Investigation of Magnetic and Electronic Properties of Sputtered Fe/Au Multilayers

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DOI 10.1007/s10948-016-3427-0

ORIGINAL PAPER

Investigation of Magnetic and Electronic Properties of Sputtered Fe/Au Multilayers

M. Lassri

¹

· A. Elamiri

^2,3

· K. Chafai

²

· M. Abid

³

· E. K. Hlil

⁴

· R. Moubah

²

· H. Lassri

²

Received: 9 November 2015 / Accepted: 21 January 2016

Abstract We present an experimental and theoretical inves- tigation of magnetic and electronic properties of sputtered Fe/Au multilayers with an emphasis on interfacial effects.

Spin-wave theory was used to simulate the change of mag- netization as a function of temperature for multilayers with different Fe thicknesses, in which several fundamental mag- netic parameters were extracted. The Fe thickness depen- dence of magnetization shows a significant increase of Fe magnetic moment at small Fe thicknesses. Close to the inter- face, the Fe moment is found to be 2.9 μ

B

, which is higher than the value reported in bulk Fe (2.2 μ

^B

). It is shown that the increase in Fe moment is mainly associated with the increase of the Fe–Fe distance close to the interface due to the lattice mismatch between Fe and Au. First-principle cal- culations were performed as well and have supported the proposed scenario.

M. Lassri

lassri [email protected] R. Moubah

[email protected]

1 Centre R´egional des M´etiers de l’Education et de Formation (CRMEF) de Marrakech-Annexe, Essaouira, Morocco

2 LPMMAT, Faculté des Sciences Ain Chock, Université Hassan II de Casablanca, B.P. 5366 Mâarif,

Casablanca, Morocco

3 LPFA, Faculté des Sciences Ain Chock, Université Hassan II-Casablanca, B.P. 5366 Mâarif, Casablanca, Morocco

4 Institut N´eel, CNRS, Universit´e J. Fourier, BP 166, 38042 Grenoble, France

Keywords Multilayers · Interface · Exchange interaction · Magnetic moment · DFT · KKR-CPA method

1 Introduction

Magnetic/non-magnetic multilayers have great potential for use in various spintronic devices. Many experimental and theoretical studies on these heterostructures have uncovered a number of peculiar physical properties due to reduced dimensions which leads to the increase of surface and inter- face contributions [1, 2]. The increase of interface effect is promising for providing captivating properties due to the prevailing correlation between charge, spin, orbital, and lattice degrees of freedom at these interfaces. As a con- sequence, many of the key magnetic properties can be changed, such as the enhancement or suppression of surface moments [3], the emergence of magnetic surface anisotropy [4], and the reduction of the ordering temperature [5].

The magnetic properties of multilayers are strongly depen- dent on their detailed structure and composition, which are in turn depend on the preparation conditions used during growth [6–9]. For example, in the case of Fe/non-magnetic multilayers, the degree of mixing between adjacent lay- ers determines the quantity of Fe capable to contribute to the magnetic properties and the degree of crystallographic texture within the layers, associated with any surface anisotropy defines the anisotropy of multilayers. The Fe/Au multilayers can be viewed as a model system to investigate, as the Fe/Au system exhibits a large giant magnetoresis- tance ratio (GMR) [10]. Moreover, due to the immiscibility between Fe and Au, solid solutions are expected to be not allowed, thus alloying at the interface could be minimized.

In this work, we investigate experimentally and theoretically

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the magnetic and electronic properties of Fe/Au multilay- ers. The thermal variation of the spontaneous magnetization versus Fe thickness is modeled using spin-wave theory. In addition, ab initio electronic structure calculations based on density functional theory (DFT) and Korringa–Kohn–

Rostoker (KKR)-coherent potential approximation (CPA) method combined with local density approximation (LSDA) [11, 12] are performed to explain the important increase of Fe magnetic moment at the interface.

2 Experimental Details

Fe/Au multilayers were prepared by RF sputtering tech- nique. The base pressure was less than 1 − 2 × 10

⁻⁷

mbar, and a working-pressure of Ar of 6.6 × 10

⁻³

mbar was used during deposition. The growth was carried at room temperature. The thickness was measured in situ using a pre-calibrated quartz monitor. The Fe layer thickness t

Fe

was varied from 7 to 72 ˚ A and the Au one (t

Au

) was fixed to 20 ˚ A. The number of bilayers was in the range of 10.

