Pd multilayers

Journal of Magnetism and Magnetic Materials 323 (2011) 596–599

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Magnetic studies in evaporated Ni/Pd multilayers K. Chafai a, H. Salhi a,b, H. Lassri a,n, Z. Yamkane a, M. Lassri a, M. Abid c, E.K. Hlil d, R. Krishnan e a Laboratoire de Physique des Mate´riaux, Micro-e´lectronique, Automatique et Thermique (LPMMAT), Faculte´ des Sciences Ain Chock, Universite´ Hassan II, B.P. 5366 Mˆ aarif, Casablanca, Maroc b Laboratoire de Me´canique, Productique et Ge´nie industriel (LMPG), Ecole supe´rieure de technologie, Universite´ Hassan II, B.P. 5366 Mˆ aarif, Casablanca, Maroc c ´ des Sciences Ain Chock, Universite´ Hassan II, B.P. 5366 Mˆ Laboratoire de Physique Fondamentale et Applique´e (LPFA), Faculte aarif, Casablanca, Maroc d Institut Ne´el, CNRS—Universite´ J. Fourier, BP 166, 38042 Grenoble, France e Laboratoire de Magne´tisme et d’Optique, URA 1531, 45 Avenue des Etats Unis, 78035 Versailles Cedex, France

a r t i c l e i n f o

a b s t r a c t

Article history: Received 16 August 2010 Received in revised form 5 October 2010 Available online 27 October 2010

The magnetic properties of Ni/Pd multilayers, prepared by sequential evaporation in ultrahigh vacuum, have been studied. The Ni thickness dependence of the magnetization and magnetic anisotropy is discussed. The temperature dependence of the spontaneous magnetization is well described by a T3/2 law in all multilayers. A spin-wave theory has been used to explain the temperature dependence of the spontaneous magnetization, and the approximate values for the exchange interactions for various Ni layer thicknesses have been obtained. & 2010 Elsevier B.V. All rights reserved.

Keywords: Ni/Pd multilayer Magnetization Spin wave excitation Exchange interaction

1. Introduction Ultrathin ferromagnetic films have attracted enormous interest, due to potential applications in the magnetic and magneto-optic storage technology as well as the fundamental curiosity for understanding the magnetic phenomena including perpendicular magnetic anisotropy. The magnetic anisotropy, together with the coercive field, the remanence, the saturation magnetization and Kerr rotation, plays an important role in finding suitable materials for information storage. Transition metal (Fe,Co,Ni)–Pd systems present fascinating magnetic properties, which are related to 3d–4d hybridization and 3d–4d exchange interactions. Nonmagnetic Pd metal tends to order ferromagnetically when alloyed with a small amount of magnetic impurities. Vogel et al. have performed direct measurements of the Pd 4d orbital and spin moments in Fe/Pd multilayers with a different Pd interlayer thickness using X ray magnetic circular dichroism (XMCD) and L2,3 absorption edges of Pd [1]. Atoms direct at the interface are strongly polarized with a total moment of 0.4 mB/atom. The orbital moments are found to be small. The thickness dependence of XMCD shows that Pd atoms are magnetically polarized up to four layers from the interface [1]. It is shown that the thermal decrease of the spontaneous magnetization of ferromagnetic transition metal differs characteristically depending on preparation conditions [2–6]. In all cases, the

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Corresponding author. E-mail address: [email protected] (H. Lassri).

0304-8853/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2010.10.020

deviations from saturation at absolute zero can be accurately described by a single temperature power, temperature power term T n, which holds up to several hundreds of kelvins. As it is well known, Bloch’s theory predicts that the spontaneous magnetization of the Heisenberg ferromagnet with bilinear nearest-neighbor interactions decreases according to T3/2 term in the first approximation [7]. In this paper we describe the results of our studies in Ni/Pd multilayers.

2. Experimental The multilayer samples were deposited onto heated mica substrates, maintained at temperatures in the range 400–500 K, by an electron beam evaporation in ultrahigh vacuum (UHV) under controlled conditions. The pressure during the film deposition was maintained in the range 3  5  10  9 Torr. The rate of deposition ˚ (about 0.3 A/s) and the final thickness were monitored by precalibrated quartz oscillators. Both layers had the same thickness ˚ The total number or (tNi ¼tPd), and were varied in the range 4–40 A. bi-layers was adjusted so as to get a total thickness of Ni layer about 1200 A˚ thick. All the samples were grown on Pd buffer layers 250 A˚ thick. In all cases the first and the last layers were Pd. Growth parameters will be designated as (Ni(tNi)/Pd(tPd))q, where q indicates the number of Ni layers. Low-angle X ray diffraction studies using CuKa radiation revealed that all Ni/Pd multilayer film had peaks characteristic of the multilayer structure. The high-angle X-ray diffraction peak around 2y ¼43.31 indicates the strong (1 1 1)

K. Chafai et al. / Journal of Magnetism and Magnetic Materials 323 (2011) 596–599

texture along the growth orientation. 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.

