Thermal variation of magnetization in Ni/V multilayers

(1)

Physica B 353 (2004) 46–52

Thermal variation of magnetization in Ni/Vmultilayers

K. Benkirane

^a,

, R. Elkabil

^a

, A. Hamdoun

^a

, M. Lassri

^b

, M. Abid

^b

, H. Lassri

^b

, R. Krishnan

^c

aLaboratoire de traitement d’information, Faculte´ des Sciences Ben’Msik Sidi-Othmane, B.P.7955 - Sidi-Othmane, Casablanca, Morocco

bLaboratoire de Physique des Mate´riaux et de Micro-e´lectronique, Faculte´ des Sciences Ain Chock, Universite´ Hassan II, B.P. 5366 Maˆarif, Route d’El Jadida, km-8, Casablanca, Morocco

cLaboratoire de Magne´tisme et d’Optique, URA 1531, 45 Avenue des Etats Unis, 78035 Versailles Cedex, France Received 21 August 2004; accepted 31 August 2004

Abstract

The magnetic properties of Ni/Vmultilayers, prepared by the RF sputtering method, have been systematically studied by magnetic measurements. The magnetization decreases with a decrease in Ni layer thickness

t_Ni

and the analysis of the results at 5 K indicates the presence of a dead Ni layer about 12 A˚ thick. The effective anisotropy

K_eff

of Ni/Vmultilayers is obtained using a torque magnetometer. The interface contribution to the magnetic anisotropy is practically negligible. A spin-wave theory has been used to explain the temperature dependence of the magnetization and the approximate values for the bulk exchange interaction

J_b;

surface exchange interaction

J_S;

and the interlayer coupling strength

J_I

for various Ni layer thicknesses have been obtained.

r

2004 Elsevier B.V. All rights reserved.

PACS:75.70.i; 75.60.Ej; 75.30.Gw; 75.30.Et

Keywords:Ni/Vmultilayers; Magnetization; Magnetic anisotropy; Exchange interactions

1. Introduction

Magnetic multilayers with suitable magnetic properties would offer improvements over con- ventional magnetic materials for applications in

high-density magnetic recording, both as recording media [1] and as heads [2]. One of the main requirements for perpendicular recording and magneto-optic recording is a high perpendicular magnetic anisotropy, which can be achieved in magnetic multilayers.

Compared with the corresponding bulk materi- als, ultrathin ﬁlms exhibit drastic differences in their magnetic properties. Long-range ferromag- netic order in solids is a collective phenomenon

www.elsevier.com/locate/physb

doi:10.1016/j.physb.2004.08.025

Corresponding author. Ecole Royale Navale, Physique, 59 rue Guercif, Appt 6, Casablanca, Morocco. Tel.: +212 22 484 160; fax: +212 22 506 188.

E-mail address:karbenkirane@yahoo.fr (K. Benkirane).

(2)

depending strongly on the coordination number, which is effectively diminished in ﬁlms consisting of only one or a few monolayers. In addition, the lowered dimensionality of thin ﬁlms in relation to the bulk leads to important changes in the shape of magnetization as a function of temperature and in critical exponents.

Research on interlayer exchange coupling of magnetic multilayers and double layers is becom- ing active, and many characteristics of interlayer coupling have been discovered, such as antiferro- magnetic, ferromagnetic, and oscillating exchange couplings [3,4]. The MðTÞ behavior and the Curie temperature T

_C

will of course not only be determined by an interlayer coupling but also by the interplay between anisotropy [5], size effects [6], and coupling effects. Furthermore, interdiffu- sion causing graded interfaces and disorder result- ing in a distribution of exchange interactions can play an important role. Especially, when the magnetic layer thickness is in the monolayer regime the latter two factors might dominate the temperature dependence.

The magnetic properties of multilayers are strongly dependent on their detailed structure and composition, which are determined by the growth conditions used during fabrication [7–9].

For example, the degree of mixing between adjacent layers determines the amount of Ni able to contribute to the magnetic properties of the ﬁlm, and the degree of crystallographic texture within the layers, combined with any surface anisotropy present, determines the overall aniso- tropy of the multilayers.

