Magnetic studies in sputtered Ni/Ti multilayers

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J Supercond Nov Magn (2011) 24:1735–1738 DOI 10.1007/s10948-010-1116-y

O R I G I N A L PA P E R

Magnetic Studies in Sputtered Ni/Ti Multilayers

H. Salhi·K. Chafai·H. Lassri·M. Abid·E.K. Hlil

Received: 2 November 2010 / Accepted: 14 December 2010 / Published online: 12 January 2011

Abstract Magnetic properties of Ni/Ti multilayers, pre- pared by the DC triode sputtering method, have been stud- ied by magnetic measurements. Both metal layers are crys- talline with a (111) fiber structure when they are thicker than 20 Å. The magnetization decreases with a decrease in Ni layer thicknesstNiand the analysis of the results at 5 K indicates the presence of a dead Ni layer about 13 Å thick. The effective anisotropy Keff of Ni/Ti multilayers is obtained using a torque magnetometer. Spin-wave theory has been used to explain the temperature dependence of the magnetization. Approximate values for bulk exchange interaction Jb, surface exchange interactionJS and interlayer coupling strength J_I for various Ni layer thicknesses have been obtained.

H. Salhi (⁾·K. Chafai·H. Lassri·M. Abid

Laboratoire de Physique des Matériaux, Micro-électronique, Automatique et Thermique (LPMMAT),

Faculté des Sciences Ain Chock, Université Hassan II, B.P. 5366 Mâarif, Casablanca, Maroc

e-mail:[email protected] H. Salhi

Laboratoire de Mécanique,

Productique et Génie industriel (LMPG). Ecole supérieure de technologie, Université Hassan II,

B.P. 5366 Mâarif, Casablanca, Maroc M. Abid

Laboratoire de Physique Fondamentale et Appliquée (LPFA).

Faculté des Sciences Ain Chock, Université Hassan II, B.P. 5366 Mâarif, Casablanca, Maroc

E.K. Hlil

Institut Néel, CNRS—Université J. Fourier, BP 166, 38042 Grenoble, France

Keywords Ni/Ti multilayers·Magnetization·Magnetic anisotropy·Spin wave excitations·Exchange interactions

1 Introduction

The study of a metallic multilayer has been a very active area of research because nanometer range thin film multilayer structures exhibit unusual physical properties, and hence they are potential candidates for various technologi- cal applications [1–6].

Since multilayers are an inherently metastable material on the nanometer scale, period modulation, layers number, and relative thickness of the magnetic layers as well as nonmagnetic layers in multilayers will result in many interest- ing properties sensitive to the microstructures. The degree of mixing between adjacent layers determines the Ni amount able to contribute to the magnetic properties of the film. In addition, the degree of crystallographic texture within the layers, combined with any surface anisotropy determines the overall anisotropy of the multilayers.

The fact that Ni is ferromagnetic, study of the magnetic properties of this system also can bring additional informa- tion on the interface state. Therefore, we have undertaken such study and related results are reported here. Magneti- zation versus Ni layer thickness are calculated and, quali- tatively as well as quantitatively, compared to experimental results.

2 Experimental

Ni/Ti multilayers have been prepared by DC triode sputtering under computer-controlled conditions. Water-cooled

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1736 J Supercond Nov Magn (2011) 24:1735–1738

Fig. 1 X-ray diffraction pattern of Ni/Ti multilayers (tNi=t_Ti=60 Å)

glass substrates have been used. The chamber was first evac- uated to a pressure of 1–2×10⁻⁷Torr. Argon of 5 N purity was used as the sputter gas and its pressure was kept constant at 6×10⁻³Torr. The thickness of each layer was monitored by individual quartz oscillators. The deposition rates of Ni and Ti were 22 and 17 Å/min, respectively. Both layers had the same thickness and were varied in the range of 10 to 120 Å. The total number of bilayers was adjusted so as to get a total Ni layer about 500 Å thick. The growth parameters will be designated as (Ni(tNi)/Ti(tTi))q, whereq indicates the number of Ni layers. Low-angle x-ray diffraction studies using CuKαradiation revealed that all Ni/Ti multilayer film had peaks characteristic of the multilayer structure.

The high-angle x-ray diffraction peak around 2θ =44.3°

indicates the Ni(111) texture along the growth orientation (Fig.1). Magnetization and anisotropy were measured with a vibrating sample magnetometer (VSM) in the temperature range 5–300 K under a maximum field of 1.7 T.

