Effect of the Interfacial Disorder on the Magnetotransport Properties in Ni81Fe19/Ti10 W 90 Multilayers

DOI 10.1007/s10948-017-3983-y

ORIGINAL PAPER

Effect of the Interfacial Disorder on the Magnetotransport Properties in Ni ₈₁ Fe ₁₉ /Ti ₁₀ W ₉₀ Multilayers

K. El Aidoudi

¹

· A. Qachaou

¹

· M. Lharch

¹

· A. Fahmi

¹

· H. Lassri

²

Received: 15 November 2016 / Accepted: 6 January 2017

© Springer Science+Business Media New York 2017

Abstract This work is a study of the interface structure effect on the magnetotransport properties in Ni

81

Fe

19

/Ti

10

W

90

magnetic multilayer. The overall weakness showed by experimental magnetoresistance rate MR

exp

is probably due to a degradation of the interface quality caused by the apparition of a disordered phase NiFeW at the interface.

Thus, we propose in this paper an extension to the Johnson- Camley semi classical model that takes in consideration the evolution of the interface structure, which makes it possi- ble to reproduce quite faithfully the experimental results MR

exp

(t

NiFe

) for all ranges of magnetic layer thicknesses, confirming the important role of the interface structure on the electronic transport properties.

Keywords Magnetic multilayers · Giant magnetoresistance · Interface · Disorder

1 Introduction

The discovery of giant magnetoresistance (GMR) [1–3] in magnetic multilayers system composed of an alternating of magnetic and nonmagnetic layers attracted a remarkable attention for their fundamental interest as well as for their many possibilities of technological applications.

K. El Aidoudi aidoudi@hotmail.fr

1 Laboratoire Physique de la Mati`ere Condens´ee, Facult´e des Sciences, Kenitra, Morocco

2 Laboratoire Physique des Mat´eriaux et Microstructure, Facult´e des Sciences Ain Chock, Casablanca, Morocco

In fact, by providing sensitive and scalable read tech- niques reading heads based on GMR effect have made possible a giant increase in the areal recording density. Thus, several experimental and theoretical studies were realized to understand the origin of the various interactions existing in this kind of systems, leading to new magnetic properties dif- ferent from those observed in the bulk. It was found that the break of symmetry along the axis perpendicular to the film (interface effect) is one of the principal factors behind those properties.

Theoretical investigations showed that the GMR effect is closely related to the spin-dependent scattering asymmetry effect of the conduction electrons both in bulk and inter- face which is a characteristic property of the transition metal (TM) elements like Fe and Ni. When an electron crosses one of the magnetic layers, it is easily transmitted if its spin is parallel to the magnetization vector of the magnetic layer leading to weak magnetoresistance (MR) ratio, whereas this electron is diffused in the contrary magnetic configuration supporting MR. Moreover, the composition and the quality of the interface also play an important role on the elec- tronic transport properties of magnetic multilayers. In fact, the values of the mean free path (MFP) λ

mx

of the trans- port electrons and the spin-dependent scattering asymmetry coefficient (SDSA) α

mx

depend strongly on the interface roughness [4, 5].

In this work, we focus more on the interface contribu- tion to the magnetotransport properties in Ni

81

Fe

19

/Ti

10

W

90

multilayers. Thus, we will propose a configuration for the interface NiFe/WTi showing the evolution of its structure and its chemical composition as function of the variation of the magnetic layer thickness. This proposition allowed us to estimate the evolution of the two interface parameters: α

mx

and λ

mx

.

The MR thus calculated using these interface parame- ters is in much better agreement with the experience than that we previously obtained [6] in the Johnson-Camley semi-classical model (J-C) [7]. Indeed, in this model, the interface parameters are considered as simple parameters of adjustment with the experiment.