3.0

M×tNi (10-4 emu.cm-2)

2.5 2.0 1.5 1.0 0.5 0.0 0

5

10

15

20

25

30

35

tNi (Å) Fig. 1. The tNi dependences of the product MtNi at 5 K.

40

45

0.1

Keff×tNi (erg.cm-2)

We have studied, by VSM, the modulation dependence of the magnetic properties of Ni/Pd multilayers prepared by evaporation UHV. It was observed that, depending on the constituent layer thickness, the magnetization and the apparent Curie temperature as well as the anisotropy varied with the multilayer period. Perpendicular anisotropy was observed to develop for periods containing two atomic planes of Ni. While it was absent for multilayers with thicker Ni layer. The low-temperature magnetization (per unit volumes of the Ni content) was found to reach values higher than that of pure Ni. Recently, the calculations using density functional theory performed for different Ni/Pd multilayers reveal that the important magnetic moment of Ni is significantly enhanced according to tPd increases due to hybridization effects between Pd and Ni mostly localized at the interface [8]. The results also indicate that Pd atoms are strongly polarized in the studied systems when compared to the pure metal. The saturation magnetization in multilayers can be expressed by the phenomenological model as follows: M¼Mb + 2dMint/tNi, where M, Mb and Mint are magnetizations of the multilayer, the bulk material and the interface region, respectively. d is the interface layer thickness of the alloy formed at each interface due to alloying effects. Plotting MtNi as a function of tNi yields a straight line, whose slope gives Mb, and the intercept on the ordinate axis gives the product 2dMint. Fig.1 shows such a plot at 5 K. By analysing the data, we calculated both Mb and the product 2dMint. We find that Mb ¼525 emu/cm3 in agreement with the value obtained on the single-layer thick film. Of course, Mint can be determined only if 2d is known. The effective anisotropy Keff of multilayers can be expressed on the basis of phenomenological model, as follows: Keff ¼KV +2KS/tNi, where KV and KS are the bulk and surface anisotropies, respectively. Fig. 2 shows the plot of the product KefftNi, as a function of Ni at 5 K. The linear dependence observed is as predicted by the phenomenological model. The fit gives a small positive KS ¼ 0.03 erg/cm2, which approximates the value obtained by den Broeder et al. [9] on Ni/Pd multilayers. From the slope in Fig. 2 we obtain KV ¼  1.4  106 erg/cm3.

0.2

0.0 -0.1 -0.2 -0.3 -0.4 -0.5 0

5

10

15

20

25

30

35

40

45

tNi (Å) Fig. 2. The tNi dependence of the product KefftNi at 295 K.

1.0

M (T) / M (5)

3. Results and discussion

597

tNi= tPd

0.9

tNi= 40 Å tNi= 20 Å tNi= 16 Å tNi= 12 Å

0.8

tNi= 8 Å 0

50

100

150

200

250

T (K) Fig. 3. Calculated (continuous line) and measured (symbols) temperature dependence of the normalized magnetization of Ni/Pd multilayers with varying Ni layer thicknesses.

Fig. 3 shows the magnetization versus temperature for several values of tNi thicknesses. It gives evidence that the Curie temperature TC decreases when tNi decreases. The low-temperature magnetization was studied in detail for a few samples. For three-dimensional magnetic films, the magnetization has a T3/2 dependence (for temperatures as high as TC/3) due to classical spinwave excitations. In such cases, according to spin-wave theory, the temperature dependence should follow the relation, M(T)¼M(5 K) (1 BT3/2). Fig. 4 shows the plot of the spin-wave constant B as a function of tNi. It is seen that B is much larger than the value of 7.5  10  6 K  3/2 ˚ and then it found for bulk Ni. One also observes a peak at tNi ¼20 A, decreases for thinner layers. We expect B to drop to its bulk value ˚ which indicates that the for samples with tPd greater than 100 A, polarization state in Pd layers is independent of the Pd layer thickness, and the interlayer coupling between the magnetic layers perhaps disappears. The data in Fig. 4 suggest that the combination of effects from both tNi and tPd might be present. Apparently, such an effect would not only emerge from the influence of the Ni/Pd interfaces (and the resulting polarization of Pd) but also it should involve an interlayer coupling through adjacent periods. The theoretical calculations were done using a model for spin wave in ferromagnetic/nonmagnetic multilayer, described