3 Results and Discussion

The in-plane M–H loops are all rectangular. The coerciv- ity first increases slightly from 21 to 26 Oe when t_Ni decreases from 120 to 80 Å, then decreases strongly to 5 Oe whentNidecreases to 40 Å, at 295 K. This decrease could be attributed to the change in the microstructure. The interlayer coupling strength J_I depends on the Ni thickness in the structure, the saturation magnetization of the layers, and their respective fields (JI=MHStNi/4) [7]. While the magnetization of the layers increases with tNi, the maximum saturation field is about 100 Oe as seen in the hysteresis loops along the easy axis.J_Iincreases from 1.4×10⁻³ to 10⁻²erg/cm²whent_Niincreases from 40 to 120 Å.

The magnetization decreases strongly with a decrease in Ni layer thickness. This could be explained in terms of a

Fig. 2 Thet_Nidependence of the productM×t_Niat 5 K

Fig. 3 Variation of the productKeff×tNiwithtNiat 5 K

magnetically dead layer of Ni at each interface due to al- loying effects. It is known from the dead layer model that the magnetization of multilayer (M) can be expressed as:

M=M0(1−2δ/tNi), whereM0is the bulk Ni value andδ is the dead layer thickness at each interface. The thickness of such dead layer can be estimated as shown in Fig.2, where we have plotted the productM×tNias a function oftNiat 5 K. The intercept of the straight line gives the dead layer thickness 2δ, and consequentlyδis equal to 13 Å at 5 K.

The effective anisotropy K_eff of the multilayers can be expressed on the basis of phenomenological model, as follows: K_eff =K_V+2KS/t_Ni, where K_V and K_S are the bulk and surface anisotropies, respectively. Fig. 3 shows the plot of the product Keff ×tNi, as a function of tNi at 5 K. The linear dependence observed is as predicted by the phenomenological model. The fit gives a small posi- tiveKS=0.16 erg/cm² which approximates the value obtained by us on Ni/Pt multilayers [8]. From the slope of the straight line in Fig.3, the volume anisotropy is found to be

−1.4×10⁶erg/cm³.

The study of low-temperature magnetization details was carried out for a few samples. Plots of the magnetization, for different Ni layers thicknesses versus temperature, were performed for the Ni/Ti multilayers (Fig.4). According to spin-

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J Supercond Nov Magn (2011) 24:1735–1738 1737

Fig. 4 Calculated (continuous line) and measured (symbols) tempera- ture dependence of the normalized magnetization of Ni/Ti multilayers with varying Ni layer thicknesses

Fig. 5 ThetNidependence of theB

wave theory, the temperature dependence should follow the relation:M(T )=M (5 K) (1−BT^3/2). In all cases, this behavior is observed for temperatures as high asT_C/3. The spin-wave constant B decreases from 47.1×10⁻⁶ K⁻^3/2 fort_Ni=35 Å to 17.4×10⁻⁶K⁻^3/2fort_Ni=120 Å. These values are much larger than the value of 7.5×10⁻⁶K⁻^3/2 found for bulk Ni. The B versus 1/tNiis plotted for the samples with 35≤t_Ni≤120 Å in Fig.5. It is seen that the experimental points align well in a straight line. The values extrapolated to 1/tNi=0 are in good agreement with those found for the bulk Ni. It was observed that the parametersB depend ontNi according to:B(tNi)=B_∞+BS/tNi, where B_∞ is the bulk spin-wave parameter of Ni andB_S surface B value. The surface anisotropy strongly affects the thickness dependence of the magnetization. The linear relation between the spin wave parameterBand the reciprocal of the magnetic film thickness was reported for Ni/Pt multilayers [8] and Fe (110) films on W(110) [9,10].

Theoretical calculation was performed using a model for spin waves in the ferromagnetic/nonmagnetic multilayer described in [11]. The basic features may be summarized

as follows. We suppose that the multilayer (Xn/Y_m)q is formed by an alternate deposition of a magnetic layer (X) and nonmagnetic one (Y). The multilayer is characterized by the number (q) of bilayers (X/Y), the number (n=√

3 (tNi−2δ)/a) of atomic planes in the magnetic layerμand the number (m) of atomic planes in the non-magnetic layer.

We chose the lattice unit vectors (e_X,e_Y,e_Z)so thate_Z is perpendicular to the atomic planes. We note by S_iαμ the spin operator of the atomi(i=1,2, . . . , N) in the planeα (α=1,2, . . . , n) of the magnetic layerμ(μ=1,2, . . . , q).

Further, we suppose that the multilayer is characterized by a rigid lattice and by perfectly sharp layer interfaces with- out structural imperfections (contamination, diffusion, is- land growth, etc.).