2 Experimental Methods

The samples studied were prepared by the DC magnetron sputtering method [8].The Ni

81

Fe

19

/Ti

10

W

90

multilayers were deposited onto water-cooled Si (100).The chamber was initially evacuated to a pressure of 1–2 × 10

⁻⁷

Torr,using turbo-molecular pump, argon of 5N purity was used as the sputter gas keeping a constant pressure of 6

× 10

⁻³

Torr in the chamber. Growth rates for NiFe and WTi were, respectively, 1.4 and 0.7 ˚ A/s (these rates were obtained from x-ray reflectivity measurement on single films grown for different time intervals). Two series of the samples were obtained by (i) varying the magnetic layer thickness (t

NiFe

) in the range of 10–100 ˚ A and fixing that of WTi layer (t

WTi

) at 20 ˚ A. (ii) The second one were obtained by varying the nonmagnetic layer thickness between t

WTi

3–40 ˚ A and fixing the magnetic layer thickness t

NiFe

at 40 ˚ A.

3 The Proposed Configuration for the NiFe/WTi Interface

As it was suggested in the J-C model, each interface is seen as a tiny layer of a fixed thickness t

mx

, composed of a mixture of magnetic and nonmagnetic atoms. This layer is characterized by its own parameters: the electronic MFP λ

^σ_mx

and the SDSA coefficient α

mx

= λ

^↑mx

λ

^↓mx

.

The previous parameters used to calculate the MR ratio are strongly dependent on the nature and quality of the con- sidered interface. Therefore, it is important to describe more in details the evolution of the structure and chemical com- position of the interface as the magnetic layer thickness change.

Thus, in our case, the interfaces between the magnetic NiFe and nonmagnetic TiW layers are supposed to be rough due to the intrinsic effects (the possible extrinsic effects caused by impurities added to the interfaces are neglected).

Thus we consider that each interface NiFe/TiW constitutes a mixed zone which contains various phases constituted by a mixture of aggregates or “particles” of alloys MW (M = Ni, Fe, NiFe) formed through an interdiffusion of atoms of magnetic and nonmagnetic layers. Furthermore, the Ti

content is very small compared to that of W, so the prob- ability of existence of alloys containing Ti is negligible.

Moreover, the overall weakness showed by MR

exp

in our samples suggests the existence of a disordered phase at the interface. In fact, this disorder is caused by the dif- fusion of nonmagnetic alloying metal W; the introduction of which, even in small proportions, can lead to an amor- phous state when the content of W exceeds a critical level (10 % for Ni–Fe–W, about 20 % for Ni–W, and beyond 40–

50 % for Fe–W [9, 10]. The ternary alloy appears to be the first to form an amorphous state, faster than the other two binary alloys; it is also magnetically softer with a sig- nificant reduction of magnetization [11, 12] when the W content increases. This would explain the significant reduc- tion of MR ratio observed in our samples. The formation of such disordered alloying phase in the interface that we suggest was also reveled in some multilayer samples [13–

15]. Thus, we suppose that the mixed zone can be divided to three areas (Fig. 1): The first one is adjacent to the NiFe magnetic layer and it contains the NiFe alloy as major- ity and { W, NiW, FeW } phases as minority. The second area is adjacent to the WTi nonmagnetic layer, and it con- tains a majority of the W element and a minority of { NiFe, NiW, NiFeW } phases. The third area is situated at the cen- ter of the interface and composed basically of the NiFeW alloy, the principal responsible of the disorder at the inter- face level. It is characterized by this set of parameters:

{ t

alloy

, α

alloy

, λ

^σ_alloy

} .

3.1 Calculation of the Interface Parameters α

mx

and λ

^σ_mx

The variation of the magnetic layer thickness causes a chem- ical pressure at the interface which affects its chemical composition. The more the NiFe diffuses in the interface, the more its cristallinity improves and the portion of the dis- ordered phase NiFeW decreases. Thus, as first approxima- tion, t

alloy

, which represents the extension of the disordered

Fig. 1 The proposed configuration of the interface NiFe/WTi

phase NiFeW, will conversely depends on the magnetic layer thickness t

NiFe

such as:

t

alloy

= A t

NiFe

A is a constant that has a dimension of an interface.

Suggesting that the NiFeW aggregates or particles has a spheroid shape (Fig. 2), we can suppose that the constant A is isomorphic to the maximal value of the external surface that an NiFeW aggregate can reach such as : A = S

^max_NiFeW

4π r

_max²

.

