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Magneto-optical Kerr spectra of nickel nanoparticles in silica glass fabricated by negative-ion implantation
Thin Solid Films 464 – 465 (2004) 268 – 272 www.elsevier.com/locate/tsf
Magneto-optical Kerr spectra of nickel nanoparticles in silica glass fabricated by negative-ion implantation H. Amekura *, Y. Takeda, N. Kishimoto Nanomaterials Laboratory, National Institute for Materials Science, 3-13 Sakura, Tsukuba, Ibaraki 305-0003, Japan Available online 17 July 2004
Abstract Magneto-optical Kerr effects, i.e., Kerr rotation and ellipticity, of nickel nanoparticles in silica glasses (SiO2) fabricated by implantation of Ni negative ions of 60 keV were studied in the wavelength region of 200 – 900 nm under a magnetic field up to f 21 kOe at room temperature. Experimental results of the Kerr spectra of the Ni nanoparticles were compared with calculations using the improved Lissberger – Saunders theory which is an extension of Maxwell-Garnett theory to magnetic composites including the size-dependent Drude free-electron function and the size-independent bound-electron term. Although the calculated spectra qualitatively agree with the experimental results, quantitative agreements were not good. Possible origins of the discrepancy are discussed. D 2004 Elsevier B.V. All rights reserved. PACS: 33.55.-b; 75.75.+a; 78.67.Bf; 78.20.Bh Keywords: Magnetic nanoparticle; Magneto-optical Kerr effect; Extended Maxwell-Garnett theory; Ion implantation
1. Introduction Magnetic nanoparticles dispersed in insulators draw much attention, because of their applicability for super high-density data storage [1] and tunneling magneto-resistance (TMR) devices [2], etc. High-flux negative-ion implantation is one of the most promising methods to fabricate metal nanoparticles in insulators, without heat treatment, with good controllability inherent in ion implantation and without surface charge accumulation [3]. Up to now, we have implanted Ni negative-ions of 60 keV to silica glasses (SiO2), and confirmed the Ni nanoparticles formation in SiO2 using cross-sectional transmission electron microscopy (TEM) [4] and the SQUID magnetometry [5]. In this paper, magneto-optical Kerr spectra of the Ni nanoparticles in SiO2 are studied. The Kerr spectra are determined from not only diagonal components of the dielectric tensor, e.g., exx, but also the off-diagonal components, e.g., exy. As for optical absorption, Ruppin [6] has succeeded in describing the spectra of non-magnetic Cu nanoparticles in glasses using the Maxwell-Garnett (MG) * Corresponding author. Tel.: +81-29-863-5479; fax: +81-29-863-5599. E-mail address: [email protected] (H. Amekura). 0040-6090/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2004.06.007
theory [7] with the mean-free-path confinement (MFPC) effect [8]. He assumed that the dielectric constants of metal nanoparticle em,xx were described as a sum of a sizesensitive free-electron contribution ef,xx(d) and a size-insensitive bound-electron contribution eb,xx; em;xx ðdÞ ¼ ef ;xx ðdÞ þ eb;xx :
ð1Þ
The free-electron contribution was approximated by the Drude model as, ef ;xx ðdÞ ¼ 1
x2p x2 þ ifx=sðdÞg
ð2Þ
where xp, s and d denote the bulk plasmon frequency, the relaxation time and the nanoparticle diameter, respectively. The size effect was introduced to the free-electron part ef,xx(d) only through the size-dependent relaxation time s(d) as, 1 1 2vF ¼ þ ð3Þ sðdÞ s0 d where so and vF denote the relaxation time of the bulk metal and the Fermi velocity, respectively. The size effect on the bound-electron part eb,xx was neglected. The bound-electron
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part eb,xx was determined as a difference between the experimental bulk value and the calculated ef,xx (d ! l) from Eqs. (2) and (3). Then the absorption spectra were derived using the MG theory. On the other hand, Lissberger and Saunders (LS) extended the MG theory with including off-diagonal parts to calculate Kerr spectra of nanoparticles in insulators [9]. However, they approximated the dielectric tensor by the Drude-type of ef,xx and ef,xy only, and neglected the boundelectron parts eb,xx and eb,xy. Since the bound-electron components cannot be neglected in actual metals, their theory failed. We have improved the LS theory by including the bound-electron contributions in both the diagonal part eb,xx and off-diagonal part eb,xy in Ruppin’s way, i.e., size-dependent ef,xx and ef,xy, and independent eb,xx and eb,xy. One of the aims of this paper is to examine to what extent the experimental Kerr spectra of Ni nanoparticles in SiO2 are reproduced by the improved LS theory, i.e., the extended MG theory and the Drude-MFPC effect with Ruppin’s inclusion of the bound-electron contribution.
