetic moments for the series Fe2xCoxVAl. The value of formation energy is minimized at the Fe (A, C) sites when Co substitutes at Fe, V and Al sites. The semi metallic behavior of Fe2VAl fades, while spin polarization is induced on Fe replaced by Co atom due to the influence of valence electrons of Co at the Fermi level. An enhancement of the total magnetic moment on increase in the Co content is observed due to the ferromagnetic coupling of Fe and Co atoms with V atoms at the B site and hybridization between Co–Co atoms at the A/C sites. Ó 2015 Elsevier B.V. All rights reserved.

1. Introduction Amongst the various half metallic materials studied such as spinels, perovskites and full Heusler alloys, the Co-based Heusler alloys are especially attractive candidates for spintronics applications, because of their half metallicity, high magnetic moment and high Curie temperatures [1,2]. Theoretical and experimental calculations indicate that Fe2VAl is nonmagnetic and exhibits semi metallic behavior making it promising as a thermoelectric material [3–6], whereas Co2VAl and CoFeVAl are predicted to be ferromagnetic, nearly half metallic and possess high spin polarization [7,8]. Previous studies show that Fe2VAl has unusual magnetic and transport properties when other nonmagnetic sp elements (B, In, Si, Ta or Ga) are doped at Al (D) site [9,10]. The partial or total replacement of V by 3d and 5d transition metals in Fe2VAl causes a variation in the density of states (DOS) near the Fermi level resulting in the fading of semi metallic behavior [11–13]. Yuichi et al. have reported that the thermoelectric performance of Fe2VAl based alloys improves due to the effects resulting from heavy element substitution and off-stoichiometric (Fe/V = 2) composition in series such as Fe2x(V0.95xTa0.05)(Al1ySiy) [14] while Nakayama et al. have observed that on Co and Ti co-doping, Fe2VAl based alloys show P type thermoelectric properties when total valence electrons are less than 24 [15]. Meinert et al. reported that Co substitution at Mn site in Mn2xCoxVAl for Co content greater than 0.5 leads to

⇑ Corresponding author. E-mail address: [email protected] (N. Lakshmi). http://dx.doi.org/10.1016/j.commatsci.2015.06.002 0927-0256/Ó 2015 Elsevier B.V. All rights reserved.

change in electronic structure and a parallel coupling of Co, Mn and V is observed [16]. In this work we have investigated the ground state properties of Co substituted Fe2VAl Heusler alloys using the generalized gradient approximation (GGA) since it gives the best description of electronic structural properties through optimization of equilibrium volumes. Using GGA, the theoretically obtained equilibrium lattice constants and magnetic moments show a good match with those obtained experimentally whereas on using local spin density approximation (LSDA) these do not match. The calculations were initiated for the L21 ordered Fe2VAl structure followed by replacing Fe atom by Co. The motivation for substitution of Fe with Co is because many of half metallic Heusler systems are based on Co and also substitution of Fe with Co is expected to increase both the magnetic moment and also the Curie temperature (Tc). 2. Computational method The full potential linear augmented plane wave (FPLAPW) method based on density functional theory has been used to perform electronic structure calculations. The exchange correlation energy was treated using the GGA parameterized by Perdew–Bur ke–Ernzerhof, implemented in WIEN2k package. The core states (3d for V, Fe, Co) were treated fully relativistically, whereas semicore states (3s, 3p for V, Fe, Co), were treated as valence electrons and the valence states were calculated semi-relativistically. Non-spherical contribution to the potential and charge density within spheres were considered up to lmax = 10. The plane-wave cutoff Rmin  Kmax was set at 7 and cutoff distance for superposition is 16.205 a.u. in the interstitial region. Using wave vectors up to

