Ab initio study of electronic and magnetic properties of the Fe3Zn intermetallic

Physica B 406 (2011) 1752–1756

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Ab initio study of electronic and magnetic properties of the Fe3Zn intermetallic$ C. Paduani a,, C. Bormio-Nunes b a b

´polis, CEP 88040-900, SC, Brazil Departamento de Fı´sica, UFSC, Floriano Escola de Engenharia Lorena, USP, Lorena, CEP 12602-860, SP, Brazil

a r t i c l e i n f o

a b s t r a c t

Article history: Received 17 December 2010 Accepted 7 February 2011 Available online 15 February 2011

First-principles calculations have been carried out to study the electronic structure and magnetic properties of the Fe3Zn compound with the full-potential linearized augmented-plane wave (FLAPW) method. The results indicate a lower magnetostriction for Fe3Zn as compared to Galfenol (Fe–Ga), as a result of a weaker spin–orbit coupling, which is due to a smaller magnetic moment induced on the Zn atom. With the Zn addition to Fe the bulk modulus and the cohesive energy (per atom) decrease, whereas the electronic specific heat coefficient g has a substantial increase. & 2011 Elsevier B.V. All rights reserved.

Keywords: Magnetostriction Electronic structure of metals and alloys Magnetic applications Ab initio calculations

1. Introduction Since the discovery of a large magnetostriction in the Fe–Ga system (Galfenol) the search for Fe-based materials with nonmagnetic elements having good magnetostrictive performance has been in the focus of attention of the materials science research. In the Fe1  xGax system a study of the phase relations in single crystals found a strong dependence of the magnetostriction on the sample thermal history as well as on the state of the chemical ordering in the alloys, besides obviously the composition [1–4]. In disordered Fe–Ga alloys with A2 structure the formation of Ga–Ga pairs aligned with the /0 0 1S direction and the strain introduced in the vicinity of these pairs have been considered as the driving mechanism responsible for the magnetostriction enhancement [4–9]. The Fe–Zn system had been seen as a promising candidate in the class of Fe-based materials with good magnetostrictive performance, considering that Zn and Ga are neighbors in the periodic table and are both diamagnetic [10]. However, experimental results showed that, although the addition of small amounts of Zn to Fe indeed does increases the magnetostriction, the effect is substantially below the performance of Ga, for reasons still unclear. In disordered Fe1  xZnx alloys the a-phase (A2 structure) is observed for 0 o x o 0:42 above room temperature and below 1055 K, which decomposes into the G-phase for 0:42 o x o0:70. The composition dependence of the unit cell

$

This work was supported by CNPq and Finep.

 Corresponding author. Tel.: + 55 48 3721 9234; fax: + 55 48 3721 9946.

E-mail address: paduani@fisica.ufsc.br (C. Paduani). 0921-4526/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2011.02.021

volume in the A2 structure is very similar to both Fe–Ga and Fe–Zn systems. For instance, the increase of the lattice parameter with the addition of 29 at% Ga is from 0.28670 nm (pure Fe) to 0.29240 nm. In the literature a lattice parameter of 0.29406 nm for Fe67Zn33 [11] has been reported. Since an investigation of the effect of the formation of pairs of Zn atoms on the electronic structure of the Fe–Zn alloy has not been performed yet, in this work is studied the electronic structure of the Fe3Zn compound by using a supercell of 16 atoms representative of a bcc lattice (in the small cell). The effect of the substitution of Zn for Fe atoms on the electronic structure is investigated by simulating a disordered B2 ordering where the body centered sites are partially occupied by Zn atoms.

2. Method The spin-polarized scalar relativistic calculations were carried out with the FLAPW method [12]. Exchange and correlation effects are treated with the generalized gradient approximation (GGA) using the Perdew–Burke–Ernzerhof parametrization [13]. Muffin-tin radii used are RFe ¼2.22 a.u. and RZn ¼2.33 a.u. The integration in the Brillouin zone was performed in 6000 k-points with the improved tetrahedron method [14]. A criterion of energy set to 10  2 mRy was used to achieve convergence. The atomic wave function expansion was set to l ¼ 10, and the charge density Fourier expansion cutoff was taken at Gmax ¼12. The cutoff is RmtKmax ¼8.0, where Kmax is the maximum value of the reciprocal lattice vector used in the plane wave expansion, and Rmt is the smallest atomic sphere radius in the unit cell. The calculations were performed for pure bcc Fe and for Fe3Zn in a supercell of

C. Paduani, C. Bormio-Nunes / Physica B 406 (2011) 1752–1756

16 atoms in C1b-type structure (space group F43mÞ as depicted in Fig. 1, which has a A2-like arrangement in the small cell. With this we want to model disordered B2 ordering in this alloy corresponding to a solute concentration of 25 at% Zn. A minimization of the total energy against unit cell volume was performed in order to obtain the equilibrium lattice spacing by fitting to the Birch–Murnaghan equation of states.

3. Results and discussion The calculated equilibrium parameters agree well with available experimental data [15–20], and are listed in Table 1, where is

Fig. 1. Supercell representing Fe3Zn.