We define the concentration of the disordered phase NiFeW as follows:

c

alloy

= t

alloy

t

mx

In the limit of law concentration, the resistivity of each canal of spin (σ =↑ or σ =↓ ) in the mixed zone is given by Mathiessen rule as follows:

ρ

_mx^σ

= μ

⁰_mx

ρ

_mx^0σ

+ μ

alloy

ρ

_alloy^σ

(1) where ρ

_mx^0σ

and μ

⁰_mx

=

^tmx−_tmx^talloy

are, respectively, the resis- tivity and the weight of the other phases existing in the interface except the disordered phase NiFeW.

ρ

_alloy^σ

and μ

alloy

=

^talloy_tmx

are, respectively, the resistivity and the weight related to the disordered phase NiFeW.

Knowing that the SDSA coefficient is defined by: α

mx

=

ρ^↓_mx

ρ^↑_mx

and using (1), we obtain α

mx

=

t

alloy

t

alloy

α

alloy

+ α

alloy

K

t

mx

− t

alloy

+ t

mx

− t

alloy

t

alloy

α

_mx⁰

K

+ α

_mx⁰

t

mx

− t

alloy

₋1

(2)

Fig. 2 NiFeW aggregates or particles

Given that the quantity ρλ is constant, one can write:

ρ

mx

λ

mx

= ρ

_mx⁰

λ

⁰_mx

and λ

mx

=

^ρρ^mx_mx⁰

λ

⁰_mx

Using always (1), we obtain

λ_mx=

tmx−talloy 1+α⁰_mx t_mx−t_alloy 1+α_mx⁰

+

t_alloyα_mx⁰

K 1+(1

α_alloy)λ⁰_mx (3)

λ

⁰_mx

and α

_mx⁰

are respectively the MFP and the SDSA coef- ficients at the interface in the absence of the disordered phase

K = ρ

_mx^0↓

ρ

_alloy^↑

and α

alloy

= ρ

_alloy^↑

ρ

^↓_alloy

ρ

_alloy^↑(↓)

denotes the resistivities of spin ↑ ( ↓ ) electrons of the disordered phase NiFeW.

The injecting of the relation c

alloy

=

^talloyt_mx

in (2) and (3) gives

α

mx

(c

alloy

) =

c

alloy

c

alloy

α

alloy

+ α

alloy

K

1 − c

alloy

+ 1 − c

alloy

c

alloy

α

⁰_mx

K

+ α

_mx⁰

1 − c

alloy

₋1

(4)

λmx(calloy)= (1−c_alloy)(1+α_mx⁰ ) (1−calloy)(1+α⁰_mx)+(calloyα_mx⁰

k )(1+(1 αalloy))

(5)

Knowing that λ

mx

=

^λ↑mx+₂^λ↓mx

and α

mx

=

^λ↑mx

λ^↓mx

, we get:

λ

^↑_mx

(c

alloy

) = 2α

mx

(c

alloy

)λ

mx

(c

alloy

)

α

mx

(c

alloy

) + 1 (6)

and

λ

⁻_mx

(c

alloy

) = 2λ

mx

(c

alloy

)

α

mx

(c

alloy

) + 1 (7)

3.2 Calculation of the MR Ratio

The calculation of MR

cal

is carried out within the frame- work of the J-C model based on the Boltzmann transport equation. The J-C model takes account primarily of the contribution of the interaction mixing the s-d electronic states to the exchange coupling between two successive magnetic layers NiFe and based on the assumption of the spin-dependent scattering asymmetry of the conduction electrons. The other contribution to the exchange described by RKKY approximation is known to be coarse enough in the case of 3d-TM and alloys like NiFe studied here [16].