All samples were grown on a 100- ˚ A-thick Au buffer layer and covered by a 20- ˚ A-thick Au layer to protect the samples against oxidation. The substrates were float glass plates. The fcc Au and bcc Fe layers are found to have (111) and (110) textures, respectively. Magnetic measurements were carried out using a vibrating sample magnetometer (VSM) with an external applied field up to 5 T.

3 Electronic and Magnetic Structure Calculations

Ab-initio calculations have been carried out using fully rela- tivistic Korringa–Kohn–Rostoker (KKR) technique [13]. To take into account the metallic atom site disorder, we used coherent potential approximation (CPA), combined with local density approximation (LDA) [14]. Muffin-tin form for the electron charge density and the crystal potential are assumed. Two systems, fcc Au

1−x

Fe

x

and bcc Fe

1−x

Au

x

, were studied, which are assumed to be disordered. The atomic sites are arbitrary occupied by Fe and Au with appro- priate probabilities. A linear change of the cell parameter as a function of composition (x) was assumed, which was obtained by utilizing Vegard formula a(x) = (1 − x)a

Fe/Au

+ xa

Au/Fe

where a

Fe

and a

Au

are the lattice constants of Fe and Au.

4 Results and Discussion

Figure 1 shows the change of the spontaneous magneti- zation as a function of temperature for different Fe thick- nesses; the Au thickness was fixed to 20 ˚ A. As can be

0 50 100 150 200 250 300

0.85 0.90 0.95 1.00

7 Å 10 Å 12.5 Å 20 Å 24 Å 54 Å 64 Å

M (T)/M (5 K)

T (K)

Fig. 1 Temperature dependence of normalized magnetization of Fe/Au multilayers with varying Fe thicknesses,the solid linespresent the fit to the experimental data which were calculated from the spin-wave theory

observed, the slopes of curves decrease with decreasing Fe thickness, showing a reduction of T

C

when the Fe thick- ness decreases. This decrease in T

C

can be explained by the reduction in the Fe–Fe exchange interaction, as a result of finite size effects.

We model the M(T) curves for different Fe thicknesses in the Fe(110)/Au(111) heterostructures. For this purpose, we use the 2D-Heisenberg lattice with in-plane magnetization:

the x- and y-axes are the directions parallel and perpendic- ular to the layer magnetization, respectively. The magnetic surface anisotropy energy is also incorporated in the model, and thus, we obtain the following Hamiltonian:

H = − J

0

i,j ν=2...n−1 μ=1...τ

S

μ,ν,i

S

μ,ν,j

− J

S

i,j ν=1,n μ=1...τ

S

μ,ν,i

S

μ,ν,j

− J

0

i∈ν,j∈ν ν=1...n−1 ν=ν+1 μ=1...τ

S

μ,i∈ν

S

μ,j∈ν

− J

1

i∈νP I,j∈νP S μ=1...τ μ=μ+1

S

μ,i∈ν_{P I}

S

μ,j∈νP S

− K

_S^⊥

iν ν=(1,n) μ=1...τ

S

_i^y_νμ²

+ K

_S

i_ν ν=(1,n) μ=1...τ

S

_i^z²

νμ

− S

^x_i²

νμ

, (1)

where J

0

and J

S

are the bulk and surface exchange inter-

actions. J

1

is the interlayer exchange coupling which is

associated to the atomic plane number m in the non-

magnetic spacer. K

_S^⊥

and K

_S

are the parameters related to

the out-of-plane and in-plane surface anisotropies direc-

tions, respectively. S

μ,ν,i

is the spin operator associated with

the atomic site i in the plane v of the ferromagnetic layer

μ. By using the Holstein–Primakoff transformation at low

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temperature and diagonalizing the Hamiltonian in k space, the spin-wave energy formula was obtained:

ω k

=8S J0

1−cos

a kx

2

cos a kz

√2

1+2 n

Js

J0−1 +

1−1

n 1−cos a kx

2

cos a ky

√2 + J1

2J0n

1−cos kyc

+6S K_S^⊥

n (2)

When T T

C

, only the planar spin waves satisfying k

x

a 1 and k

z

a 1 are excited. The retaining terms are in

quadratic order: cos

a kx 2

, cos

a k√z 2

, and cos

_{a k}

√y 2

; thus, the corresponding change of magnetization as a function of temperature was deduced:

M (T) = M (0)

⎡

⎣1 − V 8π

³

S

Z.B

e

⁻^{β ω(}^k)

1 − e

⁻^{β ω(}^k)

d

³

k

⎤

⎦ , (3)

V being the total volume occupied by magnetic layers.

