The effect of the interface roughness on the magnetotransport properties in Ni81Fe19/Zr multi-layers

The effect of the interface roughness on the magnetotransport properties in Ni 81 Fe 19 /Zr multi-layers

K. El Aidoudi ^a , A. Qachaou ^a,n , M. Lharch ^a , A. Fahmi ^a , H. Lassri ^b

a

LPMC Faculté de Sciences, Kenitra, Morocco

b

LPMatériaux Faculté de Sciences, Ain Chock, Casablanca, Morocco

a r t i c l e i n f o

Article history:

Received 15 January 2014 Received in revised form 7 July 2014

Accepted 9 July 2014 Available online 18 July 2014 Keywords:

A. Interfaces A. Magnetic materials A. Multilayers D. Magnetic properties D. Transport properties

a b s t r a c t

In this work, we study the effect of the chemical and/or structural disorder existing in the interface on the magnetotransport properties of the multilayered system NiFe/Zr. The assumption that the possible apparition of a disordered alloying phase NiFeZr is caused by diffusion of non-magnetic alloying Zr atoms at the interface is proposed. This assumed interfacial degradation is used to calculate the magnetoresistance rate MR

_cal

ðtÞ in the framework of Johnson–Camley semi-classical model. This allowed us to reproduce quite faithfully the experimental measured results MR

_exp

ð t Þ , con fi rming thus the important role of the interface roughness on the electronic transport properties. The behavior of calculated and measured magnetoresistance versus NiFe magnetic layer thickness (t ¼ t

_NiFe

) shows one maximum of 1.8% at t

_NiFe

¼ 80 A ̊ . When the thickness of the non-magnetic layer t

_Zr

varies, the MR ð t

_Zr

Þ ratio shows an oscillatory behavior with an average period (7 A ̊ ). An overall weakness is showed by measured rate probably due to a degradation of the interface quality.

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1. Introduction

Even more than a decade after the discovery of the GMR effect in Fe/Cr thin fi lm multilayers [1 – 3], magnetic multilayers systems composed of alternating of magnetic and non-magnetic layers still attract considerable amount of scienti fi c interest because of their already proved utility in data storage and magnetic sensor technique.

One of the main aims of these studies is to improve the magnetic sensitivity (S ¼ Δ R = R Δ H). Thus a special attention was given to multilayers based on NiFe layers because of the soft magnetic character that they exhibit.Theoretical investigation showed that the GMR effect is closely related to the spin dependent scattering asymmetry effect of the conduction electrons both in bulk and interface 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 MR ratio, whereas this electron is diffused in the contrary magnetic con fi g- uration supporting MR. Moreover the composition and the quality of the interface have an important role on the electronic transport proprieties [4]. In fact the values of the mean free path (MFP) and the spin dependent scattering asymmetry coef fi cient (SDSA) depend strongly on the interface roughness [5].

In this work, we present a study of the interface quality effect on the magnetotransport properties of Ni

81

Fe

19

/Zr magnetic multi- layer using the semi-classical model of Jhonson – Camely [6] based on the resolution of the Boltzmann transport equation and adapted to the interface degradation approach. A good agreement between experiment and calculation results is obtained.

2. Experimental methods

The multi-layer Ni

81

Fe

19

/Zr studied were prepared by the method of cathode sputtering with a magnetron by using NiFe and Zr targets of high purity. The pressure of the room before the deposit was about 6 10

⁸

Torr, while the pressure of the gas (ultra-high purity Ar) was maintained constant at 2 10

³

Torr.

The DC power was 80 W. The fi lms were deposited on a water- cooled Si(001) substrate maintained at a temperature of 293 K.

The multi-layers were prepared in two series of samples S

1

and S

2

follows as: (i) S

1

: Magnetic layer thickness t

_NiFe

varying in 20 A ̊ r t

NiFe

r 120 A ̊ when the non-magnetic layer thickness was fi xed at t

Zr

¼ 15 A ̊ ; (ii) S

2

: non-magnetic layer thickness t

Zr

varying within 3 A ̊ r t

Zr

r 20 A ̊ for a fi xed magnetic layer thickness at

t

NiFe

¼ 30 A ̊. The choice of t

NiFe

¼ 30 A ̊ is imposed by the fact of

being able to measure the impact of variation of the thickness of the non-magnetic Zr layer on the magnetotransport properties in NiFe/Zr. Indeed, according to high-angle X-ray (HXRD) diffraction measurements performed previously on this multilayered system [7], when the magnetic layers are thick (t

NiFe

Z 60 A ̊ ) the effect of Contents lists available at ScienceDirect

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Journal of Physics and Chemistry of Solids

http://dx.doi.org/10.1016/j.jpcs.2014.07.011 0022-3697/& 2014 Elsevier Ltd. All rights reserved.

n

Corresponding author.

