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Cu sputtered multilayers
Surface Science 482±485 (2001) 998±1003
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Magnetic anisotropy of Ni/Cu sputtered multilayers L. Albini a, G. Carlotti a,*, C. Dragoni a, G. Gubbiotti a, L. Verdini a, S. Loreti b, C. Minarini b, L. Pareti c, G. Turilli c a
Dipartimento di Fisica, Istituto Nazionale per la Fisica della Materia, Via Pascoli, I-06100 Perugia, Italy b C.R. ENEA, I-80055 Portici Napoli, Italy c Istituto MASPEC-CNR, Area delle Scienze, 43010 Parma, Italy
Abstract Ni/Cu multilayers were grown by RF sputtering. The crystal orientation, the thickness of the elemental layers and the interface quality were analysed by X-ray diraction in the h±2h con®guration. Magnetic anisotropy was investigated by both a static and a dynamic technique, namely magneto±optical Kerr eect (MOKE) and Brillouin light scattering (BLS). Longitudinal MOKE loops accounted for the in-plane orientation of the magnetization, while polar loops were used to determine the out-of-plane anisotropy ®elds, showing the existence of a minor second-order contribution in addition to the ®rst-order one. BLS was then exploited to detect thermal excited spin waves through inelastic scattering of light. The out-of-plane anisotropy ®elds evaluated by this high-frequency dynamic technique compare well with the ®rst-order values obtained by analysis of polar MOKE hysteresis cycles. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: Magnetic interfaces; Nickel; Magnetic ®lms; Metal±metal magnetic heterostructures; Surface waves; Magnons
1. Introduction The theoretical interest towards the magnetic properties of arti®cially layered systems is motivated by the fact that the reduced dimensionality strongly modi®es their magnetic behaviour with respect to those of bulk materials [1]. Moreover, magnetic ®lms and multilayers are ®nding steadily growing application in the technology of longitudinal and perpendicular magnetic recording, in magneto-optic storage technology, and in the ®eld of magnetic sensors [2].
* Corresponding author. Tel.: +39-75-5853067; fax: +39-07544666. E-mail address: [email protected] (G. Carlotti).
In this paper we present the results of the structural and magnetic properties of Ni/Cu multilayers, with dierent values of the repetition periodicity, deposited by RF sputtering on Si(1 0 0) substrates. Magneto±optical Kerr eect (MOKE) analysis, in both longitudinal and polar con®gurations, with applied ®elds up to 10 kOe, was exploited to measure hysteresis cycles and to determine the intrinsic magnetic anisotropy. The results of the above mentioned static technique (MOKE) are quantitatively compared to those obtained by Brillouin light scattering (BLS) [3] which is based on the detection of thermally activated high-frequency spin waves. This simultaneous and combined use of MOKE and BLS is particularly interesting, because signi®cant discrepancies have been reported in the literature
0039-6028/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 9 - 6 0 2 8 ( 0 0 ) 0 1 0 8 7 - 6
L. Albini et al. / Surface Science 482±485 (2001) 998±1003
between the interface anisotropy of magnetic/non magnetic multilayers containing Ni measured by dynamic and static techniques [4]. In addition, to our knowledge, no previous BLS investigations of Ni/Cu sputtered multilayers have been reported in the literature 1 [5]. 2. Experimental The specimens consist of alternating layers of Ni and Cu, deposited at room temperature on nonetched (1 0 0)-Si substrates by RF sputtering [6]. Four multilayers consisting of 15 periods have been studied. The elemental layer thicknesses, are reported in Table 1. A careful structural investigation of the multilayers was performed by X-ray diraction (XRD) analysis. The XRD measurements were carried on a Philips XÕPERT MPD diractometer equipped with a monocromator and using Cu±Ka radiation. A Bragg±Brentano con®guration with 2H values in the range 38±50°, where the (1 1 1)Cu and (1 1 1)Ni re¯ections lie, was used. Alternating gradient-®eld magnetometry (AGFM), which is described in details elsewhere [7] has been exploited to record hysteresis cycles at room temperature and to measure the values of the saturation magnetization Ms . Longitudinal and polar MOKE analysis were carried out by a dierential detection method [8] which increases the signalto-noise ratio with respect to the conventional method of nearly-crossed polarizers [9]. A further insight into the magnetic properties of the multilayers was obtained through BLS measurements, carried out using a Sandercock-type 3 3-pass tandem Fabry±Perot interferometer [10], characterized by a ®nesse of about 100 and a contrast ratio higher than 5 1010 . About 150 mW of p-polarized light, from an Ar -ion laser opera line, ted in single longitudinal mode on the 5145 A was focused onto the sample surface and the backscattered light analysed by the interferometer. Details about the experimental set-up can be found elsewhere [11]. In the used backscattering 1 A complete list of all the systems studied by BLS can be found in the recent review of Hillebrands (in Ref. [5]).