269
through a hole of the magnetic pole, i.e., the polar Kerr configuration. A wavelength resolution of the monochromator was set in 1 nm. An incident angle of the light to the sample was 7j from normal to the surface. Between the monochromator and the magnet, a polarizer and a PEM were inserted to modulate the optical retardation of the incident light. The modulation frequency was f 42 kHz. The reflected light was collected by a photomultiplier via another polarizer. Polarities of hK and gK were determined from a standard Pt60Co40 alloy film (f50 nm thick) to reproduce results shown in Ref. [13]. This definition is consistent with a proposal by IEEE [14]. However, it is different from that used in a series of studies on experimental results and band calculations of Kerr effect of Ni films [15 –17]. Although the ellipticity signal from SiO2 substrate was negligible, the rotation signal from the substrate was too large to be neglected. Hereafter, the rotation signal is shown after subtracting the linear component due to the substrate.
3. Experimental results 2. Experimental Two types of samples, namely Ni thin-films on SiO2 substrates (continuous films) and Ni nanoparticles in SiO2, were used. Optical-grade silica glasses (KU-1: OH 820 ppm) of 15 mm in diameter and 0.5 mm in thickness were used for substrates of both types of the samples. The Ni films were deposited on the SiO2 substrates by resistive heating under a base pressure of less than f 1 10 4 Pa. The film thickness of f 120 nm was determined by a stepheight profiler (DEKTAK V200SI). The Ni nanoparticles were fabricated by implantation of Ni negative-ions of 60 keV to SiO2, using a Cs-assisted plasma-sputter type negative-ion source [10]. The nanoparticles were spontaneously formed in SiO2 without any heat treatments [4]. The ion flux was 56 AA/cm2. The fluence was 3.8 1016 ions/cm2, which was also confirmed by Rutherford Backscattering Spectrometry (RBS) using 2.06 MeV He+. According to Monte-Carlo ion-range simulation code SRIM2000 [11], the projectile range of Ni ions of 60 keV and the averaged volume fraction of Ni over the ion range are 47 nm and f 0.10, respectively, in SiO2. TEM observation showed Ni nanoparticle formation of 2.9 nm in mean diameter without heat treatments [4]. Kerr rotation hK and ellipticity gK were detected using the optical retardation modulation (ORM) method using a photo-elastic modulator (PEM). Principles of the ORM method are given in Ref. [12]. A sample was set between magnetic poles of an iron-core magnet. Magnetic field was applied normal to the sample surface up to f 21 kOe. The sample was illuminated by light (k = 200 –900 nm) from a 150-W Xe lamp via a 30-cm single grating monochromator
Fig. 1 shows magneto-optical hysteresis loops of a Ni film and Ni nanoparticles in SiO2. The film shows a parallelogrammic loop with hysteresis which is characteristic of ferromagnetic materials. The coercive field was f 0.18 kOe. Contrarily, the nanoparticles show a smooth and slow-rising curve characteristic of superparamagnetic particles [5]. Within an experimental error, hysteresis was
Fig. 1. Hysteresis loops of a Ni film on SiO2 substrate and Ni nanoparticles in SiO2 detected by Kerr ellipticity gK. A low field region of the loops in (a) is magnified and shown in (b). The loops of the film are shifted vertically for clarity.
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Fig. 4. Kerr rotation (open circles) and ellipticity (closed circles) spectra of a Ni film (f120 nm thick) on SiO2 substrate determined from the loops at each wavelength at T = 300 K. Solid lines are guide for eyes. In the rotation spectra, linear components from the rotation signal of SiO2 substrate were subtracted.
Fig. 2. Kerr ellipticity loops of Ni nanoparticles in SiO2 detected at several wavelengths at T = 300 K. One division of ordinate corresponds to 0.1 degrees. Horizontal lines indicate offsets of the each loop.
not observed. The curve is well fitted by the Langevin function [18]. Fig. 2 shows Kerr ellipticity loops of Ni nanoparticles in SiO2 at several wavelengths between 200 and 900 nm. The loop changes with the wavelength, not only in magnitude, but also in polarity. All the curves are saturated at H f 21 kOe. Then the wavelength dependences of hK and gK at H = 21 kOe are plotted in Fig. 3. The spectra of rotation and ellipticity should be connected to each other by the Kramers – Kronig relations [19]. In the case of transitions between discrete levels, the S-shaped dispersion in gK corresponds to the bell-type spectral shape of gK. Although it is not always true in metals, this was observed in Fig. 3, where the center of dispersion in gK at f 4 eV coincided with the negative peak of hK. In Fig. 4, Kerr rotation and ellipticity spectra of Ni film were shown. The spectra of Ni film are fairly different from the spectra of Ni nanoparticles in SiO2: Twin peak structures in hK ( f 1.6 and f 3.1 eV) and in gK ( f 2.2 and f 3.6 eV) of the Ni film spectra become one-peak structures ( f 2.8 eV in hK and f 3.4 eV in gK) of Ni nanoparticle spectra. Additional peaks appear in the Ni nanoparticle spectra at f 5.4 eV in hK and f 5.9 eV in gK. The difference is discussed in the next section.