E-mail address: ahqachaou@yahoo.fr (A. Qachaou).

the non-magnetic Zr layer is practically masked, while for very low magnetic thicknesses (t

NiFe

r 20 A ̊ ) the effect of these magnetic layers is not probed (disappearance of the Bragg peak (111) NiFe at t

NiFe

¼ 20 A ̊).

3. Results

3.1. Measured magnetoresistance rate MR

exp

The dependence of the measured MR

exp

ð t Þ ratio on magnetic and non-magnetic layer thickness in Ni

81

Fe

19

/Zr multilayer at room temperature is shown in Figs. 1 and 2 (Symbols). Fig. 1 depicts the evolution of MR

exp

ð t ¼ t

_NiFe

Þ for the series S

1

. The main features of this evolution show that for t

NiFe

4 40 Å the MR increases with increasing t

NiFe

and exhibits a maximum of about 1.8% at t

^max_NiFe

¼ 80 Å. The MR ratio then gradually decreases with increasing t

NiFe

until it reaches a minimum of about 0.5% at t

NiFe

¼ 120 Å. For t

NiFe

o 40 A ̊ , a very weak MR ratio is obtained, showing that the magnetotransport process is strongly blocked at the interface, and generally the maximum ratio MR

^max

obtained in the present structure is much smaller compared to other ratios obtained in similar systems such as NiFe/Cu [8,9].

Fig. 2 shows the curve MR

exp

ð t

Zr

Þ for the series S

2

. MR

exp

ð t

Zr

Þ presents an oscillatory behavior re fl ecting the oscillations of the exchange coupling between ferromagnetic (F) and antiferromag- netic (AF) con fi gurations of the magnetization vectors of the adjacent magnetic layers NiFe. It shows clearly the existence of two oscillations. The fi rst one at t

Zr

¼ 7 A ̊ with ratio of 0.4% and the second one at t

Zr

¼ 14 A ̊ with ratio of 0.3%. These values of MR peaks are relatively weak because they are obtained for fi ne magnetic layers (t

NiFe

r 40 A ̊ ) where a disorder caused by the diffusion of non-magnetic alloying metal Zr in the interface provokes an important degradation of crystallinity of this interface where the existence of an amorphous phase was shown experi- mentally [7]. The average distance between MR peaks gives a period of oscillations of 7 Å which is inferior to these observed in other multilayer based on similar transition metal alloys deposited on copper such as NiFe/Cu (8.5 Å) and NiFeCo/Cu (8.5 Å) [9].

3.2. Calculated magnetoresistence ratio MR

_cal

The calculation of magnetoresistence ratio MR

cal

is carried out within the framework of the semi-classical Johnson – Camley (J – C) model based on the Boltzmann transport equation. The J – C model

takes account primarily of the interaction mixing the s – d states contribution to the exchange coupling between two successive magnetic layers NiFe and based on the assumption of 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 [10]. In the multi-layer containing TM or their alloys such as NiFe/Zr the GMR effect is attributed to the mechanisms of scattering depending on spin. The electronic conduction is supposed to be carried out in two channels of electrons with independent opposite spins ( σ ¼ ↑; ↓ ).

Indeed, the existence of a fairly strong local magnetic fi eld in these TM is a sign of a strong separation of spin exchange. The Fermi surfaces with majority and minority spins can have very different topological forms leading to notable differences in densities of states corresponding to the Fermi level [11]. Consequently the electronic probabilities of s – d transitions are different for the two directions of spin leading to two distinct currents. Then we assumed that the electron transport through the multilayer is governed by the Boltzmann equation for the electron distribution function f ð ! r ; !Þ v given in the relaxation time τ approximation by

! v : ! ∇

! r f ð ! r ; !Þðe v = m Þ ! E

! ∇

! v f ð ! r ; !Þ ¼ ððf v ð ! r ; !Þ v f

₀

ð !ÞÞ=τÞ v . Here ð ! r ; !Þ v is the canonical pair of position and velocity of an electron and f