999
Table 1 First two columns: values of the elemental Ni and Cu layer thicknesses dNi and dCu , together with the value of the interplanar distance within each layer (in parentheses). The latter are to be compared with the values expected for bulk (1 1 1)-Ni (2.034 A) Third column: value of the amplitude of and (1 1 1)-Cu (2.088 A). the Gaussian distribution function of atomic disorder at the interfaces r, together with the average value of the interplanar spacing at the interface (in parentheses). Last column: values of the saturation magnetization determined by AGFM Sample dNi (A) dCu (A) r dint (A) Ms (Oe) #1
60.10 (2.044)
37.86 (2.078)
0.416 (2.072)
465 15
#2
47.84 (2.045)
32.79 (2.083)
0.382 (2.079)
419 15
#3
39.50 (2.047)
27.88 (2.073)
0.333 (2.073)
318 12
#4
32.00 (2.041)
24.00 (2.088)
0.292 (2.080)
217 10
geometry, the conservation of momentum in the photon±magnon interaction implies that the spinwave wavevector parallel to the ®lm surface is linked to the optical wavevector ki and to the angle of incidence hi by the equation: qjj 2ki sin hi . All spectra were recorded in air at room temperature at an incidence angle of light of 45° qjj 1:73 10 5 cm 1 . 3. Results and discussion 3.1. Structural properties X-ray diraction spectra in the h±2h con®guration have been recorded and a best ®t procedure has been performed in order to obtain the values of the elemental Ni and Cu layer thicknesses (Fig. 1), the interplanar distances within each material and the interface disorder. A re®nement program (SUPREX) based on superlattice X-ray diraction formalism was used [12±14] whose results are reported in Table 1. Note that the interplanar distances for each elemental layer are slightly bigger for the Ni ®lms and smaller for the Cu ones if compared with the values expected for bulk Ni and Cu respectively. The interface disorder and roughness, modelled in the SUPREX program as a gaussian distribution of atomic positions of
1000
L. Albini et al. / Surface Science 482±485 (2001) 998±1003
amplitude r centred around an average value dint , increases with increasing the elemental layer thickness. 3.2. Static magnetic properties
Fig. 1. Experimental (points) and calculated (line) h±2h X-ray spectra of two of the Ni/Cu multilayers investigated.
In the last column of Table 1, we have listed the measured values of the saturation magnetization, determined by AGFM. It can be seen that the magnetization markedly increases with increasing the elemental layer thicknesses due to the decreasing weight of the atomic disorder and/or interdiusion at the interfaces, as already observed in Mo/Ni multilayers [15]. Representative longitudinal MOKE hysteresis loops measured at room temperature are shown in Fig. 2. The loops are well open indicating that the magnetization easy axis lies in the ®lm plane, due to the predominant contribution of the magnetostatic term (shape anisotropy) in the magnetic energy. The absolute Kerr intensity reduces with dNi , consistently with the reduction of Ms measured by AGFM. It can also be observed that the coercive ®eld Hc decreases with dNi , as a consequence of the increased grain size.
Fig. 2. Longitudinal MOKE hysteresis cycles for the four multilayers analyzed.
L. Albini et al. / Surface Science 482±485 (2001) 998±1003
As a second step of our MOKE characterization we measured hysteresis cycles in the polar con®guration, i.e. with the ®eld applied along the ®lm normal, which is a hard-axis direction. External ®elds as high as a few thousands Oe were necessary to achieve saturation, even if the saturation ®elds are lower than those expected for the shape anisotropy (4pMs ), indicating the occurrence of other appreciable anisotropy contributions. In addition, complete reversibility (no hysteresis) was observed, as shown in Fig. 3(a), where a sequence of experimental loops is presented. Concerning the loop
shape, it appears a predominant linear approach to the saturation, due to the ®rst-order anisotropy, followed by a slight curvature at high magnetic ®elds caused by the presence of a second-order anisotropy term [4]. Therefore, the general expression for the magnetic free energy density can be written as: E
K eff 1 cos2 h
K eff 2 cos4 h
Ms H cosh
1
where h is the angle between the magnetization and the ®lm normal, and K eff 1 cos2 h and K eff 2 cos4 h represent ®rst- and second-order anisotropy energy, respectively. The last term describes the interaction between the external applied ®eld and the magnetization. The equilibrium magnetization orientation as a function of the magnetic ®eld strength is given by [16]: cosheq
H 1 Hsat
1
Fig. 3. Polar MOKE hysteresis cycles for the four multilayers analysed. In the inset, a comparison between the normalized experimental points and the curves calculated taking into account both ®rst- and second-order anisotropy ®elds is shown.