In the multilayer containing TM or their alloys as FeNi/TiW

the GMR effect is interpreted like due to the mechanisms of

scattering depending on spin. The electronic conduction is supposed carried out in two channels of electrons with inde- pendent opposite spins (σ =↑ , ↓ ). Indeed, the existence of a fairly strong local magnetic field in this TM is a sign of a strong separation of spin exchange. The Fermi surfaces with majority and minority spins can have very different topo- logical forms leading to notable differences in densities of states corresponding to the Fermi level [17]. Consequently, the electronic probabilities of s-d transitions are different for the two directions of spin leading to two distinct cur- rents. Then, we assumed that the electron transportthrough the multilayer is governed by the Boltzmann equation:

v. ∇

r

f

^σ

( r, v) − e

m E. ∇

v

f

^σ

( r, v) = −

f

^σ

( r, v)

− f

⁰

( v)

τ

^σ

= − g

^σ

( r, v)

τ

^σ

(8)

g

^σ

( r, v) is the difference between the equilibrium state pop- ulation f

₀^σ

(v) and the perturbed state populationf

^σ

(z, v), owing to the interfaces and the electric field; e and m denote the electron charge, and electron-effective mass, and E is the applied electric field.

As the multilayered system is stacked along the direction z, the translational invariance in the plane of the layers (x, y) implies that the final solution depends only on the direction z and the Boltzmann equation becomes:

∂

∂z g

^σ_±

(z, v) + 1 τ

^σ

v

z

g

_±^σ

(z, v) = eE mv

z

∂

∂v

x

f

⁰

( v) (9)

The general solution of the Boltzmann equation can be written as:

g

_±^σ

= eEτ

^σ

m

∂f

0

∂v

x

1 + F

_±^σ

exp ∓ z

τ

^σ

v

z

(10)

where F is an arbitrary function of velocity v, determined by the boundary conditions, and τ

^σ

=

^λv^σ_ϕ

is the spin- dependent relaxation time. Once the F ’s are known, and thus the g’s, the current density in each region is obtained by integrating g

^↑(↓)

(z, v):

J

^σ

∝ dz

v

x

g

^σ

(z, v)d

³

v (11)

Finally, MR

cal

is given by:

MR

cal

= ρ

AP

− ρ

P

ρ

P

= J

P

− J

AP

J

AP

(12)

ρ

AP

and ρ

P

(J

AP

and J

P

) are, respectively, the resistiv- ities (electrical currents) in the antiparallel and parallel configurations of magnetizations.

4 Analysis and Discussion

4.1 Analysis of the Obtained MFP and SADS Coefficient of the Mixed Zone

In Fig. 3 we report the variation of α

mx

(c

alloy

). It emerges that the SDSA coefficient decreases rapidly enough as the concentration of the disordered phase c

alloy

increases inside the interval 0.6 ≤ α

mx

(c

alloy

) ≤ 0.9 with a non con- tinuous derivative at a “critical pint” c

_alloy^c

= 50 %. The existence of two different slopes of tangents to the right dα

mx

dc

alloy

₊

= − 0.34 and left dα

mx

dc

alloy

₋

− 0.26 of the curve α

mx

(c

alloy

) at this point may reflect a = change in physical behavior of the NiFe/TiW interface. In fact the constant c

^c_alloy

= 50 % represents a critical con- centration corresponding to NiFe magnetic layer thickness t

c

= 39 ˚ A beyond which important modification in MR behavior and interface structure can be expected. Indeed this is in accordance with XRD results [8] that shows for t

NiFe

= 35 ˚ A, an absence of the coherent stacking is observed for fine thickness because of the large lattice mismatch between the NiFe and WTi. Therefore, the spin-dependent diffusion asymmetry process that is directly responsible for GMR phenomena is strongly deformed as soon as the disordered phase portion increases in the mixed zone. This leads to a very low MR ratio confirming the behavior of the MR experimental results.

The highest value of α

⁰_mx

(c

alloy

) is obtained for c

alloy

= 0 and it is equal α

mx

(c

alloy

= 0) = α

_mx⁰

= 0.9.