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Gmax = 12 a.u.1, the potential and charge density were expanded as a Fourier series. Relativistic effects were taken into account and muffin tin (MT) sphere radius for both Fe and Co was 2.28 ± 0.02 a.u., 2.24 ± 0.02 a.u. for V and 2.11 ± 0.02 a.u. for Al. Energy chosen was 12.0Ry to separate core and valence states. The number of k-points for sampling in the irreducible part of the Brillouin Zone (BZ) was performed with 3000 k-mesh points. The lattice parameters were determined by the volume optimization technique and a tolerance of 0.0001e and 0.0001Ry had been taken as convergence criteria for self consistent calculations for electron charge and energy of the system respectively. The unit cell of most full-Heusler alloys consists of a face centered cubic cell with four atomic positions A (1/4, 1/4, 1/4), B (1/2, 1/2, 1/2), C (3/4, 3/4, 3/4) and D (0, 0, 0). In general, two types of full Heusler alloys structures are possible (1) normal Heusler alloy (AlCu2Mn-type) and (2) inverse Heusler alloy (CuHg2Ti) type. In normal Heusler alloys X atom occupies A or C positions and is at A or B positions in inverse Heusler alloys. Fe2VAl has a normal Heusler alloy structure with Fm-3m space group as illustrated in Fig. 1. The two equivalent crystallographic sites (designated as A and C) are occupied by Fe atoms and the B and D sites by V and Al atoms respectively. The V atoms at B site are surrounded by eight Fe [A, C] first nearest neighbors (nn) which forms a face centered cubic (fcc) arrangement. Consequently, each of the Fe [A, C] atoms has four V [B] and four Al [D] first nearest neighbors (nn). With respect to each other, the four Al [D] and the four V [B] site form a relative tetrahedral arrangement. All the compounds were modeled using a 2  2  2 super cell of Fe2VAl Heusler alloy. 3. Results and discussion 3.1. Structural properties Phase stability and site preference on substitution of Co in Fe2xCoxVAl was studied in terms of formation energy. The formation energy Eform is defined as [17]

Eform ¼ Etot ðFe2x Cox VAlÞ  ð2  xÞEtot ðFeÞ  xEtot ðCoÞ  Etot ðVÞ  Etot ðAlÞ

ð1Þ

where Etot (Fe2xCoxVAl) is the total energy per atom of the Fe2xCoxVAl unit cell; Etot (Fe), Etot (Co), Etot (V) and Etot (Al) are the total energy per atom of the pure Fe, Co, V, and Al unit cell in their bulk stable states, respectively. In the present series the value of formation energy is found be minimum in case of Co doped at A and C sites as shown in Fig. 2 implying that on doping, Co would

Fig. 2. Formation energy for Fe2xCoxVAl on doping Co at the A, B, C and D sites for different values of x.

preferentially substitute into the A/C, i.e. the Fe sites. We have therefore confined the investigation of electronic structure properties of the series considering the substitution of Fe by Co at the A/C sites. To obtain the optimized lattice constant for Fe2xCoxVAl, the experimental value of the lattice constant for Fe2VAl was used as a starting point and then minimized for total energy for each value of x. Energy and volume curves plotted for Fe2xCoxVAl are shown in Fig. 3. The total energy as a function of the volume per formula unit is given by Muranghan Equation of State (EOS):

" EðVÞ ¼ Eo þ BV o

1



V Bp ðBp  1Þ V o

1þBp þ

1 V 1  Bp V o Bp  1

# ð2Þ

where B is the bulk modulus, Bp is the pressure derivative of the bulk modulus and V is equilibrium volume. The obtained lattice constant (a), the bulk modulus (B), and the pressure derivative of the bulk modulus (Bp) for Fe2xCoxVAl at zero pressure are listed in Table 1. After geometry optimization, the calculated lattice constant is 5.7166 Å for Fe2VAl and 5.7684 Å for Co2VAl which are very close to reported experimental and other theoretically calculated values [4–8]. The pressure derivative (Bp) obtained is slightly lower while the calculated bulk modulus (B) is consistent with other reported values [18,19]. The calculated bulk modulus decreases exponentially with addition of Co in the alloys leading to an increase in the equilibrium volume of the unit cell as evident from Fig. 4a. The minimum conservation energy decreases linearly (Fig. 4b) and consequently results in a linear increase in the lattice parameter (Fig. 4c) due to the concentration of Co as

Fig. 1. Crystal structure of (a) Fe2VAl, (b) FeCoVAl and (c) Co2VAl.

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V.K. Jain et al. / Computational Materials Science 108 (2015) 56–61

Fig. 3. Plots of energy vs. volume for Fe2xCoxVAl.