1001
2
2
Hsat cos2 heq 2
where Hsat 2K eff 1 =Ms and Hsat 4K eff 2 =Ms are the ®rst- and second-order contributions to the saturation ®eld, respectively. A quantitative de 1 2 termination of Hsat and Hsat has been carried out by a best ®t of the experimental data to the calculated magnetization curves, as shown in the inset of Fig. 3(a). The obtained values of the ®rst- and second-order ®elds are reported in Fig. 3(b). It can be seen that the second-order anisotropy contributions are much lower than the ®rst-order ones. From the latter, we have derived the eective ®rst 1 order anisotropy constant K eff 1 Ms Hsat =2. The eff 1 plot of the product K dNi as a function of the ®lm thickness is a straight line, as shown in Fig. 1 4(a). The negative sign of Keff indicates an easy axis parallel to the ®lm plane, due to the predominant contribution of shape anisotropy 2pM 2 to the magnetic energy. In order to evaluate other possible contributions to the magnetic anisotropy the following expression can be used: 2K eff 1 2 ks 1 Hsat 2pMs2 KV 2 Ms Ms dNi 2KV ks 4pMs 4 3 Ms dNi Ms where KV and ks represent the phenomenological ®rst-order bulk and interface anisotropy
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L. Albini et al. / Surface Science 482±485 (2001) 998±1003
Fig. 4. Anisotropy constants behaviour as a function of the Ni elemental layer thickness, determined by MOKE (open circles) and BLS (solid squares). The values of the bulk and interface anisotropy constants are obtained by the slope of the linear regression line and by its intercept with the vertical axis, respectively.
length comparable to that of light. The anisotropy contributions which are sources of additional effective ®elds in the ferromagnetic ®lm, are felt by the precessing spins and can be derived from a measurement of the spin-wave frequency. In order to evaluate independently the anisotropy constant by the spin-wave study, BLS measurements have been taken as a function of the external applied ®eld in the range 0.5±4.0 kOe. The inset of Fig. 5 shows a measured BLS spectrum from sample #1. The peaks due to the spin waves of the multilayer stack, consisting of a band of standing modes which can be described, in the dipolar approximation, by an analytical expression containing the external ®eld, the spectroscopic separation factor 1 g, the anisotropy ®eld Hsat and a band parameter w which varies between 0 and 1 [17]. The peaks exhibit a remarkable Stokes±anti-Stokes asymmetry, caused by the elliptical spin precession, typical of magnons in thin ferromagnetic ®lms of absorptive materials [18]. In addition, the contribution from the surface Damon±Eshbach mode appears only on the left side of the spectra, due to the non-reciprocal character of this mode. We have therefore performed a best ®t procedure of the experimental frequency of the right-hand peak, reported in Fig. 5, to the curves calculated for the band of standing modes, determining the values of 1 Hsat and thereafter the values of the anisotropy
constants, respectively. An inspection of Eq. (3) evidences that a positive (negative) sign of these constants implies an out-of-plane (in-plane) easy axis contribution. In Fig. 4(b) the behaviour of KV dNi 2ks is plotted as a function of dNi . A linear behavior is observed, and the intrinsic volume and interface anisotropy constants correspond to the slope and the intercept at dNi 0 of the linear regression curve, respectively. The values obtained are KV 9:90 0:76105 erg/cm3 and ks 0:15 0:02 erg/cm2 . 3.3. Spin-wave study Dierent from MOKE, BLS is a dynamic technique, testing spin-wave excitations with wave-
Fig. 5. Experimental (circles) and calculated (solid curves) spinwave mode frequency as a function of the applied ®eld for sample #1. The inset shows a Brillouin spectrum relative to sample #1 for an applied magnetic ®eld H 2500 Oe.