_o

is the Fermi – Dirac distribution. Then we can write, for each spin σ : f

^σ

ð ! r ; !Þ ¼ v f

^σ₀

ð !Þþ v g

^σ

ð ! r ; !Þ v , where g

^σ

ð ! r ; !Þ v de fi nes the difference between the ground state population f

^σ₀

ð !Þ v and the perturbed state population f

^σ

ð ! r ; !Þ v owing to the interfaces and the electric fi eld. It corresponds to only electrons involved in transport phenomena. For a static and uniform electric fi eld ! E

applied along the direction ! x of a multilayered system stacked along the direction ! z , the translational invariance in the plane of the layers (x,y) implies that the fi nal solution depends only the direction ! z and the Boltzmann equation becomes

∂

∂ z g

^σ₇

ð ! r ; !Þþ v 1 τ

^σ

v

z

g

^σ₇

ð ! r ; !Þ ¼ v eE mv

z

∂

∂ v

x

f

⁰

ð !Þ v ð 1 Þ

leading to the solution g

^σ₇

ð z ; v

z

Þ ¼ eE τ

^σ

m

∂ f

₀

∂ v

x

1 þ F

^σ₇

exp z τ

^σ

v

z

ð 2 Þ where F is an arbitrary function of velocity v , determined by the boundary conditions, e and m denote respectively the electron

Fig. 1.

Comparison of MR

calðtNiFeÞ

(continuous curve) with MR

expðtNiFeÞ

(symbols).

Fig. 2.

Variation of MR

calðtZrÞ

(continuous curve) and MR

exp

(t

Zr

) (Symbols).

charge and electron effective mass and τ

^σ

is the spin-dependent relaxation time. Once the Fs are known, and thus the g, the current density in each region may be given by I ð z Þ ¼ 2e ½ m = h

³

R v

x

½ g

^↑

ð v

z

; z Þþ g

^↓

ð v

z

; z Þ d

³

v and then the current density in the whole structure is I ¼ R

I ð z Þ dz and thus the effective resistivity may be found.

Therefore, calculating the current in the two con fi gurations of magnetization (parallel (P) and anti-parallel (AP)), we can obtain the MR ratio for the entire structure by

MR

cal

¼ ρ

P

ρ

AP

ρ

AP

¼ I

P

I

AP

I

AP

ð 3 Þ

ρ

AP

and ρ

P

(I

AP

and I

P

) are respectively the resistivities (electrical currents) in the antiparallel and parallel con fi gurations of magnet- izations.

The electronic mean free path (MFP) λ

^σ

, the relaxation time τ

^σ

and the spin-dependent scattering asymmetry (SDSA) coef fi cient α ¼ λ

^↑

=λ

^↓

used to calculate MR ratio are strongly dependent on the nature and quality of the considered interface. It is therefore necessary to specify these interfaces.

3.3. The NiFe/Zr interface con fi guration proposed

In the present study, we supposed that the interfaces between the magnetic NiFe and non-magnetic Zr layers to be rough due to the intrinsic effects (possible extrinsic effects caused by impurities added to the interfaces are neglected). For this purpose, we consider that each interface NiFe/Zr constitutes a mixed zone which contains a disordered phase constituted by a mixture of aggregates or ‘ particles ’ of alloys MZr (M ¼ Ni, Fe, NiFe) formed through an interdiffusion of atoms from magnetic and non- magnetic layers. This disorder is probably caused by the diffusion of non-magnetic alloying metal Zr whose introduction, even in small contents, can lead to an amorphous state as observed experimentally [7]. Furthermore the low iron content in the studied samples, and the weak miscibility between zirconium and iron, in addition to a relatively very low mobility of Zr atoms [12], can suggest that the probability of existence of FeZr particle within the interface is negligible. Similarly, the two elements Fe and Zr both promote a reduction of Ni [13]. Thus, the NiFe/Zr interface probably contains a con fi guration consisting of a mixture of ‘ particles ’ NiZr, NiFe and NiFeZr alloys. Fig. 3 depicts a rough partition of the interface containing these ‘ particles ’ with a predominance of NiFeZr phase around the center of the interface.