As Ni is ferromagnetic, a study of the magnetic properties of this system also can bring additional information on the state of the interface. There- fore, we have undertaken such a study and describe our results here. We calculate the thermal variation of the magnetization as a function of Ni layer thickness and compare it, qualitatively and quantitatively, with experimental results.

2. Experimental

The multilayers were deposited onto water- cooled glass substrates by RF diode sputtering.

The chamber was ﬁrst evacuated to a pressure of 1–2 10

⁷

Torr using a turbomolecular pump.

Argon of 5N purity was used as the sputter gas and its pressure was kept constant at 6 10

³

Torr: The RF power density was 2.1 W/cm

²

. The thickness of each layer was monitored by individual quartz oscillators. The Ni layer thick- ness t

Ni

varied from 18 to 96 A˚ and that of Vlayer t

V

was ﬁxed at 20 A˚. The number q of bilayers were in the range 5–15. All the samples were grown on vanadium buffer layers 100 A˚ thick. In all the cases the ﬁrst and the last layers were V. In what follows, the growth parameters of the samples will be indicated as ðt

_Ni

=t

_V

Þ

_q

: The samples were studied using the X-ray diffraction. Magnetization M was measured using a vibrating sample magnetometer under magnetic ﬁelds up to 2 T and in the temperature range 5–300 K.

3. Results and discussion

The multilayer structure is found, by X-ray diffraction, to be polycrystalline and has FCC Ni(1 1 1) texture in the ﬁlm growth direction (Fig. 1). FCC Ni (1 1 1) and BCC V(1 1 0) have close lattice plane spacing (2.034 and 2.14 A˚, respectively) in the ﬁlm growth direction. So it is reasonable to consider that atomic intermixing may occur during sputtering. Ni and Vlayers are

Fig. 1. High-angle X-ray diffraction pattern of Ni(40 A˚)/

V(20 A˚) multilayer using CuKaradiation.

(3)

complicated alloys, which makes the Ni/Vmulti- layer a compositional modulated structure con- sisting of Ni- and V-rich layers.

The hysteresis loops of Ni/Vmultilayer mea- surements in parallel and perpendicular ﬁelds reveal that the easy magnetization of all our Ni/Vmultilayers lies in the ﬁlm plane. The magnetization decreases strongly with a decrease in Ni layer thickness. Due to the decrease in the Curie temperature with t

Ni

; the decrease in M at 300 K is stronger for thinner Ni layers. Therefore, let us consider the results only at 5 K which are shown in Fig. 2. The general t

_Ni

dependence of M could be explained in terms of a dead layer of Ni at each interface, due to alloying effects. The thick- ness of such a Ni layer is estimated to be in the range 11–13 A˚. The calculated curves are also shown in Fig. 2.

Torque studies yield the effective anisotropy K

eff

: The t

Ni

dependence of K

eff

could be analyzed on the basis of the well known phenomenological model which predicts the following relation:

K

eff

¼ K

V

þ 2K

S

=t

Ni

; where K

V

and K

S

are the bulk and surface anisotropies (the latter is the contribution of the surface atoms), respectively.

The bulk anisotropy K

_V

¼ 2pM

²

þ K

_cryst

; where

the ﬁrst term is the demagnetizing energy arising from geometry and the second term is the crystal- line anisotropy.

By plotting K

eff

t

Ni

as a function of Ni one obtains a straight line whose slope is K

V

; and the intercept on the ordinate axis gives 2K

S

: So graphically one obtains these values. Fig. 3 shows the results at 5 K in order to avoid the effects arising when lowering T

C

for thinner Ni layer samples. The present results show that there is no contribution to K

_S

from the Ni atoms. This is in agreement with our result on Ni/Ag [10] and on Ni/Pd by den Broeder et al. [11]. However, we have shown that in the Ni/Pt system a strong perpendicular anisotropy is present arising from the surface anisotropy [12]. It is well known that the surface anisotropy arises from the local crystal ﬁelds and hence should not only depend on the state of the interface but also on the electronic structure of the neighboring metal. It can be seen that all the samples studied show K

eff

o 0; in other words, the magnetization is in-plane.