L. Albini et al. / Surface Science 482±485 (2001) 998±1003
constants, which are reported in Fig. 4(a) and (b), together with those obtained by MOKE. From the ®t procedure we could also determine the values of the spectroscopic separation factor g, which was found to be 2:08 0:02 for all the specimens. As seen in Fig. 4(a) and (b) the values of the bulk and interface anisotropy constants determined by MOKE and BLS are in very good agreement, in spite of the dierent approach of the two techniques. In particular, we notice that BLS probe produces very small deviations of the magnetization from its equilibrium direction and therefore it is sensitive to the ®rst-order eective anisotropy K eff 1 . In contrast, in a polar MOKE measurement one forces the magnetization to rotate out of the surface plane, being sensitive also to higher-order anisotropy contributions. Dierent from previous anomalous results in multilayers containing Ni [4], the present results indicate that the higher order anisotropy terms are much smaller than ®rst-order ones. Concerning the speci®c values of the anisotropy constants, one can note that: · the bulk constant KV , which includes the magnetocrystalline and magnetoelastic contributions, is positive i.e. tends to favour a perpendicular direction of the magnetization; its value is much lager than the magnetocrystalline constant of bulk Ni, indicating the predominant presence of a magnetoelastic contribution induced by the lattice distortion. · the surface constant ks instead is negative, reinforcing the in-plane magnetization of Ni ®lms; both its sign and absolute value are consistent with previous studies of multilayers containing Ni [19,20].
1003
Acknowledgements This work was partially supported by the INFM under the SIMBRIS advanced research project and by the Consiglio Nazionale delle Ricerche. References [1] S. Demokritov, E. Tsymbal, J. Phys. C 6 (1994) 7145. [2] B. Dieny, J. Magn. Magn. Mater. 136 (1994) 335. [3] F. Nizzoli, J.R. Sandercock, in: G.K. Horton, A.A. Maradudin (Eds.), Dynamical Properties of Solids, vol. 6, North Holland, Amsterdam, 1990, p. 307. [4] M.J. Pechan, I.K. Schuller, Phys. Rev. Lett. 59 (1987) 132. [5] B. Hillebrands, in: M. Cardona, G. G untherodt (Eds.), Light Scattering in Solids VII, Springer Series in Topics Applied Physics, Springer, Berlin, 1999. [6] G. Carlotti, et al., J. Magn. Magn. Mater. 165 (1997) 424. [7] P.J. Flanders, J. Appl. Phys. 63 (1988) 3940. [8] L. Albini, Tesi di Laurea, University of Perugia, 1998. [9] C.A. Ballentine, R.L. Fink, J. Araya-Pochet, J.L. Erskine, Appl. Phys. A 49 (1989) 459. [10] J.R. Sandercock, in: M. Cardona, G. G untherodt (Eds.), Light Scattering in Solids III, Springer Series in Topics in Applied Physics, vol. 51, Springer, Berlin, 1982, p. 173. [11] G. Gubbiotti, G. Carlotti, G. Socino, in: E. Bonetti, D. Fiorani (Eds.), Nanophase Materials, Trans Tech, Zurich, 1995, p. 215. [12] I.K. Schuller, Phys. Rev. Lett. 44 (1980) 1597. [13] W. Sevenhans, M. Gijs, Y. Bruynseraede, H. Homma, I.K. Schuller, Phys. Rev. B 34 (1986) 5955. [14] E.E. Fullerton, I.K. Schuller, H. Vanderstraeten, Y. Bruynseraede, Phys. Rev. B 45 (1992) 9292. [15] A. Kueny, M.R. Khan, I.K. Schuller, M. Grimsditch, Phys. Rev. B 29 (1984) 2879. [16] M.J. Pechan, I.K. Schuller, Phys. Rev. Lett. 59 (1987) 132. [17] R.E. Camley, T.S. Rahman, D.L. Mills, Phys. Rev. B 27 (1983) 261. [18] R.E. Camley, P. Grunberg, C.M. Mayr, Phys. Rev. B 26 (1982) 2609. [19] G. Bochi, C.A. Ballentine, H.E. Ingle®eld, C.V. Thompson, R.C. OÕHandley, Phys. Rev. B 52 (1995) 7311. [20] G. Bochi, C.A. Ballentine, et al., Phys. Rev. B 43 (1991) 3532.