Table 1 Calculated equilibrium parameters for Fe3Fe, Fe3Zn and Fe3Ga lattice constant (bohr), bulk modulus B (GPa) magnetic moments (mB ), cohesive energy (eV/atom), and electronic specific heat coefficient g (mJ/mol cell K2).

Fe3Ga

msp

md

Fe

Zn

Fe

Zn

–  0.10

2.30 2.54

– 0.04

5.382 5.516

186.62 133.25

 0.05  0.03

a

B

msp

5.72

264.35

md

Fe

Ga

Fe

Ga

 0.02

 0.10

2.52

0.00

Ecoh

g

6.31 4.90

3.20 5.06

Ecoh

g

5.43

3.97

3.0

μFe 0.10

Fe3Fe E-Eo (eV)

Fe3Fe Fe3Zn

B

also included calculated results [21] for Fe3Ga. According to the Fe–Zn phase diagram, alloys quenched from high temperatures are stabilized with bcc structure, and at 25 at% Zn the reported experimental lattice parameter is 5.524 a.u. [15]. The calculated equilibrium lattice parameter for Fe3Zn shown in Table 1 is in good agreement with the experimental result. Hence, as one sees in Table 1 the lattice expands with the Zn addition to Fe, the bulk modulus decreases and the electronic specific heat coefficient g increases substantially, whereas the cohesive energy (per atom) decreases. This is indicative of a decreased stiffness, higher conductivity as well as smaller hardness for Fe3Zn. The calculated magnetic moment on the Fe atom in Fe3Zn and Fe3Ga is higher than in pure Fe, as shown in Table 1. The contributions from the conduction band msp and from d-electrons (md ) are also included in Table 1. These contributions have opposite signs, as typically is observed in ferromagnetic compounds. In Table 1 one sees that msp is similar for both Zn and Ga atoms. However, although in Fe3Ga no contribution to the atomic magnetic moment of the Ga atom from d-electrons is found, in Fe3Zn a small positive contribution arises from the d-electrons of the Zn atom, which thus gives a smaller moment on the Zn atom. As a consequence, this leads to a weaker spin–orbit coupling in Fe3Zn as compared with Fe3Ga. In Fig. 2 one sees a monotonic decrease of the Fe moment, which collapses under lattice compression. Although no report has been found concerning measurements for the magnetic moment carried by the Fe atoms in Fe–Zn alloys, in a disordered Fe–Zn alloy with 25 at% Zn the estimated average moment is about 1:57 mB , corresponding to a saturation magnetization of about 160 emu/g at room temperature [15]. In Fe3Zn the formation of Zn–Zn pairs leads to a slight increase in the magnetic moment on the neighboring Fe atoms. In Fig. 2 one sees that the moment on the Fe atom in the supercell is similar to Fe3Zn and Fe3Fe, for cell volumes above and below the equilibrium value. The calculated band structures and the total density of states (DOS) are shown in Fig. 3 for pure Fe (Fe3Fe) and Fe3Zn. From a comparison of the DOS plots one sees that the additional electrons of the Zn atoms completely fill the majority spin channel in Fe3Zn. The highly localized deep sp-states from the Zn atoms create the sharp resonant peak at about  7 eV below the Fermi level, which arises from extremely flattered bands. The sharp peaks seen in pure Fe are smeared into smaller peaks in Fe3Zn within an energy range of about 5 eV below EF in the majority spin channel. Conversely, for minority spins the peaky structure seen in the DOS for Fe, at about 2 eV below EF, tends to merge into a sharp peak in Fe3Zn at about 1.2 eV, due to the accumulation of states arising from the flattered bands at the

0.05

Fe3Zn

Magnetic moment (μB)

a

1753

2.5

Fe3Zn Fe3Fe

0.00 2.0 140

160

180

200

unit cell volume (bohr3)

220

140

160

180

200

unit cell volume (bohr3)

Fig. 2. (a) Total energy versus unit cell volume; (b) Fe moment versus unit cell volume.

220

1754

C. Paduani, C. Bormio-Nunes / Physica B 406 (2011) 1752–1756

2

2

1

1

Energy (eV)

0

EF

0

-1

-1

-2

-2

-3

-3

-4

-4

-5

-5

-6

-6

-7

-7

-8

-8

-9

-9

dn

up

-10 W

L

Λ

Γ

Δ

X Z W K 10

5

00

5

Energy (eV)

EF

10 W

L

Λ

Γ

Δ

-10 X ZWK

DOS (states/eV.cell)

2

2

1

1

Energy (eV)

0

EF

0

-1

-1

-2

-2

-3

-3

-4

-4

-5

-5

-6

-6

-7

-7

-8

-8

-9

up

-10 W

L

Λ

Γ

Δ

X Z W K 10

5

-9

dn 00

5

Energy (eV)

EF

10 W

L

Λ

Γ

Δ

-10 XZWK

DOS (states/eV.cell) Fig. 3. Band structure along symmetry directions around the Fermi level and total DOS for Fe3Zn and pure Fe (Fe3Fe).