On the other hand, the rate of diffusion of Zr atoms in the magnetic layer is very small; the formed alloy particles (NiZr and NiFeZr) correspond to very low contents of Zr promoting amor- phization of these particles [14] which is in fact revealed by interfacial texture measurements in studied multilayer NiFe/Zr [7]. Thus, the overall weakness showed by our measured magne- toresistence rate MR

exp

can be explained by the existence of this

amorphization related to the reduced crystallinity of the interfaces when Zr atoms are introduced. The formation of such disordered alloying phase in the interfaces that we suggest seems to be a general characteristic of this type of multilayer [8,15 – 17].

As a fi rst approximation, we considered that the alloy phase NiFeZr can be regarded as playing the same role as that of a layer of impurities with a thickness ʻ t

_impurity

ʼ ¼ t

_alloy

inserted in the mixed zone such that t

alloy

o t

mx

. The thickness t

mx

is fi xed while t

alloy

depends on magnetic layer thickness t

NiFe

. If t

⁰_mx

is the thickness of the phase NiZr (i.e. is one of the interface in the absence of the disordered phase), we have t

⁰_mx

þ t

_alloy

¼ t

mx

¼ cte.

Thus, in the limit of low concentrations of these ‘ impurities NiFeZr ’ , the resistivity of each canal of spin ( σ ¼ ↑ or σ ¼ ↓ ) in the mixed zone, due to the ‘ particles ’ NiZr and impurities NiFeZr diffusing into NiFe is given by the Matthiessen rule ρ

^σmx

ðμ

⁰mx

; μ

alloy

Þ ¼ μ

⁰mx

ρ

⁰mx^σ

þμ

alloy

ρ

^σalloy

, where μ

alloy

and ρ

^σalloy

are respectively the weight and the resistivity of the alloying phase

‘ NiFeZr ’ , while μ

⁰mx

and ρ

⁰mx^σ

are respectively the weight and the resistivity of NiZr alone in the mixing zone. Then, the facts that μ

⁰mx

þμ

alloy

¼ 1 and t

⁰_mx

þ t

alloy

¼ t

mx

¼ cte allow us to de fi ne μ

alloy

and μ

⁰mx

as μ

alloy

¼ ð t

alloy

= t

mx

Þ and μ

⁰mx

¼ ð t

⁰_mx

= t

mx

Þ . Therefore, substituting in the Matthiessen rule above, we have for each spin σ : ρ

^σmx

ðμ

⁰mx

; μ

alloy

Þ ¼ ð t

⁰_mx

= t

mx

Þρ

⁰mx^σ

þð t

alloy

= t

mx

Þρ

^σalloy

. The SDSA coef fi cient α

mx

, de fi ned by α

mx

¼ ðρ

^↓mx

=ρ

^↑mx

Þ , is then given by α

^mx

¼ ð t

alloy

ρ

^↓alloy

þ t

⁰_mx

ρ

⁰mx^↓

= t

alloy

ρ

^↑alloy

þ t

⁰_mx

ρ

⁰mx^↑

Þ Eliminating t

⁰_mx

by t

⁰_mx

¼ t

mx

t

alloy

, we have the expression

α

mx

¼ t

_alloy

t

alloy

α

alloy

þα

alloy

Kðt

mx

t

alloy

Þ þ t

mx

t

alloy

ðt

alloy

α

⁰mx

=KÞþα

⁰mx

ðt

mx

t

alloy

Þ

₁

ð 4 Þ with K ¼ ρ

⁰mx^↓

=ρ

^↓alloy

and α

alloy

¼ ρ

^↑alloy

=ρ

^↓alloy

. Similarly, the mean free path in the mixed zone λ

^mx

can be obtained by assuming that the contribution of the resistivity term to the mean free path inverse ρλ is constant. So λ

⁰mx

ρ

⁰mx

¼ λ

mx

ρ

mx

and λ

mx

¼ ðρ

⁰mx

=ρ

mx

Þλ

⁰mx

where ðρ

⁰mx

=ρ

mx

Þ ¼ ð t

⁰_mx

ðρ

⁰mx^↑

þρ

⁰mx^↑

ÞÞ=ð t

⁰_mx

ðρ

⁰mx^↑

þρ

⁰mx^↑

Þþ t

alloy

ðρ

^↑alloy

þρ

^↓alloy

ÞÞ is the ratio of arithmetic means of the resistivities in the mixed zone without and with impurities. Then we have