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Magnetic anisotropy of Ni/Cu sputtered multilayers L. Albini a, G. Carlotti a,*, C. Dragoni a, G. Gubbiotti a, L. Verdini a, S. Loreti b, C. Minarini b, L. Pareti c, G. Turilli c a
Dipartimento di Fisica, Istituto Nazionale per la Fisica della Materia, Via Pascoli, I-06100 Perugia, Italy b C.R. ENEA, I-80055 Portici Napoli, Italy c Istituto MASPEC-CNR, Area delle Scienze, 43010 Parma, Italy
Abstract Ni/Cu multilayers were grown by RF sputtering. The crystal orientation, the thickness of the elemental layers and the interface quality were analysed by X-ray diraction in the h±2h con®guration. Magnetic anisotropy was investigated by both a static and a dynamic technique, namely magneto±optical Kerr eect (MOKE) and Brillouin light scattering (BLS). Longitudinal MOKE loops accounted for the in-plane orientation of the magnetization, while polar loops were used to determine the out-of-plane anisotropy ®elds, showing the existence of a minor second-order contribution in addition to the ®rst-order one. BLS was then exploited to detect thermal excited spin waves through inelastic scattering of light. The out-of-plane anisotropy ®elds evaluated by this high-frequency dynamic technique compare well with the ®rst-order values obtained by analysis of polar MOKE hysteresis cycles. Ó 2001 Elsevier Science B.V. All rights reserved. Keywords: Magnetic interfaces; Nickel; Magnetic ®lms; Metal±metal magnetic heterostructures; Surface waves; Magnons
1. Introduction The theoretical interest towards the magnetic properties of arti®cially layered systems is motivated by the fact that the reduced dimensionality strongly modi®es their magnetic behaviour with respect to those of bulk materials [1]. Moreover, magnetic ®lms and multilayers are ®nding steadily growing application in the technology of longitudinal and perpendicular magnetic recording, in magneto-optic storage technology, and in the ®eld of magnetic sensors [2].
* Corresponding author. Tel.: +39-75-5853067; fax: +39-07544666. E-mail address: [email protected] (G. Carlotti).
In this paper we present the results of the structural and magnetic properties of Ni/Cu multilayers, with dierent values of the repetition periodicity, deposited by RF sputtering on Si(1 0 0) substrates. Magneto±optical Kerr eect (MOKE) analysis, in both longitudinal and polar con®gurations, with applied ®elds up to 10 kOe, was exploited to measure hysteresis cycles and to determine the intrinsic magnetic anisotropy. The results of the above mentioned static technique (MOKE) are quantitatively compared to those obtained by Brillouin light scattering (BLS) [3] which is based on the detection of thermally activated high-frequency spin waves. This simultaneous and combined use of MOKE and BLS is particularly interesting, because signi®cant discrepancies have been reported in the literature
0039-6028/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 9 - 6 0 2 8 ( 0 0 ) 0 1 0 8 7 - 6
L. Albini et al. / Surface Science 482±485 (2001) 998±1003
between the interface anisotropy of magnetic/non magnetic multilayers containing Ni measured by dynamic and static techniques [4]. In addition, to our knowledge, no previous BLS investigations of Ni/Cu sputtered multilayers have been reported in the literature 1 [5]. 2. Experimental The specimens consist of alternating layers of Ni and Cu, deposited at room temperature on nonetched (1 0 0)-Si substrates by RF sputtering [6]. Four multilayers consisting of 15 periods have been studied. The elemental layer thicknesses, are reported in Table 1. A careful structural investigation of the multilayers was performed by X-ray diraction (XRD) analysis. The XRD measurements were carried on a Philips XÕPERT MPD diractometer equipped with a monocromator and using Cu±Ka radiation. A Bragg±Brentano con®guration with 2H values in the range 38±50°, where the (1 1 1)Cu and (1 1 1)Ni re¯ections lie, was used. Alternating gradient-®eld magnetometry (AGFM), which is described in details elsewhere [7] has been exploited to record hysteresis cycles at room temperature and to measure the values of the saturation magnetization Ms . Longitudinal and polar MOKE analysis were carried out by a dierential detection method [8] which increases the signalto-noise ratio with respect to the conventional method of nearly-crossed polarizers [9]. A further insight into the magnetic properties of the multilayers was obtained through BLS measurements, carried out using a Sandercock-type 3 3-pass tandem Fabry±Perot interferometer [10], characterized by a ®nesse of about 100 and a contrast ratio higher than 5 1010 . About 150 mW of p-polarized light, from an Ar -ion laser opera line, ted in single longitudinal mode on the 5145 A was focused onto the sample surface and the backscattered light analysed by the interferometer. Details about the experimental set-up can be found elsewhere [11]. In the used backscattering 1 A complete list of all the systems studied by BLS can be found in the recent review of Hillebrands (in Ref. [5]).