Let us now examine the volume anisotropy energy K

V

: To ﬁrst order the magnetic cubic anisotropy energy of a single Ni crystal is K

cryst

¼ 5:7 10

⁴

erg=cm

³

at 0 K [13]. The observed anisotropy energy equals K

_V

¼ 1:5 10

⁶

erg=cm

³

; which is almost 26 times larger than

Fig. 2.tNi dependence of the magnetization at 5 K; the solid lines represent the variation of the magnetization assuming

dead Ni layers of thickness 12 A˚. Fig. 3. Variation of the productK_efft_Niwitht_Niat 5 K.

(4)

the anisotropy energy of Ni bulk. The demagnetiz- ing energy in the ﬁlms results in the increase of K

_V

: Basically, the two main sources of the magnetic anisotropy are magnetic dipolar interaction and the spin–orbit interaction. Because of its long range character, the dipolar interaction generally results in a contribution to the anisotropy, which depends on the shape of the specimen. It is of particular importance in thin ﬁlms, and is largely responsible for the in-plane magnetization usually observed. The shape effect of dipolar interaction can be described, via an anisotropic demagnetizing ﬁeld.

In all real systems, there is, in addition to any short-range exchange interaction, a long-range dipole–dipole interaction always present between the magnetic moments. In many theoretical studies of magnetic systems this dipolar interaction is neglected, the rational for this being the small magnitude of the dipolar interaction relative to the magnitude of the exchange interaction.

The low-temperature magnetization was studied in detail for a few samples. Plots of the magnetiza- tion, for different thicknesses of Ni layers, versus temperature were drawn for the Ni/Vmultilayers (Fig. 4). According to spin-wave theory, the

temperature dependence should follow the relation Mð5KÞ MðTÞ

Mð5KÞ ¼ BT

³⁼²

: (1)

In all cases this behavior is observed for temperatures as high as T

C

=3: The spin-wave constant B decreases from 92 10

⁶

K

³⁼²

for t

Ni

¼ 18 A to 26 ( 10

⁶

K

³⁼²

for t

Ni

¼ 96 A: ( These values are much larger than the value of 7:5 10

⁶

K

³⁼²

found for bulk Ni.

The B versus 1=t

_Ni

is plotted for the samples with 18 p t

_Ni

p 96 A in ( Fig. 5. It is seen that the experimental points align well in a straight line.

The values extrapolated to 1=t

_Ni

¼ 0 are in good agreement with those found for the bulk Ni. It was observed that the parameters B in Eq. (1) depend on t

_Ni

according to

Bðt

Ni

Þ ¼ B

1

þ B

S

=t

Ni

; (2) where B

1

is the bulk spin-wave parameter of Ni and B

_S

surface B value. The surface anisotropy strongly affects the thickness dependence of magnetization. The linear relation between the spin-wave parameter B and the reciprocal of the magnetic ﬁlm thickness was reported for Co/V multilayers [14] and Fe (1 1 0) ﬁlms on W(1 1 0)

Fig. 4. Calculated (continuous line) and measured (symbols) temperature dependence of the normalized magnetization of

Ni/Vmultilayers with varying Ni thickness. Fig. 5. Thet¹_Ni dependence of theB.

(5)

[15,16]. Recently, Pinettes et al. [17] examined the inﬂuence of the anisotropy on the thickness dependence of the spin-wave excitation spectra and calculated the thermal variation of magnetiza- tion as a function of ﬁlm thickness.