λ

mx

¼ ð t

mx

t

alloy

Þð 1 þα

^0mx

Þ

ð t

mx

t

alloy

Þð 1 þα

^0mx

Þþð t

alloy

α

^0mx

= K Þð 1 þð 1 =α

alloy

ÞÞ λ

⁰mx

ð 5 Þ Moreover, the extent of phase alloy t

_alloy

is directly related to the thickness of the magnetic layer. We assumed that t

alloy

varies inversely with t

NiFe

. As t

NiFe

decreases, more t

alloy

extends in the mixed zone follows as:

t

_alloy

d t

NiFe

A ð 6 Þ

The constant A is an adjustment parameter. The formed alloying phase can be characterized by concentration c de fi ned by 0 r c ¼ t

_alloy

= t

mx

r 1. The zero value of c describes a smooth inter- face, while c ¼ 1 (or c ¼ 100%) means that the disordered alloying phase extends over the entire mixed zone. The interface properties α

^mx

ð c Þ , λ

^mx

ð c Þ and λ

^σmx

ð c Þ can then be obtained as functions of the alloy concentration c using Eqs.(4) – (6) follows as:

α

mx

ð c Þ ¼ c

c α

alloy

þα

alloy

K ð 1 c Þ þ 1 c ð c α

⁰mx

= K Þþ α

⁰mx

ð 1 c Þ

1

ð 7 Þ

λ

mx

ð c Þ ¼ ð 1 c Þð 1 þα

⁰mx

Þ

ð 1 c Þð 1 þα

⁰mx

Þþð c α

⁰mx

= K Þð 1 þð 1 =α

alloy

ÞÞ λ

⁰mx

ð 8 Þ Using λ

mx

as an arithmetic mean of λ

^σmx

, i.e. λ

mx

¼ ðλ

^↑mx

þλ

^↓mx

= 2 Þ , and α

mx

¼ ðλ

^↑mx

=λ

^↓mx

Þ ¼ ðτ

^↑mx

=τ

^↓mx

Þ , we have

Fig. 3.

The proposed representation of NiFe/Zr interface.

λ

^↑mx

ð c Þ ¼ 2 α

mx

ð c Þλ

mx

ð c Þ

α

^mx

ð c Þþ 1 ð 9a Þ

λ

^↓mx

ð c Þ ¼ 2 λ

mx

ð c Þ

α

^mx

ð c Þþ 1 ð 9b Þ

(9a) and (9b) are different if α

^mx

ð c Þa 1. The corresponding relaxa- tion times τ

^σmx

ð c Þ are then deducted using λ

^σmx

¼ τ

^σmx

v

F

where v

F

, is the velocity of electrons at the Fermi level, as follows

τ

^↑mx

ð c Þ ¼ λ

^↑mx

ð c Þ v

F

¼ 2

v

F

α

mx

ð c Þλ

mx

ð c Þ

α

^mx

ð c Þþ 1 ð 10a Þ

τ

^↓mx

ð c Þ ¼ λ

^↓mx

ð c Þ v

F

¼ 2

v

F

λ

^mx

ð c Þ

α

mx

ð c Þþ 1 ð 10b Þ

This allows us to express the solution g

^σ₇

ð z ; v

z

Þ (Eq. 2) of the Boltzmann equation (Eq. 1), used to calculate the MR, in terms of the properties of the interface as

g

^↑₇

ðz; v

z

; α

mx

; λ

mx

; cÞ ¼ 2eE m v

F

∂ f

₀

∂v

x

α

mx

ð c Þλ

mx

ð c Þ

α

mx

ðcÞþ1 1 þF

^↑₇

exp z 2

v

_F

v

z

α

mx

ð c Þþ 1 α

mx

ðcÞλ

mx

ðcÞ

ð 11a Þ g

^↓₇

ð z ; v

z

; α

mx

; λ

mx

; c Þ ¼ 2eE

m v

F

∂f

0

∂v

x

λ

mx

ðcÞ

α

mx

ðcÞþ1 1 þ F

^↓₇

exp z 2

v

F

v

z

α

mx

ðcÞþ1 λ

mx

ðcÞ

ð 11b Þ 4. Analysis and discussion

4.1. Obtained MFP and SADS coef fi cient of mixed zone

The description of the MR effect in alloys can be qualitatively made taking into account both the mechanisms of electron diffusion in inhomogeneous medium and the magnetic properties of small ‘ particles ’ that are very different from those of bulk ferromagnetic. In the present study, the dependence of magneto- transport properties on the evolution of impurity ‘ particles ’ (con- centration c, α