In case of k

B

T 4SJ

1

and k

B

T 4SJ

1

, (3) can be expressed as the following:

If k

B

T << 4SJ

1

M(T) ∼ = M(0)

⎡

⎢ ⎢

⎣ 1 − 3 √ 6 S

2 T

θ

0

³₂

m +

^√_n²^c_a

1 + m +

²_n

1

S

− 1 m +

_n¹

_c

a

2

1 +

²_n

1 S

− 1

∞ ν=1

e

⁻

ν θ2 n T

ν

³²

⎤

⎥ ⎥

⎦ (4)

And

If k

B

T >> 4SJ

1

M(T ) ∼ = M(0)

⎡

⎢ ⎢

⎣ 1 − 3 √ 6 S 2

T θ

0

³₂

m +

^√_n² _a^c

1 + m +

²_n

1 S

− 1

√ m

1 +

_n²

1 S

− 1

∞ ν=1

e

⁻^{n T}^ν ^(θ¹⁺^θ²⁾

ν

³²

×

1 + ν n T θ

1

e

⁻

c2 a2

T θ0

3π S m ν

⎤

⎥ ⎥

⎦ (5)

where

θ

0

= 24π J

0

S

²

k

B

, m = 1 − 1/n, = J

0

J

1

,

s

= J

0

J

s

, θ

1

= 4 J

1

S k

B

and θ

2

= 6K

^⊥_S

S k

B

(6) By utilizing (5), we have modeled the M(T) data for differ- ent Fe thicknesses of Fe/Au multilayers. The obtained M(T) theoretical curves for various Fe thicknesses (t

Fe

= 10, 12.5, 20, 54, and 72 ˚ A) are shown in Fig. 1 (solid lines). As can be seen, reasonable fits were obtained. The deduced J

0

and J

S

values for all samples are found to be equal to 90 ± 5 and 45 ± 5 K, respectively (S = 1, J

1

, and K

S

are negligible).

We note that J

0

is in agreement with the value reported in Fe bulk [15, 16], which shows the applicability of the model studied here.

The change of magnetization as a function of Fe thick- ness recorded at 4.2 and 300 K is reported in Fig. 2. The magnetization depends sensitively on the Fe thickness. At

300 K, for Fe thicknesses ranging from 24 to 72 ˚ A, the mag- netization is found to be around 1700 ± 80 emu/cm

³

, for t

Fe

< 24 ˚ A, there is an increase of M with decreasing Fe thickness. At 5 K, there is a significant increase of M for t

Fe

≤ 18 ˚ A and a peak value of M of 2200 emu/cm

³

at around t

Fe

= 10 ˚ A, giving rise to an average Fe moment of ∼ 2.6 μ

^B

. This corresponds to an increase in M of about 20 % with respect to that of Fe bulk, and it is well above the error bars. The enhancement of Fe magnetic moment at small Fe thicknesses can be understood by the increase of the Fe–Fe distance due to the difference in the lattice parameters between Fe and Au. The strength of exchange interaction of Fe depends on the interatomic distance nor- malized to the radius of the unfilled d-shell and can be described by the Bethe–Slater curve. Thus, the increase of the Fe–Fe distance will increase the magnetic interaction [17].

To have more information on the origin of the observed

enhancement of magnetization close to the interface, we

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0 10 20 30 40 50 60 70 80 1700

1800 1900 2000 2100

T = 300 K

M (e mu/cm )

t (Å)

T = 4.2 K

Fig. 2 Magnetization as a function of Fe thickness (tFe) recorded at different temperatures: 4.2 and 300 K

have carried out first-principles calculations based on KKR-CPA approach. At the Fe/Au interface, three expected situations can be assumed: (1) Epitaxial growth of Fe takes place for first Fe layers on fcc Au leading to layers with fcc Fe having a lattice parameter close to the Au one, (2) Fe is incorporated in the fcc Au matrix, or (3) Au is inserted in bcc Fe.

In the first situation, in which Fe grows epitaxially on Au (the Fe–Fe distances increase), the simulations show an Fe magnetic moment of 2.9 μ

^B

, highlighting the enhancement of Fe moment with respect to the Fe bulk value.

For the remaining situations, we display in Figs. 3 and 4 the calculated Fe and total magnetic moments as a function of x contents for fcc Au

1−x

Fe

x

and bcc Fe

1−x

Au

x

alloys, respectively. The change of cell constant as a function of x is also reported.