To understand better how the interlayer ex- change coupling between neighboring Ni layers affects the magnetic behavior of these ﬁlms, we extended the model for spin waves in ferromag- netic thin ﬁlms proposed by Pinettes et al. [17] to the case of ferromagnetic/non-magnetic multi- layers. We suppose that the multilayer ðX

_n

=Y

_m

Þ

_q

is formed by an alternate deposition of a magnetic layer ðXÞ and a non-magnetic one ðYÞ: The multilayer is characterized by the number ðqÞ of bicouches ðX=YÞ; the number ðnÞ of atomic planes in the magnetic layer m; and the number ðmÞ of atomic planes in the non-magnetic layer. We chose the lattice unit vectors (~ e

x

;~ e

y

; ~ e

z

Þ so that ~ e

z

is perpendicularto the atomic planes. We note by S

iam

the spin operator of the atom iði ¼ 1; 2; . . . ; NÞ in the plane aða ¼ 1; 2; . . . ; nÞ of the magnetic layer mðm ¼ 1; 2; . . . ; qÞ:

The system Hamiltonian is given by

H ¼ H

_e

þ H

_a

þ H

_z

: (3) H

e

describes the exchange interactions in the same magnetic layer (bulk and surface) as well as the exchange interactions between adjacent magnetic layers

H

_e

¼ J

_b

X

b hiam;jami

S

_iam

S

_jam

þ X

hiam;ja⁰mi

S

_iam

S

_ja⁰_m

" #

J

s

X

s hiam;jami

S

iam

S

jam

J

_I

X

I hiam;ja⁰⁰m⁰⁰i

S

iam

S

ja⁰⁰m⁰⁰

; ð4Þ

where J

b

and J

S

are the bulk and surface exchange interactions. J

I

is the interlayer coupling strength which depends on the number m of atomic planes in the non-magnetic layer.

The contribution of the surface anisotropy is estimated by

H

a

¼ D

^?

X

iam

s

S

^Z_iam²

þ D

^k

X

iam

s

ðS

^X_iam²

S

^Y_iam²

Þ; (5)

where D

^?

and D

^k

are the surface anisotropy parameters for the uniaxial out of plane and in- plane components.

The Hamiltonian H

z

is considered in the case where a magnetic ﬁeld H

app

is applied to the system in the z direction:

H

_Z

¼ gm

_B

H

_app

X

iam

S

^z_iam

: (6) Further we denote by P

X

the summation, the summation on the sites of the bulk layer planes by X ¼ b; that on surface layer planes by X ¼ S and on the surfaces planes coupled via the non- magnetic layer by X ¼ I: The symbol h i denotes the pairs of nearest-neighbor atoms or adjacent magnetic planes.

In the Holstein–Primakoff formulation [18], the creation and annihilation operators (a

iam

and a

^þ_iam

) for each atomic spin are related to the spin operators by

S

^X_iam

þ iS

^Y_iam

¼ ð2SÞ

¹⁼²

f

_iam

ð2SÞa

iam

and

S

^X_iam

iS

^Y_iam

¼ ð2SÞ

¹⁼²

a

^þ_iam

f

_iam

ð2SÞ: ð7Þ In the framework of non-interacting spin-wave theory, the linear approximation of the Holstein–- Primakoff method is sufﬁcient to describe the main magnetic behavior and the correction terms are quite-small at low temperatures ðT o T

_C

=3Þ [19,20]. So, the value of f

_iam

ð2SÞ is ﬁxed to 1.

We pass from atomic variables ða

iam

; a

^þ_iam

Þ to magnon variables ðb

kam

; b

^þ_kam

Þ after a two-dimen- sional Fourier transformation and we show that H ¼ H

₀

þ A X

k;am

s

b

kam

b

kam

þ b

^þ_kam

b

^þ_kam

þ X

k;am

s

B

_k

b

^þ_kam

b

_kam

þ X

k;am

b

C

_k

b

^þ_kam

b

_kam

þ X

k;ham;a⁰mi

D

k

b

^þ_kam

b

ka⁰m

þ X

I k;ham;a⁰⁰m⁰⁰i

E

k

b

^þ_kam

b

ka⁰⁰m⁰⁰

; ð8Þ

where A ¼ 2D

^k

S;

B

_k

¼ ðJ

_s

ð2n

^jj

ðl

^þ_k

þ l

_k

ÞÞ þ 2J

_b

n

^?