^mx

, λ

^σmx

and τ

^σmx

) in the mixed zone is discussed phenomenologically assuming that the effect of introducing of Zr atoms is the parameter most in fl uencing the mechanisms of electronic diffusions. We assumed indeed, that the insertion of Zr atoms even in very small quantities causes amorphization of

‘ particles ’ alloy FeNiZr in the mixed zone. This effect, in addition to the alloying effect, could induce signi fi cant change in the electro- nic structure. It is also known for this type of transition-metal base amorphous alloys that the main contribution to the Fermi level still arises from d electrons in spite of the important reduction which may be due, among other things, to the effects of charge transfer and/or hybridization. The problem of NiFeZr impurity in the mixed zone can be approximately discussed by analogy with that of a magnetic impurity state in transition-metal base amor- phous alloys treated basically in d-band hosts.

Qualitatively, the main contribution to perturbation potential V

^mx_{s d}

due to Zr atom introduction causes a mixture of states ‘ s ’ of Zr and ‘ d ’ of the transition metal. This may induce signi fi cant changes in the topology of the Fermi surfaces. The transition probabilities W

^mx_s-d

, the relaxation times τ

^σmx

, the mean free path λ

^σmx

and densities of states D

^σ_d

ð E

F

Þ in the vicinity of these Fermi surfaces can also undergo signi fi cant distortion following the introduction of Zr atoms. These quantities can be linked roughly by a relation- ship type Fermi rule:

_mx

W

_s^mx_d

V

_{s d}^mx

D E

_{d F}

h . Thus, the

reduction in the mean free path in the mixed zone λ

^σmx

(ie the resistivity ρ

^σmx

increases) when the concentration c of the dis- ordered phase NiFeZr increases could mean that the mixture of states (V

^mx_{s d}

) and or the density of states D

d

ð E

F

Þ increased with increasing c.

In Fig. 4, we report the variation of the SDAS coef fi cient α

mx

versus alloying phase concentration c. It emerges that α

mx

ð c Þ shows drastic decrease inside the interval 6 : 7 rα

^mx

ð c Þr 1. Indeed, it drops by 83.5% at c ¼ 46%. This concentration is related to the magnetic layer thickness t

NiFe

¼ 30 A ̊ beyond which important modi fi cation in MR behavior and structure can be expected.

Indeed the XRD results show an absence of crystalline structure for t

NiFe

o 30 Å [7] which re fl ects a maximum disorder and con- sequently a very weak MR ratio. Therefore the spin dependent scattering asymmetry process – directly responsible for the GMR phenomena – is strongly distorted as soon as the proportion of disordered phase increases in the mixed zone, leading to very weak MR ratio, con fi rming the weakness of MR measured values.

The highest value of α

mx

ð c Þ is obtained for c ¼ 0 and it is equal to:

α

mx

ð c ¼ 0 Þ ¼ α

⁰mx

¼ 6 : 7. It can be related to a con fi guration where the interface contains a mixture composed only of binary alloys NiFe (in majority) corresponding to α

NiFe

9 : 5[18] and NiZr (in minority) with α

NiZr

7 : 5[19]. The lowest value α

mx

ð c ¼ 1 Þ ¼ α

¹mx

1, describes the important modi fi cation of the interface magnetic state caused by the introduction of Zr atoms leading, even for weak contents of Zr atoms, to a paramagnetic state with

Fig. 4.

Variation of

αmx

(c).

Fig. 5.

Variation of

λ^σmxðcÞ.

λ

↑

¼ λ

↓

. The case c ¼ 1 may correspond to a con fi guration made by a mixture of the Zr-rich alloys NiZr and NiFeZr.