It can be related to a configuration of where the interface contains, only the binary alloys NiFe, NiW, and FeW with a large majority for NiW (as the proportion of Fe is very small compared to that of Ni). This explains the fact that this value is closer to that given for NiW α

NiW

= 0.5 [18, 19], that of NiFe alloy is very far α

NiFe

= 9.2 [18]. The low- est value α

mx

(c

alloy

= 1) = α

_mx¹

= 0.6 is also of the same order of magnitude describing the important deterioration of the interface caused by the introduction therein of atoms

0 10 20 30 40 50 60 70 80 90 100

0,5 0,6 0,7 0,8

0,9 _α

mx (c) (dα_mx/dc)-

c^c (dα_mx/dc)+

c^c

αmx

c_alloy(%) c^c_alloy NiFe/TWi

Fig. 3 Variation ofαmxas function ofcalloy

of W, even for very small quantities. Similarly, as shown in Fig. 4, the curves λ

^σ_mx

(c

alloy

) shows that the MFP of the two kinds of population decrease notably with increasing con- centration of the disordered phase c

alloy

but the probability scattering for spin up electrons is higher than the probability scattering of spin down electrons. Physically, The size of the NiFeW particles at the interface get higher with increasing concentration of disordered phase presenting then an obsta- cle for the electrons motion; consequently the MFP will be delimited as soon as the disordered phase is dominant lead- ing to smaller electronic flux across the NiFe/TiW interface.

At c

alloy

= 100 % the two kinds of λ

^σ_mx

(c

alloy

) drop to zero which means that at this concentration, the magnetism is destroyed by the introduction of W atoms.

4.2 Comparison Between MR

cal

and MR

exp

4.2.1 Comparison Between MR

cal

(t

NiFe

) and MR

exp

(t

NiFe

) The parameters α

mx

(c

alloy

) , λ

mx

(c

alloy

) , and λ

^σ_mx

(c

alloy

) derived from the analysis above are introduced into the Boltzmann equation to calculate the MR

cal

(t

NiFe

).

Figure 5 shows the evolution of the MR

cal

(t

NiFe

) for dif- ferent values of the adjustment parameter A. The best adjustment for the experimental data obtained for A = 80 agrees satisfactory with the experimental results confirm- ing the position of the maximum at t

_NiFe^max

= 50 ˚ A and the corresponding rate value MR

max

= 08 % thus validating our assumption of disordered interface.

The adjustment constant A is regarded as measure of a planar surface of the NiFeW aggregates. If we assume that the form of an aggregate is spheroid with maximal radius r

max

, A is approximately A ≈ 4π r

_max²

. The diameter 2 r

max

of a NiFeW particle measures the thickness of the mixed layer. This maximal surface is reached when the disorder is maximal and the amorphous phase occupies the whole mixed zone (t

alloy

= t

mx

).

0 10 20 30 40 50 60 70 80 90 100

-2 0 2 4 6 8 10 12 14 16 18

20 NiFe/WTi

λσ mx(c)

c_alloy(%)

λ_mx λ_mx

Fig. 4 Variation ofλ^σ_mxas function ofcalloy

20 40 60 80 100

0,0 0,2 0,4 0,6 0,8 1,0

MR(%)

tNiFe(Å)

A=84 A=80 A=82 A=86 A=88 A=78 NiFe/WTi

Fig. 5 Comparison between MRcal(tNiFe) and MRexp(tNiFe) (full squares). The input parameters are:λ^↑_NiFe =125 ˚A,λ^↓_NiFe =13.58 ˚A, αNiFe = 9.2 [18], λWTi = 191 ˚A[20], λ⁰_mx = 18 ˚A,α⁰_mx = 0.9, tmx ≈ 4.2 ˚A,αalloy =0.6,K=2

The value of A = 80 corresponds to a maximal radius of the NiFeW particles of r

max

2.5 ˚ A in agreement with the size obtained by experimentation; in fact it was found that the seize of the amorphous NiFeW particles is around r ≈ 2.1 ˚ A [12] and t

mx

≈ 4.2 ˚ Ais in agreement with those given in literature [5, 7].

The weakness of the MR values observed mainly for the fine magnetic layers thickness t

NiFe

≤ 40 ˚ A can be explained by combination of two effects, namely, the exis- tence of the amorphous phase “NiFeW” inside the interface discussed before and the effect of a shunt at the level of the nonmagnetic layer. For the thicknesses increasing within t

NiFe

≤ 40 ˚ A, the crystallization of the aggregates in the interface is wider and the contribution of the inter- face in spin-dependent scattering mechanism becomes more important leading to an MR rate increase until reaching a maximum at t

_NiFe^max

= 50 ˚ A; beyond, it the MR(t

NiFe

) ratio decreases with increasing magnetic layer thickness.