þ 2D

^?

ÞS

þ 2J

I

n

^l

S þ gm

_B

H

app

;

(6)

C

k

¼ ð4n

^?

þ 2n

^k

ðl

^þ_k

þ l

_k

ÞÞJ

b

S þ gm

_B

H

app

; D

_k

¼ J

_b

Sl

⁰_k

;

E

k

¼ J

I

Sl

⁰⁰_k

: ð9Þ

H

0

is a constant term, coefﬁcients l

^þ_k

; l

_k

; l

⁰_k

and l

⁰⁰_k

depend on the crystallographic structure of the magnetic layer. n

^k

represents the number of nearest-neighbor sites in the same atomic plane, while n

^?

ðn

^l

Þ is the number of nearest neighbors in the adjacent plane in the same (adjacent) magnetic layer. For FCC (1 1 1) (n

^k

¼ 6 and n

^?

¼ 3) with the lattice constant a and in the case where the non-magnetic layer does not disturb the succession order of the magnetic atomic planes ðn

^l

¼ 3Þ:

l

^þ_k

¼ l

_k

¼ 4 cosðak

_x

p

6=4Þ cosðak

_y

p 2=4Þ þ 2 cosðak

y

p 2=2Þ

l

⁰_k

¼ l

⁰⁰_k

¼ 4 cosðak

x

p 6=12Þ cosðak

y

p 2=4Þ þ 2 cosðak

_x

p

6=6Þ: ð10Þ

The spin system is characterized by 2nq 2nq equations, and then the resulting secular equation is given by a ð2nq 2nqÞ matrix:

W

^ð2nq2nqÞ

¼ U

^ðnqnqÞ

V

^ðnqnqÞ

V

^ðnqnqÞ

U

^ðnqnqÞ

!

;

where

U

^ðnqnqÞ

¼

U^ðnnÞ₁ U^ðnnÞ₂ U^ðnnÞ₃ U^ðnnÞ₁ U^ðnnÞ₂

U^ðnnÞ₃ U^ðnnÞ₁ U^ðnnÞ₂ U^ðnnÞ₃ U^ðnnÞ₁ 0

BB BB BB BB BB BB BB B@

1 CC CC CC CC CC CC CC CA

;

V

^ðnqnqÞ

¼

V

^ðnnÞ

V

^ðnnÞ

0 B B B B B B B B

@

1 C C C C C C C C A

;

U

^ðnnÞ₁

¼

B

k

D

k

D

k

C

k

D

k

D

_k

C

_k

D

_k

D

_k

B

_k

0 B B B B B B B B B B B B B B

@

1 C C C C C C C C C C C C C C A

;

U

^ðnnÞ₂

¼

0 0

0 E

_k

0 0 0

B B B B B B B B B B B @

1 C C C C C C C C C C C A

;

U

^ðnnÞ₃

¼

0 0 E

_k

0 0 0

0 B B B B B B B B B B B @

1 C C C C C C C C C C C A

;

V

^ðnnÞ

¼ 2A

0 0 2A 0

B B B B B B B B B B B B B B

@

1 C C C C C C C C C C C C C C A

: ð11Þ

Among the 2 ðn qÞ eigenvalues of the matrix

W

^ð2nq2nqÞ

; we consider the n q positive ones

(7)

which correspond to the n q magnon excitation branches o

^r_k

ðr ¼ 1; 2; . . . ; n qÞ: The reduced magnetization versus temperature is computed numerically from

mðT Þ ¼ 1 1 N

k

nqS

X

k;r

1 expðo

^r_k

=k

B

TÞ 1 : (12) The coefﬁcient N

_k

indicates the number of k points taken in the ﬁrst Brillouin zone.

Using Eq. (12), satisfactory ﬁts were obtained for the MðT Þ data for all of the Ni/Vﬁlms. The interfacial alloy is considered within the model by using the real magnetic layer thickness (Ni layer thickness t

Ni

-dead layer thickness).