598

K. Chafai et al. / Journal of Magnetism and Magnetic Materials 323 (2011) 596–599 u

H0 is a constant term, the coefficients lk and lk depend on the crystallographic structure of the magnetic layer. n// represents the number of nearest-neighbors sites in the same atomic plane, while ? n? S and nV are the numbers of surface and volume nearestneighbors in the adjacent plane in the same magnetic layer, respectively. For a given site in the surface plane of the magnetic layer, nz represents the number of nearest neighbors sites in the adjacent layer across the nonmagnetic layer. For fcc (1 1 1) ? ðnT ¼ 6, n? S ¼ 3 and nV ¼ 6Þ with the lattice constant a and in the case where the nonmagnetic layer does not disturb the succession order of the magnetic atomic planes (nz ¼3):

70 60

B (10-6 K-3/2)

50 40 30 20

lk ¼ 4 cosðakx O6=4Þcosðaky O2=4Þ þ 2 cosðaky O2=2Þ

10

luk ¼ 4 cosðakx O6=12Þcosðaky O2=4Þ þ2 cosðakx O6=6Þ

0 0

4

8

12

16

20

24

28

32

36

40

tNi (Å) Fig. 4. Variation of B versus tNi for Ni/Pd multilayers.

in Ref. [10]. Basic features may be summarized as follows. We suppose that the multilayer (Nin/Pdm)q is formed by an alternate deposition of a magnetic layer (Ni) and a nonmagnetic one (Pd). The multilayer is characterized by the number (q) of bi-layers (Ni/Pd), the number n of atomic planes in the magnetic layer m and the number m of atomic planes in the nonmagnetic layer. ! ! ! ! We chose the lattice unit vectors ð e X , e Y , e Z Þ, so that e Z is ! perpendicular to atomic planes. We note that by S iam the spin operator of the atom i (i¼1, 2,y,N) in the plane a (a ¼1, 2,y,n) of the magnetic layer m (m ¼1, 2,y,q). Further we assume that the multilayer is characterized by a rigid lattice and by perfectly sharp layer interfaces without structural imperfections (contamination, diffusion, island growth, etc.). The linear approximation of the Holstein–Primakoff [11] method leads to the expression of the Heisenberg-type system Hamiltonian H ¼ H0 þ A

S X

S X þ þ ðb! b ! þ b! b þ! Þ þ Bk b! b! k am  k am k am  k am k am k am ! ! k am k am

X þ þ Ck b! b! þ Dk b! b! am k k am k am k aum ! ! k am k ðam, aumÞ I X þ þ Ek b! b! k am k a00 m00 ! k ðam, a00 m00 Þ þ

b X

ð1Þ

ð3Þ

The spin system is characterized by 2nq  2nq equations, then the resulting secular equation is as follows: 8 þ < ðCk þ Bk þ okam Þbkam þ Dk bkaum þEk bkaumu þ2Abk am ¼ 0 ð4Þ þ þ þ : 2Abkam þ Dk bkaum þEk bkaumu þðCk þ Bk okam Þbk am ¼ 0 We consider the nq positive ones which correspond to the nq magnon excitation branches ork ðr ¼ 1,2,. . .,nqÞ. These branches can be classified into n groups of q quasi-degenerate components in the usual case where JI remains sufficiently small when compared to the effective intralayer exchange strength (Fig. 5). The reduced magnetization versus temperature is computed numerically from 1 X 1 ð5Þ mðTÞ ¼ 1 Nk nqS k,r expðork =kB TÞ1 The coefficient Nk indicates the number of k points taken in the first Brillouin zone. In Eq. (5), the zero-point fluctuation effects have not been taken into account. The M(T) theory curves obtained from the fits for Ni layers with the thickness ranging from tNi ¼8–40 A˚ films are shown in Fig. 3, well matching the experimental data points. Taken S ¼0.3270.02, DT ¼0 K and D? ¼  0.25 K (0.03 erg/cm2), the values of Jb and JS are found to be equal to 250710 and 90 710 K, respectively, for all multilayers. The derived bulk exchange interaction constants all consistently fall in the range expected for the bulk exchange interaction of Ni [12]. The interlayer coupling strength was varied ˚ which is in the range of the 0.05 K for tNi ¼8–0.15 K for tNi ¼ 40 A, greater than the interlayer coupling strength in Ni/Au multilayer system [10]. These results suggest that the Pd atoms, directly at the interface, are strongly polarized when compared to the Au atoms. Therefore, the spin polarization mechanism should exist in 2800

where  S ? D D00 2 z 00 ? Bk ¼ 2SðJs ðn00 lk Þ þ Jb n? S þ JI n Þ þ Sð3D þ D Þ Ck ¼ 2Jb Sððn00 lk Þ þ n? Þ V u Dk ¼ Jb Sl! k u Ek ¼ JI Sl! k