zone boundaries (L and X points in the diagram). In Fig. 3 one can observe an increased localization (in energy) of valence states in the minority spin channel for Fe3Zn. The Fermi level lies on a shoulder of a prominent peak, and is observed tendency for the formation of degenerate bands at the zone center. The l-projected DOS plots for d-states (eg and t2g) are shown in Fig. 4. The profile of the partial DOS for Fe3Zn is similar to Fe3Ga [21], except for EF lying exactly on the peaks for both eg and t2g states. The increased localization of valence d states in Fe3Zn is clearly seen. One can see in Fig. 4 that both eg and t2g orbitals are shifted up to higher energies, which implies a weakening of interactions in Fe3Zn, as compared with pure Fe. This is also reflected in the lower cohesive energy for Fe3Zn, as seen

in Table 1. From a comparison with pure Fe one sees that in the conduction band region peaks are seen only in the minority spin channel, with preponderance of t2g states. It is noteworthy that from first-principles calculations it has been also reported the appearance of an additional peak in the spin-down t2g manifold near the Fermi level in Fe–Ga alloys [4]. A further splitting of this peak is exactly the reason claimed by Wu [4] for the large magnetoelastic coupling in the L60 structure of Galfenol, which is expected to be resulting from the lowering from the local symmetry around the Fe atom upon Ga doping, caused entirely by the existence of /1 0 0S Ga–Ga pair ordering in the alloy. Figs. 5(a) and (b) show the charge density distribution (3D plots and contour plots) for spin-up and spin-down in the

C. Paduani, C. Bormio-Nunes / Physica B 406 (2011) 1752–1756

plane z ¼ 14 (see Fig. 1) for Fe3Zn. The higher peaks in the 3D plots indicate Zn atoms, and the smaller ones indicate Fe atoms. The completely filled spin channel from Zn atoms in Fe3Zn gives rise to the sharp peaks in the 3D plots shown in Fig. 5, whereas the unfilled minority spin channel of Fe atoms are responsible for

-5 8 6

Fe3 Zn up

-4

-3

-2

-1

0

2

1

2

EF

eg

d-states

1

t 2g

4 2 0 8

DOS (states/eV.F.U.)

6

Fe3 Zn dn

4 2 0 8 6

Fe3Fe up

4 2 0 8 6

Fe3Fe dn

4 2 0 -5

-4

-3

-2

-1

0

Energy (eV) Fig. 4. Projected DOS for eg states (shaded area) and t2g states (dotted line).

1755

the smaller peaks. The bonding characteristic is metallic, and there is no propensity for the formation of covalent or ionic bonding (Fe and Zn have close electronegativities). It is interesting to observe in Fig. 5 a stronger hybridization for the minority spin channel in the plane of the Zn atoms, one feature also depicted in Fig. 4 for the eg and t2g states in Fe3Zn. It can be seen an observable interaction between the Zn and the neighboring Fe atoms. The calculated hyperfine field at the Fe nuclei in Fe3Zn is  251.64 kG, with contributions of 61.55 kG from semicore electrons and  313.19 kG from core electrons. For Fe3Fe these are  26.55,  278.79 and 305.34 kG, respectively. The contributions from core electrons and valence electrons to the spin density at the Fe nuclei have opposite signs in Fe3Zn. In pure bcc Fe the experimental result is 330 kG. As the centroid of the DOS is shifted to lower energies (see Fig. 3) there is an increase in the core polarization, which contributes to increase the density of s-electrons at the Fe nuclei as well as to increase the antiferromagnetic interaction between localized valence electrons and conduction electrons, causing therein the increase of the Fe moment. With the substitution of Zn for Fe atoms there is a small increase in the number of spin up electrons in the Fe MT spheres and a decrease in the number of spin down electrons. Finally, in order to make an assessment of the magnitude of the spin-orbit coupling we performed relativistic calculations for both Fe3Zn and Fe3Ga. By comparing the band degeneracy between the two relativistic calculations we observed that the degree of degeneracy in the scalar relativistic treatment is reduced at K point due to spin-orbit coupling. Hence, the energy splittings at K point have been taken as a magnitude of spin-orbit interaction:  0.32 eV for Fe3Zn and  0.64 eV for Fe3Ga. A ratio of two is obtained, which thus corroborates the experimental finding of a much higher magnetostriction for Galfenol. As a conclusion, the present calculations in supercells representing the bcc lattice for a disordered B2 ordering in Fe3Zn indicate that the lower magnetostriction observed in this compound, as compared to Fe3Ga, is ascribed to a weaker spin– orbit coupling as a consequence of the smaller moment on the solute (Zn) atoms, in addition to a smaller bulk modulus and lower cohesive energy. In Fe3Zn we found an induced moment on

Fig. 5. 3D plots and contour plots for the valence charge density distribution of spin up (a) and spin down (b), for Fe3Zn in the plane z ¼

1 4

(see Fig. 1).

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C. Paduani, C. Bormio-Nunes / Physica B 406 (2011) 1752–1756

the Zn atoms of about  0.06 mB , which is consistent with results of measurements of X-ray magnetic circular dichroism, which yields 0.05 mB .

[9] [10] [11] [12]

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