Similarly, as shown in Fig. 5, the curves λ

^σmx

ð c Þ show that the two types of electron population with different spins σ decrease with increasing concentration of the disordered phase c. The signi fi cant difference in behavior of these two curves for low impurity concen- tration (c o 0 : 4) can be explained as probably due to the existence of the element Zr in very small amounts causing amorphization of the alloy NiFezr, which further accentuates the differences in topology of the Fermi surfaces, inducing differences in the density of states for majority and minority spin populations at the Fermi level. For these low concentrations (c o 0 : 4), the probability scattering of electrons with spin up is higher than the probability scattering of electrons with spin down, suggesting a predominance of the ferromagnetic phase in this range of values of c. At c 0 : 4, the interface becomes paramagnetic and scattering probabilities become equal. In fact, it was found that amorphous Ni

x

Zr

1x

and Fe

x

Zr

1x

are paramagnetic at already low contents of Zr. The critical content for the transition to the paramagnetic state was found to be y ¼ 1 x ¼ 0 : 10 in the case of alloys with iron [20] and 0.15 in the case of Ni[20,21]. Physically, the size and/or number of the MZr ‘ particles ’ (M ¼ Ni, NiFe) at the inter- face get higher with increasing c presenting then an obstacle for the electrons motion. Consequently the MFP will be delimited as soon as the disordered phase is dominant leading to smaller electronic fl ux across the NiFe/Zr interface. At c ¼ 1 the two types of λ

^σmx

ð c Þ drop to zero which means that at this concentration the magnetism is practically destroyed by the introduction of the alloying non- magnetic Zr atoms.

4.2. Comparison between calculated MR

_cal

ð t Þ and measured MR

exp

ð t Þ

4.2.1. Effect of magnetic layer thickness

The interface properties α

mx

ð c Þ , λ

mx

ð c Þ and λ

^σmx

ð c Þ derived from the analysis above are introduced into the solution g

^σ₇

ð z ; v

z

; α

mx

; λ

^mx

; c Þ (Eq. 11a and 11b) of Boltzmann equation to calculate the MR

cal

ð t Þ . Fig. 1 shows the evolution of the MR

cal

ð t

NiFe

Þ (continuous curve) compared with the measured MR

exp

ð t

NiFe

Þ (Symbols). The input parameters are λ

^↑NiFe

¼ 114 Å, λ

^↓NiFe

¼ 12 Å, α

NiFe

¼ 9 : 5 [19], λ

Zr

¼ 16 : 37 Å [25,26], α

⁰mx

¼ 6 : 7, α

alloy

¼ 1, λ

⁰mx

¼ 68 A ̊, t

mx

¼ 6 Å , and K ¼ 0 : 18. The best adjustment is obtained for A ¼ 113 reproducing quite faithfully the experimental results con fi rming the position of the maximum at t

^max_NiFe

¼ 80 A ̊ and the corresponding rate value MR

max

¼ 1.8% validating thus our assumption of disordered inter- face. For A ¼ 0; which means total absence of the disordered phase at the interfaces we get a bad agreement. We also note that in comparison with our previous preliminary study [27], where the interface properties α

^mx

, λ

^mx

and λ

^σmx

were considered simply as free parameters controlled by the adjustment with the experi- mental values, the calculated expressions α

mx

ð c Þ (Eq. (7)) and λ

mx

ð c Þ (Eq.(8)) and λ

^σmx

(Eqs. (9a) and (9b) that we obtained in the present work lead to a theoretical reproduction MR

cal

ð t

NiFe

Þ of the experi- mental values MR

exp

ð t

NiFe

Þ (Fig. 1) which is much better even for very low magnetic thicknesses for which the agreement is now very satisfactory as compared with the results of the previous study (Fig. 3 of [27]).

Otherwise, the adjustment constant A as given by Eq. (6) can be regarded as measuring the area of the MZr ‘ aggregates ’ or ‘ particles ’ in the interface. For the present analysis, we assumed that the form of an aggregate is spheroid with maximal radius r

max

. A is then approxi- mately A 4 π r

²_max

giving for a value of A ¼ 113 a particle size d ¼ 2r

max

5 : 99 Å which is in line with the values obtained by previous works where it was found that the average size of the amorphous NiZr ‘ particles ’ is of atomic scale (d 5 10 A ̊ ). The amorphous phase is referred to as grain boundary phase between nanocrystallites and it is formed by a segregated grain boundary layer

with the typical width t ¼ d. The crystallite size given in these works is again 10 times larger and it is found to be in the range of 10 30 nm [16,22 – 24]. The size d ¼ 2r

max

that we obtained for a ‘ particle ’ of NiFeZr is therefore consistent with an amorphous state. It also provides a measure of a maximum thickness of the mixed layer t

^max_mx

¼ d ¼ 2r

max

in agreement with those given in literature ð t

^max_mx

5 6 Å Þ [5,6,13].