999
Table 1 First two columns: values of the elemental Ni and Cu layer thicknesses dNi and dCu , together with the value of the interplanar distance within each layer (in parentheses). The latter are to be compared with the values expected for bulk (1 1 1)-Ni (2.034 A) Third column: value of the amplitude of and (1 1 1)-Cu (2.088 A). the Gaussian distribution function of atomic disorder at the interfaces r, together with the average value of the interplanar spacing at the interface (in parentheses). Last column: values of the saturation magnetization determined by AGFM Sample dNi (A) dCu (A) r dint (A) Ms (Oe) #1
60.10 (2.044)
37.86 (2.078)
0.416 (2.072)
465 15
#2
47.84 (2.045)
32.79 (2.083)
0.382 (2.079)
419 15
#3
39.50 (2.047)
27.88 (2.073)
0.333 (2.073)
318 12
#4
32.00 (2.041)
24.00 (2.088)
0.292 (2.080)
217 10
geometry, the conservation of momentum in the photon±magnon interaction implies that the spinwave wavevector parallel to the ®lm surface is linked to the optical wavevector ki and to the angle of incidence hi by the equation: qjj 2ki sin hi . All spectra were recorded in air at room temperature at an incidence angle of light of 45° qjj 1:73 10 5 cm 1 . 3. Results and discussion 3.1. Structural properties X-ray diraction spectra in the h±2h con®guration have been recorded and a best ®t procedure has been performed in order to obtain the values of the elemental Ni and Cu layer thicknesses (Fig. 1), the interplanar distances within each material and the interface disorder. A re®nement program (SUPREX) based on superlattice X-ray diraction formalism was used [12±14] whose results are reported in Table 1. Note that the interplanar distances for each elemental layer are slightly bigger for the Ni ®lms and smaller for the Cu ones if compared with the values expected for bulk Ni and Cu respectively. The interface disorder and roughness, modelled in the SUPREX program as a gaussian distribution of atomic positions of
1000
L. Albini et al. / Surface Science 482±485 (2001) 998±1003
amplitude r centred around an average value dint , increases with increasing the elemental layer thickness. 3.2. Static magnetic properties
Fig. 1. Experimental (points) and calculated (line) h±2h X-ray spectra of two of the Ni/Cu multilayers investigated.
In the last column of Table 1, we have listed the measured values of the saturation magnetization, determined by AGFM. It can be seen that the magnetization markedly increases with increasing the elemental layer thicknesses due to the decreasing weight of the atomic disorder and/or interdiusion at the interfaces, as already observed in Mo/Ni multilayers [15]. Representative longitudinal MOKE hysteresis loops measured at room temperature are shown in Fig. 2. The loops are well open indicating that the magnetization easy axis lies in the ®lm plane, due to the predominant contribution of the magnetostatic term (shape anisotropy) in the magnetic energy. The absolute Kerr intensity reduces with dNi , consistently with the reduction of Ms measured by AGFM. It can also be observed that the coercive ®eld Hc decreases with dNi , as a consequence of the increased grain size.
Fig. 2. Longitudinal MOKE hysteresis cycles for the four multilayers analyzed.
L. Albini et al. / Surface Science 482±485 (2001) 998±1003
As a second step of our MOKE characterization we measured hysteresis cycles in the polar con®guration, i.e. with the ®eld applied along the ®lm normal, which is a hard-axis direction. External ®elds as high as a few thousands Oe were necessary to achieve saturation, even if the saturation ®elds are lower than those expected for the shape anisotropy (4pMs ), indicating the occurrence of other appreciable anisotropy contributions. In addition, complete reversibility (no hysteresis) was observed, as shown in Fig. 3(a), where a sequence of experimental loops is presented. Concerning the loop
shape, it appears a predominant linear approach to the saturation, due to the ®rst-order anisotropy, followed by a slight curvature at high magnetic ®elds caused by the presence of a second-order anisotropy term [4]. Therefore, the general expression for the magnetic free energy density can be written as: E
K eff 1 cos2 h
K eff 2 cos4 h
Ms H cosh
1
where h is the angle between the magnetization and the ®lm normal, and K eff 1 cos2 h and K eff 2 cos4 h represent ®rst- and second-order anisotropy energy, respectively. The last term describes the interaction between the external applied ®eld and the magnetization. The equilibrium magnetization orientation as a function of the magnetic ®eld strength is given by [16]: cosheq
H 1 Hsat
1
Fig. 3. Polar MOKE hysteresis cycles for the four multilayers analysed. In the inset, a comparison between the normalized experimental points and the curves calculated taking into account both ®rst- and second-order anisotropy ®elds is shown.