Table 1 Structure, space group, minimum energy, volume, optimized lattice parameter, bulk modulus, bulk modulus derivative and spin polarization of Fe2xCoxVAl. Structure

Space group

Minimum energy Eo (Ry)

Volume Vo (a.u.)3

Lattice parameter a (Å)

Bulk modulus B (GPa)

Pressure derivative of bulk modulus Bp (GPa)

Spin polarization P (%)

Fe2VAl

Fm-3m (225) P-43m (215) Pn3m (224) P-43m (215) F43m (216) P-43m (215) Pn3m (224) P-43m (215) Fm-3m (225)

7475.623

315.17

5.7166

230.54

4.77

0.5

7535.958

315.81

5.7205

220.93

4.83

54

7596.293

316.62

5.7253

217.64

4.55

80

7656.626

318.01

5.7337

211.47

4.97

83

7716.960

319.19

5.7408

209.42

2.42

90

7777.297

320.09

5.7462

207.22

4.82

92

7837.636

321.16

5.7526

206.18

4.45

96

7897.973

322.27

5.7592

201.27

4.74

96

7958.312

324.65

5.7684

203.76

4.51

94

Fe1.75Co0.25VAl Fe1.5Co0.5VAl Fe1.25Co0.75VAl FeCoVAl Fe0.75Co1.25VAl Fe0.5Co1.5VAl Fe0.25Co1.75VAl Co2VAl

anticipated, since the size of the Co atom is larger than that of Fe. The excellent agreement of lattice parameter with the value determined experimentally points to the correctness of choice of pseudo potentials and the GGA approximation used for the current study. 3.2. Electronic and band structural calculations Fig. 5 shows band structures for Fe2VAl, FeCoVAl and Co2VAl majority and minority spin bands respectively and Fig. 6 shows DOS of all samples. Detailed analysis shows drastic changes of DOS at the Fermi energy level (Ef) when going from Fe2VAl to Co2VAl. In the DOS of Fe2VAl, the majority and minority spin

densities show a pseudo gap at the Ef due to almost zero density of electrons, characteristic of semi-metallic behavior [12]. The band structure calculation is in good agreement (Fig. 5a and b) with DOS (Fig. 6a) as both majority and minority spin bands show a small band gap at the gamma (C) point indicative of a semiconducting behavior. At the X point, both conduction and valence bands overlap typifying metallic behavior. These calculations show that Fe2VAl is a nonmagnetic semimetal because of the equal DOS for majority and minority spins and due to the presence of a considerable pseudo gap at the Ef. However, doping with other elements or the presence of anti-site defects (Fe atoms in V positions in the present case) in real samples can lead to the formation of magnetic states [20,21].

V.K. Jain et al. / Computational Materials Science 108 (2015) 56–61

Fig. 4. (a) Bulk modulus, (b) minimum energy and (c) lattice parameters as a function of Co concentration (x).

In the case of FeCoVAl, both band structure calculations (Fig. 5c and d) and the DOS (Fig. 6e) show metallic behavior in the majority spin band, while a small energy band gap is observed near the Fermi energy level in the minority spin band. Band structure calculations indicate that both valence band and conduction bands meet at the C and K points at Ef in the majority spin band. Near the Fermi level, energy band gaps of 0.1 eV at the X point and 0.5 eV at the C point are observed in the minority spin band. An analysis of partial contributions to the DOS is presented in Fig. 5e which shows that at the Fermi level, density is equally contributed by Fe, Co and V in the majority spin band, while in the minority spin band, Fe and Co show zero densities and V has only a small electron density. In the case of Co2VAl, both band structure calculations (Fig. 5e and f) and DOS (Fig. 6i) indicate metallic behavior in the majority spin band, while an energy band gap of 0.3 eV is observed at the Fermi energy level in the minority spin band. The majority spin conduction bands cross the Fermi level, while there is an energy gap at all points shows at the Fermi level for the minority spin bands. The band gap is of the order of 0.5 eV at the C point and 0.3 eV at the X point. The partial contributions to the DOS presented in Fig. 6(i) shows that the major contribution to the density is from Co and V only has a small contribution in the valence band. At the Fermi energy level, Co and V contribute equally to both the majority and minority spin bands. However in the conduction band, V has a large contribution to both the majority and minority spin bands near Ef. The electron spin polarization (P) at Fermi energy (Ef) of a material is defined by [22]