The MðTÞ theory curves obtained from the ﬁts for the t

_Ni

¼ 18; 24, and 48 A˚ ﬁlms are shown in Fig. 4, well matching the experimental data points.

The values of J

_b

; J

_S

; and J

_I

obtained from the ﬁts are listed in Table 1 for all ﬁlms (taken S ¼ 0:3 and D ¼ 0 K). The derived bulk exchange interaction constants all consistently fall in the range expected for the exchange interaction of bulk Ni [13], compared to the bulk exchange interaction. How- ever, the interlayer coupling is considerably weak.

4. Conclusions

In conclusion, we have prepared Ni/Vmulti- layers by RF sputtering. The surface and volume

contributions to the anisotropy have been deter- mined at 5 K. The spin-wave constant B is found to decrease inversely with t

Ni

: A simple model has allowed us to obtain numerical estimates for the exchange interactions and the interlayer coupling strength for various Ni layer thicknesses.

References

[1] N. Sato, K. Habu, T. Oyama, IEEE Trans. Magn. MAG- 23 (1987) 2614.

[2] F.W.A. Dirne, J.A.M. Tolboom, H.J. de Wit, C.H.M.

Witmer, J. Appl. Phys. 66 (1989) 748.

[3] P. Gru¨nberg, J. Barnas, F. Saurenbach, J.A. Fuss, A.

Wolf, M. Vohl, J. Magn. Magn. Mater. 93 (1991) 58.

[4] S.S.P. Parkin, R. Bhadra, K.P. Roche, Phys. Rev. Lett. 66 (1991) 2152.

[5] M.A. Continentino, E.V. Lins de Mello, J. Phys.: Condens.

Matter 2 (1990) 3131.

[6] U. Gradmann, Appl. Phys. 3 (1974) 161.

[7] P.J. Grundy, S.S. Babkair, M. Ohkoshi, IEEE Trans.

Magn. MAG-25 (1989) 3626.

[8] R. Krishnan, H. Lassri, M. Seddat, M. Porte, M. Tessier, Appl. Phys. Lett. 64 (1994) 2312.

[9] M. Abid, H. Ouahman, H. Lassri, A. Khmou, R.

Krishnan, J. Magn. Magn. Mater. 202 (1999) 335.

[10] R. Krishnan, J. Physique IVcolloque C3 supple´ment au j. Physique III, volume 2, de´cembre 1992.

[11] F.J.A. den Broeder, W. Hoving, P.J.H. Bloemen, J. Magn.

Magn. Mater. 93 (1991) 562.

[12] R. Krishnan, H. Lassri, M. Porte, M. Tessier, P.

Renaudin, Appl. Phys. Lett. 59 (1991) 3649.

[13] D. Jiles, Introduction to Magnetism and Magnetic Materials, Ames, IA, USA, 1991, p. 134.

[14] M. Lassri, M. Omri, H. Ouahmane, M. Abid, M. Ayadi, R. Krishnan, Physica B 344 (2004) 319.

[15] K. Wagner, N. Weber, H.J. Elmers, U. Gradmann, J. Magn. Magn. Mater. 167 (1997) 21.

[16] J. Korecki, M. Przybylski, U. Gradmann, J. Magn. Magn.

Mater. 89 (1990) 325.

[17] C. Pinettes, C. Lacroix, J. Magn. Magn. Mater. 166 (1997) 59.

[18] T. Holstein, Primakoff, Phys. Rev. 58 (1940) 1098.

[19] F.J. Dyson, Phys. Rev. 102 (1956) 1217.

[20] T. Oguchi, Phys. Rev. 117 (1960) 117.

Table 1

The ﬁtting results from Eq. (12) for NiðtNiÞ=VðtV¼20AÞ:( Jbis the bulk exchange interaction between neighbouring Ni atoms, JSis the surface exchange interaction, andJI is the interlayer coupling

tNiðAÞ( J_b=k_B(K) J_S=k_B(K) J_I=k_B(K)

18 300 49 0.05

24 301 48 0.07

48 300 49 0.11