The linear approximation of the Holstein–Primakoff [12]

method leads to the expression of the Heisenberg-type system Hamiltonian:

H=H0+A S kαμ

b_kαμ b₋_kαμ+b⁺

kαμb⁺

−kαμ

+ S kαμ

B_kb⁺

kαμb_kαμ + b kαμ

C_kb⁺

kαμb_kαμ

+

k(αμ,αμ)

D_kb⁺

kαμb_kα_μ+ I

k(αμ,αμ)

E_kb⁺

kαμb_kα _μ (1)

where

A=S 2

D^⊥−D^||

Bk=2S

Js(n^||−λk)+Jbn^⊥_S +JIn +S

3D^||+D^⊥ C_k=2JbS

(n^||−λ_k)+n^⊥_V Dk= −JbSλ

k

E_k= −J_ISλ

k

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Hdescribes the exchange interactions in the same magnetic layer (bulk and surface) as well as the exchange interactions between adjacent magnetic layers. J_b andJ_S are the bulk and surface exchange interactions.JI is the interlayer coupling strength which depends on the numbermof atomic planes in the nonmagnetic layer.D^⊥andD^||are the surface anisotropy parameters for the uniaxial out of plane and in plane components, respectively, andD_eff² =(D^⊥)²+(D^||)². Deff(K)=KSa²/ kB, whereais the lattice constant andkB

is the Boltzmann constant.

H0is a constant term, the coefficientsλk andλ_k depend on the crystallographic structure of the magnetic layer. n^||

represents the number of nearest-neighbors sites in the same atomic plane, whilen^⊥_S andn^⊥_V are the numbers of surface and volume nearest–neighbors in the adjacent plane in the same magnetic layer, respectively. For a given site in the surface plane of the magnetic layer,nrepresents the number

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1738 J Supercond Nov Magn (2011) 24:1735–1738 of the nearest neighbors’ sites in the adjacent layer across

the nonmagnetic layer; for fcc (111) (n^||=6, n^⊥_S =3 and n^⊥_V=6)with the lattice constantaand in the case where the nonmagnetic layer does not disturb the succession order of the magnetic atomic planes (n=3):

λ_k=4 cos(akx

√6/4)cos(aky

√2/4)+2 cos(aky

√2/2), λ_k=4 cos(akx

√6/12)cos(aky

√2/4)+2 cos(akx

√6/6).

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The spin system is characterized by 2nq×2nqequations, then the resulting secular equation:

⎧⎪

⎪⎪

⎪⎨

⎪⎪

⎩

(C_k+B_k+ω_kαμ)b_kαμ+D_kb_kαμ+E_kb_kαμ

+2Ab₋⁺_kαμ=0

2Abkαμ+D_kb₋⁺_kα_μ+E_kb⁺₋_kα_μ +(Ck+Bk−ωkαμ)b₋⁺_kαμ=0

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We consider the n×q positive ones which correspond to then×q magnon excitation branchesω_k^r (r=1,2, . . . , n×q). These branches can be classified intongroups ofq quasi-degenerate components in the usual case whereJ_Ire- main sufficiently small compared to the effective intralayer exchange strength (Fig.6). The reduced magnetization versus temperature is computed numerically from:

m(T )=1− 1 N_knqS

k,r

1 exp ω^r_k

kBT

−1. (5) The coefficient Nk indicates the number ofk points taken in the first Brillouin zone. In (5), the zero-point fluctuations effects have not been taken into account.

TheM(T )theory curves obtained from the fits for Ni layers with the thickness ranging fromtNi=35 totNi=120 Å films are shown in Fig.4, well matching the experimental data points. TakenS=0.3,D^||=D^⊥=0 K, the values of JbandJSare found to be equal to 250±10 K and 70±10 K, respectively, for all multilayers. The derived bulk exchange

Fig. 6 Spin-wave excitation spectrum vs.k_x(ky=k_x√

2) for fcc(111) ferromagnetic multilayer withq=1,t_Ni=35 Å,S=0.3;J_b=250 K, J_S=70 K;D^||=D^⊥=0 K andJ_I=10⁻²K

interaction constants all consistently fall in the range ex- pected for the bulk exchange interaction of Ni [13]. Com- pared to the bulk exchange interaction coupling, however, the interlayer coupling is considerably weak (JI≤0.1 K).

Nonetheless, its effect on the magnetic properties is rather significant.

4 Conclusion

The Ni/Ti multilayers were prepared by DC sputtering. The surface and volume contributions to the anisotropy have been determined at 5 K. Magnetization temperature depen- dences have been investigated for various Ni layers thicknesses. The spin-wave constantB is found to decrease in- versely witht_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.

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