1001
2
2
Hsat cos2 heq 2
where Hsat 2K eff 1 =Ms and Hsat 4K eff 2 =Ms are the ®rst- and second-order contributions to the saturation ®eld, respectively. A quantitative de 1 2 termination of Hsat and Hsat has been carried out by a best ®t of the experimental data to the calculated magnetization curves, as shown in the inset of Fig. 3(a). The obtained values of the ®rst- and second-order ®elds are reported in Fig. 3(b). It can be seen that the second-order anisotropy contributions are much lower than the ®rst-order ones. From the latter, we have derived the eective ®rst 1 order anisotropy constant K eff 1 Ms Hsat =2. The eff 1 plot of the product K dNi as a function of the ®lm thickness is a straight line, as shown in Fig. 1 4(a). The negative sign of Keff indicates an easy axis parallel to the ®lm plane, due to the predominant contribution of shape anisotropy 2pM 2 to the magnetic energy. In order to evaluate other possible contributions to the magnetic anisotropy the following expression can be used: 2K eff 1 2 ks 1 Hsat 2pMs2 KV 2 Ms Ms dNi 2KV ks 4pMs 4 3 Ms dNi Ms where KV and ks represent the phenomenological ®rst-order bulk and interface anisotropy
1002
L. Albini et al. / Surface Science 482±485 (2001) 998±1003
Fig. 4. Anisotropy constants behaviour as a function of the Ni elemental layer thickness, determined by MOKE (open circles) and BLS (solid squares). The values of the bulk and interface anisotropy constants are obtained by the slope of the linear regression line and by its intercept with the vertical axis, respectively.
length comparable to that of light. The anisotropy contributions which are sources of additional effective ®elds in the ferromagnetic ®lm, are felt by the precessing spins and can be derived from a measurement of the spin-wave frequency. In order to evaluate independently the anisotropy constant by the spin-wave study, BLS measurements have been taken as a function of the external applied ®eld in the range 0.5±4.0 kOe. The inset of Fig. 5 shows a measured BLS spectrum from sample #1. The peaks due to the spin waves of the multilayer stack, consisting of a band of standing modes which can be described, in the dipolar approximation, by an analytical expression containing the external ®eld, the spectroscopic separation factor 1 g, the anisotropy ®eld Hsat and a band parameter w which varies between 0 and 1 [17]. The peaks exhibit a remarkable Stokes±anti-Stokes asymmetry, caused by the elliptical spin precession, typical of magnons in thin ferromagnetic ®lms of absorptive materials [18]. In addition, the contribution from the surface Damon±Eshbach mode appears only on the left side of the spectra, due to the non-reciprocal character of this mode. We have therefore performed a best ®t procedure of the experimental frequency of the right-hand peak, reported in Fig. 5, to the curves calculated for the band of standing modes, determining the values of 1 Hsat and thereafter the values of the anisotropy
constants, respectively. An inspection of Eq. (3) evidences that a positive (negative) sign of these constants implies an out-of-plane (in-plane) easy axis contribution. In Fig. 4(b) the behaviour of KV dNi 2ks is plotted as a function of dNi . A linear behavior is observed, and the intrinsic volume and interface anisotropy constants correspond to the slope and the intercept at dNi 0 of the linear regression curve, respectively. The values obtained are KV 9:90 0:76105 erg/cm3 and ks 0:15 0:02 erg/cm2 . 3.3. Spin-wave study Dierent from MOKE, BLS is a dynamic technique, testing spin-wave excitations with wave-
Fig. 5. Experimental (circles) and calculated (solid curves) spinwave mode frequency as a function of the applied ®eld for sample #1. The inset shows a Brillouin spectrum relative to sample #1 for an applied magnetic ®eld H 2500 Oe.