Figure 3 shows that the Fe magnetic moment decreases with increasing x in fcc Au

1−x

Fe

x

system, until it drops to 0 for x > 0.55. For low x values, the Fe magnetic moment is equal to 2.9 μ

^B

, which is bigger than the value reported in pure bcc Fe. This behavior is attributed to the larger Fe–

Fe distance at small Fe content. The drop of the Fe moment at x higher than 0.55 is anomalous and can be explained by

0.0 0.2 0.4 0.6 0.8 1.0

2.8 3.0 3.2 3.4 3.6 3.8 fcc Au_1-xFe_x

Fe moment Total moment Lattice parameter 0.0

0.5 1.0 1.5 2.0

B 2.5 Å

Fig. 3 The change of the calculated Fe and total magnetic moments and cell parameter as a function ofxcontent for fcc Au1−xFexalloys

0.0 0.2 0.4 0.6 0.8 1.0

2.8 3.0 3.2 3.4 3.6 3.8 bcc Fe_1-xAu_x

Fe moment Total moment Lattice parameter 0.0

0.5 1.0 1.5 2.0 2.5 3.0

Cell parameter (Å)

Magnetic moments (µB)

Fig. 4 The dependence of the calculated Fe and total magnetic moments and cell parameter as a function of x content for bcc Fe1−xAuxsystem

the stabilization of the fcc Fe phase at high Fe concentra- tion. fcc Fe is known to have different complex magnetic structures, including paramagnetic, antiferromagnetic, fer- rimagnetic, or low-moment ferromagnetic [18–20]. This is due to the fact that the Fe magnetic moment is very sensitive to its environment in fcc structure; thus, the modifications of the interatomic distances drastically affect the Fe magnetic moment (see for instance Refs. [18–20]). We found that the Au magnetic moment is very small. The total magnetic moment increases with increasing x due to the increase of Fe concentration, and at x > 0.55, it drops to 0. The lattice parameter is found to decrease with increasing Fe content due to the smaller cell parameter of Fe with respect to the Au one.

In the case of bcc Fe

1−x

Au

x

(Fig. 4), the Fe magnetic moment is enhanced with increasing Au concentration from 0 to 0.55 with a maximum of around 3.25 μ

B

at x = 0.53.

This increase can be explained by the increase of the Fe–Fe distance when the Au concentration increases. Above x = 0.53, the Fe moment suddenly decreases. No Au magnetic polarization is observed for this case. The total magnetic moment is found to decrease with increasing Au content, due to the fact that Au is non-magnetic.

In all the tree studied cases, the calculations show the enhancement of Fe magnetic moment when Fe grows epi- taxially on Au, Au

1−x

Fe

x

, and Fe

1−x

Au

x

phases. Accord- ing to Fe and Au phase diagrams, the probability of having an alloy at the Fe/Au interface even in multilayer structure is too weak. Therefore, we can eliminate the existence of alloying at the Fe/Au interface. However, we can argue that for the first Fe deposited layers, where the Fe–Fe distance increases, an enhancement of Fe magnetic moment occurs.

Once the Fe thickness increases, the strain due to the lattice mismatch between Fe and Au disappears and Fe stabilizes its usual bcc phase with corresponding Fe magnetic moment equal to 2.2 μ

B

.

To have more information on the magnetic properties of

the Fe/Au multilayers, we display the total density of states

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(DOS), deduced from the band structure calculations for bcc Fe

20

Au

80

in Fig. 5a. The Fermi level presents no zero DOS, highlighting a metallic behavior. One can notice that there is a shift between the spin-up and spin-down bands showing a polarized nature. Figure 5b, c displays the l- decomposed DOS of like states 2s, 2p, and 3d, for Fe atom and 5s, 5p, 5d, and 6f for Au atom. It can be seen that the total DOS is principally due the 5d Au state in the valence band, while the 3d Fe band takes part in both occu- pied and unoccupied states close to Fermi level. The Au

-14 -12 -10 -8 -6 -4 -2 0 2

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

Down Up

n

Au

(sts./eV )

Energy (eV)

Total 5s 5p 5d 6f

Au

(c)

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

n

tot

(sts./eV )

Total Fe Au

Down Up

(a)

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4

Down Up

n

Fe

(sts./eV )

Total 2s 2p 3d

Fe

(b)

Fig. 5 aTotal and partial Au and DOSs for fcc Fe_0.2Au_0.8. The l- decomposed DOS of like states s, p, and d ofbFe andcAu

(6s, 6p) and Fe (4s, 4p) DOS like-states contributions to both occupied and unoccupied states are negligible com- pared with the other bands. The electronic calculations of Fe (3d) bands show that the spin-up density increases and spin- down lowers in fcc Fe(3d) with respect to bcc Fe(3d). Such population dissimilarity is essentially the magnetic moment if we ignore the spin-orbital coupling. Therefore, we can argue that the expansion of the Fe–Fe distance is the driving force of the increase of Fe magnetic moment at the Fe/Au interface.