P¼

q " ðEf Þ  q # ðEf Þ q " ðEf Þ þ q # ðEf Þ

ð3Þ

q" (Ef) and q; (Ef) are the majority and minority DOS at the Fermi energy. If any one of the electron density, either q" or q;, is equal to zero and the other is non-zero, then the electrons at Ef are fully spin polarized (i.e. spin polarization = 100%) and is also called

59

half-metallic. The values of spin polarization P have been calculated using Equation (3), and are listed in Table 1 for Fe2xCoxVAl. Spin polarization for Fe2VAl is negligible due to the equal majority and minority DOS and has almost zero density of electrons at the Fermi level. An analysis of partial contributions to the DOS in (Fig. 6) shows that the top of the valence band is mostly contributed by Fe, while the bottom of the conduction band by both Fe and V. Density contributions of both Fe and V are zero at the Fermi energy level. There is a shift in the DOS in the majority spin on addition of Co atom in Fe2xCoxVAl, but the spin minority DOS is still in the pseudo gap and Fe2xCoxVAl are half-metallic ferromagnets. When the value of x increases, the spin polarization also increases because of the increase in the majority density with the substitution of Fe with Co along with a zero minority density and so P becomes nearly 95%. Fe2xCoxVAl thus exhibits nearly halfmetallic behavior for all values of x P 1. From the detailed analysis of partial DOS, shown in Fig. 6, we observe that when the value of x is increased, the DOS shifts toward the valence band in the case of majority spins. This shift appears due to highly contributing density of Co at the Fermi level. In the case of minority spin, when x = 0, Fe and V have zero density at the Fermi level, but when the value of x increases, Fe and Co densities show band gap at the Fermi energy level indicative of half metallic behavior while V has some density till x = 1. At higher values of x, the V density shifts toward the conduction band and shows band gap at the Fermi level. Fe0.75Co1.25VAl, Fe0.5Co1.5VAl, Fe0.25Co1.75VAl and Co2VAl thus shows high spin polarization and ferromagnetic behavior. Co2VAl with L21 structure exhibits half-metallic behavior, because valence band and conduction bands cross each other at the X point in the majority spin, while there is an energy gap between valence and conduction band around the Fermi level in the minority spin bands. The degradation of the half-metallicity for Co2VAl sample is due to deviation of stoichiometric composition in the matrix L21 phase. First principles calculations have confirmed that the antisite Co defects in half-metallic Co2YZ Heusler alloys give rise to additional electronic states at the Fermi level in the minority-spin energy gap [23]. In Heusler alloys, the covalent hybridization between the lower energy d states of high valence transition metal atoms such as Co or Ni and high energy d states of the lower valence d state of transition metals like Mn or V leads to a band gap in the minority states. This results in the formation of bonding and anti bonding bands with a gap in between [24]. 3.3. Spin magnetic moment The values of total and partial spin magnetic moments of Fe2xCoxVAl have been calculated based on the Co and Fe concentrations and are summarized in Table 2. The obtained values of magnetic moment are consistent with the Slater–Pauling curve (SPC) for full Heusler alloys, in which the magnetic moment per unit cell in multiples of Bohr magnetons (lB) can be calculated as follows [25]:

Mtotal ¼ N  24

ð4Þ

Mtotal denotes the total magnetic moment and N denotes total valence electrons in the unit cell. Here, for Fe2VAl, N = (2  8) + 5 + 3 = 24, i.e. the moment Mtotal will be zero using Equation (4). In Fe2VAl, the interaction between 3d electron of Fe and 3d electrons of V are in opposite directions and cancel the overall moment. To increase the magnetic moment of Fe2VAl, Fe atoms have been replaced by Co atoms and the calculated magnetic moment are listed in Table 2. For FeCoVAl, N = 8 + 9 + 5 + 3 = 25, i.e. the moment Mtotal is 1lB. Similarly, for Co2VAl, N = 26, i.e. the moment Mtotal will be 2lB. Our results match with the Slater – Pauling curve as shown in Table 2. The magnetic moment of Al is

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Fig. 5. Band structure of (a) Fe2VAl majority, (b) Fe2VAl minority, (c) FeCoVAl majority, (d) FeCoVAl minority, (e) Co2VAl majority and (f) Co2VAl minority.