L. Albini et al. / Surface Science 482±485 (2001) 998±1003
constants, which are reported in Fig. 4(a) and (b), together with those obtained by MOKE. From the ®t procedure we could also determine the values of the spectroscopic separation factor g, which was found to be 2:08 0:02 for all the specimens. As seen in Fig. 4(a) and (b) the values of the bulk and interface anisotropy constants determined by MOKE and BLS are in very good agreement, in spite of the dierent approach of the two techniques. In particular, we notice that BLS probe produces very small deviations of the magnetization from its equilibrium direction and therefore it is sensitive to the ®rst-order eective anisotropy K eff 1 . In contrast, in a polar MOKE measurement one forces the magnetization to rotate out of the surface plane, being sensitive also to higher-order anisotropy contributions. Dierent from previous anomalous results in multilayers containing Ni [4], the present results indicate that the higher order anisotropy terms are much smaller than ®rst-order ones. Concerning the speci®c values of the anisotropy constants, one can note that: · the bulk constant KV , which includes the magnetocrystalline and magnetoelastic contributions, is positive i.e. tends to favour a perpendicular direction of the magnetization; its value is much lager than the magnetocrystalline constant of bulk Ni, indicating the predominant presence of a magnetoelastic contribution induced by the lattice distortion. · the surface constant ks instead is negative, reinforcing the in-plane magnetization of Ni ®lms; both its sign and absolute value are consistent with previous studies of multilayers containing Ni [19,20].
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Acknowledgements This work was partially supported by the INFM under the SIMBRIS advanced research project and by the Consiglio Nazionale delle Ricerche. References [1] S. Demokritov, E. Tsymbal, J. Phys. C 6 (1994) 7145. [2] B. Dieny, J. Magn. Magn. Mater. 136 (1994) 335. [3] F. Nizzoli, J.R. Sandercock, in: G.K. Horton, A.A. Maradudin (Eds.), Dynamical Properties of Solids, vol. 6, North Holland, Amsterdam, 1990, p. 307. [4] M.J. Pechan, I.K. Schuller, Phys. Rev. Lett. 59 (1987) 132. [5] B. Hillebrands, in: M. Cardona, G. G untherodt (Eds.), Light Scattering in Solids VII, Springer Series in Topics Applied Physics, Springer, Berlin, 1999. [6] G. Carlotti, et al., J. Magn. Magn. Mater. 165 (1997) 424. [7] P.J. Flanders, J. Appl. Phys. 63 (1988) 3940. [8] L. Albini, Tesi di Laurea, University of Perugia, 1998. [9] C.A. Ballentine, R.L. Fink, J. Araya-Pochet, J.L. Erskine, Appl. Phys. A 49 (1989) 459. [10] J.R. Sandercock, in: M. Cardona, G. G untherodt (Eds.), Light Scattering in Solids III, Springer Series in Topics in Applied Physics, vol. 51, Springer, Berlin, 1982, p. 173. [11] G. Gubbiotti, G. Carlotti, G. Socino, in: E. Bonetti, D. Fiorani (Eds.), Nanophase Materials, Trans Tech, Zurich, 1995, p. 215. [12] I.K. Schuller, Phys. Rev. Lett. 44 (1980) 1597. [13] W. Sevenhans, M. Gijs, Y. Bruynseraede, H. Homma, I.K. Schuller, Phys. Rev. B 34 (1986) 5955. [14] E.E. Fullerton, I.K. Schuller, H. Vanderstraeten, Y. Bruynseraede, Phys. Rev. B 45 (1992) 9292. [15] A. Kueny, M.R. Khan, I.K. Schuller, M. Grimsditch, Phys. Rev. B 29 (1984) 2879. [16] M.J. Pechan, I.K. Schuller, Phys. Rev. Lett. 59 (1987) 132. [17] R.E. Camley, T.S. Rahman, D.L. Mills, Phys. Rev. B 27 (1983) 261. [18] R.E. Camley, P. Grunberg, C.M. Mayr, Phys. Rev. B 26 (1982) 2609. [19] G. Bochi, C.A. Ballentine, H.E. Ingle®eld, C.V. Thompson, R.C. OÕHandley, Phys. Rev. B 52 (1995) 7311. [20] G. Bochi, C.A. Ballentine, et al., Phys. Rev. B 43 (1991) 3532.