2400

A¼

2000

ωk

1600

ð2Þ

H describes the exchange interactions in the same magnetic layer (bulk and surface) as well as the exchange interactions between adjacent magnetic layers. Jb and JS are the bulk and surface exchange interactions, respectively. JI is the interlayer coupling strength, which depends on the number m of atomic planes in the nonmagnetic layer. D? and D// are the surface anisotropy parameters for the uniaxial out of plane and in plane components, respectively, and D2eff ¼ D2? þ D299 . Deff (K)¼KSa2/kB, where a is the lattice constant and kB is the Boltzmann constant.

1200 800 400 0 0

1

2

3

4

kx pffiffiffi Fig. 5. Spin-wave excitation spectrum versus kx ðky ¼ kx 2Þ for fcc(1 1 1), ferromagnetic multilayer with q¼ 1, n¼ 8; S ¼0.32 K; Jb ¼ 250 K, JS ¼ 90 K; DT ¼ 0 K; D? ¼  0.25 K and JI ¼ 0.1 K.

K. Chafai et al. / Journal of Magnetism and Magnetic Materials 323 (2011) 596–599

these systems, and the RKKY (Ruderman–Kittel–Kasuya–Yosida) interaction couples impurity spin via polarization of the conduction electrons. The interlayer coupling strength depends on the Ni thickness in the structure, the saturation magnetization (MS) of the layers and their respective fields (JI ¼MSHStNi/4, where HS is the saturation field) [13]. Compared to the bulk exchange interaction coupling, however, the interlayer coupling is considerably weak. Nonetheless, its effect on magnetic properties is rather significant. The Ni layers are coupled together by an interlayer exchange coupling, and that the spin waves extend across the whole multilayer sample. The propagation of spin waves through the Pd layers implies the existence of spin polarization within the Pd.

4. Conclusions In conclusion, the temperature dependence of the magnetization of Ni/Pd multilayers has been investigated for various Ni layer thicknesses. The spin-wave constant B was observed to depend on tNi nonmonotonically, which suggested that the combination of effects from both tNi and tPd might be present. A simple model has allowed us to obtain numerical estimates for the exchange

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interactions (bulk and surface), and the interlayer coupling strength for various Ni layer thicknesses. References [1] J. Vogel, A. Fontaine, V. Cros, F. Petroff, J.P. Kappler, G. Krill, A. Rogalev, J. Goulon, J. Magn. Magn. Mater. 165 (1997) 96. [2] N.K. Flevaris, R. Krishnan, J. Magn. Magn. Mater. 104–107 (1992) 1760. [3] W. Staiger, A. Michel, V. Pierron-Bohnes, N. Hermann, M.C. Cadville, J. Mater. Res. 12 (1) (1997) 161. [4] R. Krishnan, H. Lassri, S. Prasad, M. Porte, M. Tessier, J. Appl. Phys. 73 (1993) 6433. [5] F. Wilhelm, P. Poulopoulos, G. Ceballos, H. Wende, K. Baberschke, P. Srivastava, D. Benea, H. Ebert, M. Angelakens, N.K. Flevaris, D. Niarchos, A. Rogalev, N.B. Brookes, Phys. Rev. Lett. 85 (2000) 413. [6] M. Lassri, M. Omri, H. Ouahmane, M. Abid, M. Ayadi, R. Krishnan, Physica B 344 (2004) 319. ¨ [7] U. Kobler, J. Phys.: Condens. Matter 14 (2002) 8861. [8] G. Gomez, G.F. Cabeza, P.G. Belelli, J. Magn. Magn. Mater. 321 (2009) 3478. [9] F.J.A. den Broeder, W. Hoving, P.J.H. Bloemen, J. Magn. Magn. Mater. 93 (1991) 562. [10] H. Salhi, K. Chafai, K. Benkirane, H. Lassri, M. Abid, E.K. Hlil, Phys. B: Condens. Matter 405 (2010) 1312. [11] T. Holstein, H. Primakoff, Phys. Rev. 58 (1940) 1098. [12] D. Jiles, Introduction to Magnetism and Magnetic Materials, Ames, Iowa, USA, 1991 p. 134.. [13] S.S.P. Parkin, Phys. Rev. Lett. 67 (1991) 3598.