Fig. 6. Total and partial DOS of Fe2xCoxVAl.

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V.K. Jain et al. / Computational Materials Science 108 (2015) 56–61 Table 2 The calculation of partial, total magnetic moment in lB. Sample

Magnetic moment as per SPC (lB)

Total magnetic moment (lB)

Total Fe (lB)

Total Co (lB)

Total V (lB)

Total Al (lB)

Interstitial (lB)

Fe2VAl Fe1.75Co0.25VAl Fe1.5Co0.5VAl Fe1.25Co0.75VAl FeCoVAl Fe0.75Co1.25VAl Fe0.5Co1.5VAl Fe0.25Co1.75VAl Co2VAl

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

0.00 0.21 0.47 0.72 0.97 1.23 1.50 1.75 2.00

0.00 0.06 0.09 0.29 0.49 0.32 0.05 0.07 –

– 0.18 0.39 0.52 0.64 0.97 1.32 1.59 1.89

0.00 0.00 0.04 0.02 0.05 0.04 0.20 0.19 0.22

0.00 0.00 0.01 0.01 0.02 0.02 0.02 0.02 0.02

0.00 0.02 0.03 0.06 0.09 0.08 0.06 0.08 0.09

lattice parameter, bulk modulus, magnetic moment, half metallicity, band gap and spin polarization have been investigated as a function of variation in Co concentration. Formation energy calculations suggest the preferential site occupation by Co at Fe site on doping in Fe2xCoxVAl and electronic structure calculations enable the tuning of the Fermi level. It is confirmed that full-Heusler alloy Fe2VAl exhibits semi-metallic behavior and Co2VAl exhibits half metallic ferromagnetism with the magnetic moments of 0lB and 2lB per formula unit respectively. The calculated magnetic moment matches well with that obtained from experimental studies and also follows the Slater Pauling curve behavior. Also, doping the above system with Co enhances the magnetic moment and as such is capable of producing materials suitable for thermoelectric and spintronics devices. Acknowledgements This work is supported by UGC-BSR Research Fellowship, collaborative research schemes UGC–DAE CSR, Indore, UGC DSA and DST-FIST schemes of the Department of Physics, M L Sukhadia University, Udaipur. Fig. 7. Total magnetic moment (Mtotal) and individual magnetic moments as a function of Co concentration (x).

almost zero and so its contribution is negligible to the total moment. Overall moment increases with the increase in the value of x because of increase in the concentration of Co atoms. From Fig. 7, it is also evident that Fe moment increases with increase in the value of x and becomes maximum when x is equal to 1 after which its moment decreases. This change in the magnetic behavior is due to smaller Co–V hybridization in comparison with Co–Fe hybridization. Thus for x > 1, the moment on V increases due to Co–V hybridization. However, since moments on Fe and V are aligned opposite to each other, the moment on Fe now decreases. In this series, the main group atoms (Al) occupy the D sites, the transition metal atoms, represented by both Co and Fe, occupy the A and/or C-sites as discussed earlier, and the V atoms which have relatively less valence electrons in comparison to Co and Fe atoms occupy the B site. The increasing hybridization between Co–Co atoms (at the A/C sites which are second nearest neighbors to each other) and also the ferromagnetic coupling of the Fe and Co atoms with V atoms (at the B site which are first nearest neighbor to Fe and Co) on increase in the Co concentration in the series results in an enhancement of the total magnetic moment. The total magnetic moment value of 2lB per formula unit calculated for Co2VAl and 1lB for FeCoVAl evidences it to be a half metallic ferromagnet, since an integer value of the magnetic moment is one of the characteristics of half metallic ferromagnets. 4. Conclusion The aim of this work is to study the electronic structure properties of Fe2VAl brought about by replacing Fe atom by Co atom. The

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