Indeed, for these larger thicknesses, the magnetic layer can be divided into an active part, contributing to MR, and an inactive part distant from interfaces which shunts the current leading to decreasing MR.

4.2.2 Comparison Between MR

cal

(t

TiW

) and MR

exp

(t

TiW

) For samples NiFe/TiW with fixed magnetic layer thickness at t

NiFe

= 40 ˚ A and varying t

TiW

. The MR

cal

(t

TiW

) evolu- tion is obtained using estimated parameters deduced from the concentration c

alloy

= 50 %, corresponding to t

NiFe

= 40 ˚ A: α

mx

= 0.77, λ

^↑mx

= 9.59 ˚ A and λ

^↓mx

= 12.45 ˚ A.The MR

cal

(t

TiW

) is shown in Fig. 6 (continuous curve). It is only meaningful to compare the calculated results with the envelope of the MR

exp

(t

TiW

) maximas (full squares).

Then, the MR

cal

reflects only the antiferromagnetic con-

figuration of the magnetization vectors of the adjacent

0 5 10 15 20 25 30 35 40 0,1

0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

MR(%)

t_WTi(Å)

NiFe/WTi

Fig. 6 Variation of MR according totTiW. MRcal(tTiW): continuous curve; MRexp(tTiW):full squares

magnetic layers. The agreement between MR

cal

(t

TiW

) and MR

exp

(t

TiW

) maximums using the same input parameters used for MR

cal

(t

NiFe

) is good, confirming thus our assump- tion of the existence of an amorphous phase at the interface.

Thus, let us note that the calculated as well as measured MR(t

TiW

) decrease as t

TiW

increases. In fact, when the sep- arating layer is increasing the number of collisions in this layer, the increase limits the MFP of the conduction elec- trons and leads to a progressive decoupling of the successive magnetic layers. This variation of MR(t

TiW

) is fixed by the ratio of t

TiW

on the MFP λ

TiW

of this layer. When t

TiW

increases, the probability that an electron can probe two suc- cessive magnetic layers decreases. Indeed, the interface is supposed as made of two areas: (i) a nonmagnetic area cor- responding to an MTiW alloy with a high TiW concentration which induces a diffusion with inversion of spins reducing MR, and (ii) a magnetic area constituted by MTiW alloy with TiW concentration lower than the limit of disappear- ance of magnetism in the magnetic MTiW alloys. This area also leads to a reduction of asymmetry between the popu- lations with spin up and spin down and consequently to the reduction of MR. Moreover, for these low TiW contents, the existence of an amorphous phase FeNiTiW inside interface, shown by texture and FMR measurements on these sam- ples [21] also leads to a weakening of MR. These effects, together, are in agreement with low values obtained for the interface parameters used in the resolution of the J-C model for the studied multilayer.

5 Conclusion

In this work, we showed the important role of the interface quality on the magnetotransport properties of the multi- layered samples NiFe/TiW. The wall weakness showed

MR

exp

(t

NiFe

) was explained by the apparition of a mixed zone containing a disordered alloying phase NiFeW at the interface characterized by an SDSA coefficient α

mx

(c

alloy

) and an MFP λ

mx

(c

alloy

) such that: α

mx

(c

alloy

) decreases as the concentration of the alloying phase increases show- ing a behavior with a phase transition at c

_alloy^c

= 50 %.

λ

mx

(c

alloy

) show also the same evolution as α

mx

(c

alloy

) with increasing c

alloy

The calculated MR

cal

(t

NiFe

) using the calculated inter- face properties α

mx

(c

alloy

) and λ

mx

(c

alloy

) is in good agree- ment with MR

exp

(t

NiFe

) Thus, the alloying phase NiFeW leads to an interface inhomogeneities giving rise to spin- dependent diffuser centers and to a strong electronic braking and consequently to a smaller electronic flux across the NiFe/TiW interface.

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