The weakness of the MR values observed mainly for the fi ne magnetic layer thickness t

NiFe

r 40 A ̊ can be explained by combination of two effects, namely, the possible existence of the amorphous phase

‘ MZr ’ (M ¼ Ni, NiFe) inside the interface discussed above and the effect of a shunt at the level of the non-magnetic layer. For the thicknesses increasing within t

NiFe

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

^max_NiFe

¼ 80 A ̊ beyond which 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 the magnetoresis- tance, and an inactive part distant from interfaces which shunts the current leading to decreasing MR.

4.2.2. Effect of non-magnetic layer thickness

For samples NiFe/Zr with fi xed magnetic layer thickness at t

NiFe

¼ 30 Å and varying t

Zr

, the calculated magnetoresistance evolu- tion MR

cal

ð t

Zr

Þ is obtained using parameters α

^mx

¼ 1 : 17, λ

^↑mx

¼ 7 : 95 A ̊ and λ

^↓mx

¼ 6 : 79 A ̊ deduced for the alloy concentration c ¼ 46%, corre- sponding to t

NiFe

¼ 30 Å and t

mx

5 Å. The MR

cal

ð t

Zr

Þ is shown in Fig. 2 (continuous curve). It is meaningful to compare the calculated results only with the envelope of the measured MR maxima (sym- bols). Then the calculated MR re fl ects only the antiferromagnetic con fi guration of the magnetization vectors of the adjacent magnetic layers. The oscillation present in the MR evolution cannot be explained in the framework of the semi-classical J – C approach. They may re fl ect exchange interactions which may be described in an approach of kind RKKY, but the validity of this approach has been criticized for the case of transition metals and alloys. The agreement between the maxima of magneto-resistance measured and calculated envelope of these max- ima MR

cal

ð t

Zr

Þ using the same input parameters used above for the case MR

cal

ð t

NiFe

Þ is good. Thus let us note that MR

cal

ð t

Zr

Þ as well as maximum MR

exp

ð t

Zr

Þ decrease as t

Zr

increases. In fact, the separating layer increasing the number of collisions in this layer increases limiting MFP of the conduction electrons leading to a progressive decoupling of the successive magnetic layers. This variation of MR(t

Zr

) is fi xed by the ratio of t

Zr

to the MFP λ

Zr

of this layer. When t

Zr

increases the probability that an electron can probe two successive magnetic layers decreases. Indeed, the interface is made of two areas speci fi ed magnetically as: (i) a non-magnetic area corresponding to a MZr alloy with a high Zr concentration which induces a diffusion with inversion of spins reducing MR, (ii) a magnetic area constituted by MZr alloy with Zr concentration lower than the limit of disappearance of magnetism in the magnetic MZr alloys. This area also leads to a reduction of asymmetry between the populations with spin up and spin down and consequently to the reduction of MR. Moreover, for these low Zr contents, the probable existence of an amorphous phase

‘ MZr ’ (M ¼ Ni, NiFe) inside interface 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 an important role of the interface

quality on the magnetotransport properties of the multilayered

samples NiFe/Zr.

The wall weakness showed by the measured ratio MR

exp

ð t Þ with t ¼ t

NiFe

and t ¼ t

Zr

was explained by the apparition of a mixed zone containing a disordered alloying phase NiFeZr at the interface characterized by an SDSA coef fi cient α

mx

ð c Þ and a MFP λ

mx

ð c Þ showing a brutal decrease as the concentration of the alloying phase c increases. Thus the alloying phase leads to interface inhomogeneities, giving rise to spin-dependent diffuser centers and to a strong electronic braking and consequently to a smaller electronic fl ux across the NiFe/Zr interface.

Using the obtained interface properties α

^mx

ð c Þ and λ

^mx

ð c Þ , the calculated magnetoresistence MR

cal

ð t

NiFe

Þ and the calculated envel- ope of the maxima of magnetoresistence MR

cal

ð t

Zr

Þ are in good agreement with the measured MR

exp

ð t

NiFe

Þ and the measured maxima of MR

exp

ð t

Zr

Þ respectively.

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