5 Conclusions

In conclusion, we have prepared Fe/Au multilayers by RF sputtering and studied their magnetic and electronic prop- erties. The thermal variation of magnetization is calculated using spin-wave theory. A simple model has allowed us to obtain numerical estimates for the bulk exchange interac- tion J

0

and the surface exchange interaction J

S

for different Fe thicknesses. Electronic structure calculations concluded that the enhanced Fe magnetic moment at the interface can be understood by the increase of Fe–Fe distance.

For additional layers, the strain induced by Au disappears and Fe recovers its original bcc structure with magnetic moment of 2.2 μ

B

. Finally, this study will be useful to understand the magnetic and electronic properties of Fe/Au multilayers.

References

1. Agra, K., Gomes, R.R., Della Pace, R.D., Dorneles, L.S., Bohn, F., Corrˆea, M.A.: J. Magn. Magn. Mater. 393, 593 (2015)

2. Moubah, R., Colis, S., Schleicher, F., Najjari, N., Majjad, H., Versini, G., Barre, S., Ulhaq-Bouillet, C., Schmerber, G., Bowen, M., Dinia, A.: Phys. Rev. B82, 024415 (2010)

3. Li, C., Freeman, A.J., Fu, C.L.: J. Magn. Magn. Mater83, 51 (1990)

4. Gradmann, U.: J. Magn. Magn. Mater.54–57, 733 (1986) 5. Schneider, C.M., Bressler, P., Schuster, P.S., Kirschner, J., de

Miguel, J.J., Miranda, R.: Phys. Rev. Lett.64, 1059 (1990) 6. Akbulut, S., Akbulut, A., ¨Ozdemir, M., Yildiz, F.: J. Magn. Magn.

Mater.390, 137 (2015)

7. Krishnan, R., Das, A., Porte, M.: J. Magn. Magn. Mater.168, 15 (1997)

8. Kuru, H., Kockar, H., Alper, M.: J. Magn. Magn. Mater.373, 135 (2015)

9. Chechenin, N.G., Chernykh, P.N., Dushenko, S.A., Dzhun, I.O., Goikhman, A.Y., Rodionova, V.V.: J. Supercond. Nov. Magn.27, 1547 (2014)

10. Monchesky, T.L., Enders, A., Urban, R., Myrtle, K., Heinrich, B., Zhang, X.-G., Butler, W.H., Kirschner, J.: Phys. Rev. B71, 214440 (2005)

11. Yang, L., Liu, B., Luo, H., Meng, F., Liu, H., Liu, E., Wang, W., Wu, G.: J. Magn. Magn. Mater.382, 247 (2015)

(6)

12. El Amiri, A., Moubah, R., Lmai, F., Abid, M., Hassanain, N., Hlil, E.K., Lassri, H.: J. Magn. Magn. Mater. 398, 86 (2016)

13. Ebert, H.: Electronic structure and physical properties of solids.

In: Dreysse, H. (ed.) Lecture Notes in Physics, vol. 535, p. 191.

Springer, Berlin (2009)

14. Moubah, R., Fnidiki, A., Omari, N., Abid, M., Hlil, E.K., Lassri, H.: J. Supercond. Nov. Magn. 28, 2149 (2015)

15. van Schilfgaarde, M., Antropov, V.P.: J. Appl. Phys.85, 4827 (1999)

16. El Khiraoui, S., Sajieddine, M., Hehn, M., Robert, S., Lenoble, O., Bellouard, C., Sahlaoui, M., Benkirane, K.: Physica B403, 2509 (2008)

17. Zamani, A., Moubah, R., Ahlberg, M., Stopfel, H., Arnalds, U.B., Hallén, A., Hjörvarsson, B., Andersson, G., Jönsson, P.E.: J. Appl.

Phys.117, 143903 (2015)

18. Moruzzi, V.L., Markus, P.M., Kubler, J.: Phys. Rev. B39, 6957 (1989)

19. Zhou, Y.-M., Zhang, W.-Q., Zhong, L.-P., Wang, D.-S.: J. Magn.

Magn. Mater.145, L273 (1995)

20. Wu, R., Freeman, A.J.: Rev. Phys. B47, 3904 (1993)