4. Calculations and discussion Fig. 3. Kerr rotation (open circles) and ellipticity (closed circles) spectra of Ni nanoparticles in SiO2 determined from the loops at each wavelength at T = 300 K. Solid lines are guide for eyes. In the rotation spectra, linear components from the rotation signal of SiO2 substrate were subtracted.
To understand the Kerr spectra of Ni nanoparticles in SiO2 and those of Ni film, we have improved the LS theory with the inclusion of the bound-electron contributions, and
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calculated the spectra of the nanoparticles in SiO2 from the literature spectra of Ni film [15]. Although dielectric tensor of isotropic media at zero field is given by only diagonal part exx, the magnetic field induces off-diagonal component exy as, 1 1 0 0 exx 0 0 exx exy 0 C C B B C C B B C C: B ð4Þ e¼B 0 e e 0 ! e 0 xx C Hp0 B xy xx C B A A @ @ 0 0 exx 0 0 ezz Real and imaginary parts of the off-diagonal exy V and exyU are given from the Kerr rotation hK and ellipticity gK as, exyV ¼ nð1 n2 þ 3k 2 ÞhK kð1 3n2 þ k 2 ÞgK exyW ¼ kð1 3n2 þ k 2 ÞhK þ nð1 n2 þ 3k 2 ÞgK :
271
value of 2.33 108 cm/s was used [11] for the Fermi velocity vF. Effective dielectric tensors of SiO2 including Ni nanoparticles (Ni:SiO2 composite) are derived from the extension of MG theory [9] as, eeff ;xx ¼ ed;xx
em;xx ð1 þ 2pÞ þ 2ed;xx ð1 pÞ em;xx ð1 pÞ þ ed;xx ð2 þ pÞ
eeff ;xy ¼ pem;xy
3ed;xx em;xx ð1 pÞ þ ed;xx ð2 þ pÞ
2 ð8Þ
where p and ed,xx denote volume fraction of the nanoparticles and a diagonal dielectric component of SiO2. From the effective dielectric tensor (eeff)ij, Kerr rotation heff,K and ellipticity geff,K of the composite are given [19] as,
ð5Þ
where n and k denote refractive index and extinction coefficient, respectively [19]. From the Kerr rotation and ellipticity spectra in Ref. [15], the off-diagonal components em,V xy and em, W xy of pure Ni metal are derived using Eq. (5). Values of n and k are obtained from literature [20]. The diagonal and off-diagonal components of Ni nanoparticles, em,xx(d) and em,xy(d), are assumed to be described as a sum of size-sensitive free-electron contribution ef,ij (d) and size-insensitive bound-electron contribution eb,ij;
heff ;K ¼
2 2 nð1 n2eff þ 3keff Þeeff V ;xy þ kð1 3n2eff þ keff Þeeff W ;xy 2 2 2 2 2 ðneff þ keff Þfð1 neff keff Þ þ 4keff g
geff ;K ¼
2 2 kð1 3n2eff þ keff Þeeff V ;xy þ nð1 n2eff þ 3keff Þeeff W ;xy 2 2 2 2 2 ðneff þ keff Þfð1 neff keff Þ4keff g
ð9Þ
em;xx ðdÞ ¼ ef ;xx ðdÞ þ eb;xx em;xy ðdÞ ¼ ef ;xy ðdÞ þ eb;xy
ð6Þ
The diagonal and off-diagonal free-electron contributions are approximated by the Drude model as shown in Eq. (2) and, ef ;xy ðdÞ ¼ i
xxc x2p fx2 þ i½x=sðdÞ g2 x2 x2c
ð7Þ
where xc = eB/m denotes the cyclotron frequency [19]. Values of 4.23 eV and 83.8 meV were determined for ¯hxp and ¯h/s, respectively, so that the Eq. (2) fits the bulk literature values of n(x) and k(x) [20]. Two kinds of size effects are known in metallic nanoparticles, i.e., the classical MFPC effect [8] and the quantum size effect (QSE) [21]. In this paper, only the MFPC effect is taken into account, which has given a success in the absorption calculation of noble metal nanoparticles in insulators [6]. The MFPC effect is introduced through the size-dependent relaxation time s(d) described in Eq. (3). Only the free-electron components ef,xx(d) and ef,xy(d) suffer the size effect. A
Fig. 5. Kerr rotation (upper half) and ellipticity (lower half) spectra of Ni nanoparticles in SiO2 calculated by the improved LS theory. The dottedbroken, broken and dotted lines indicate the results of the nanoparticle diameters of 1, 3 and 10 nm, respectively. The spectra calculated without the size effect are also shown by solid lines. Open and closed circles indicate the experimental results. A volume fraction of p = 0.10 is assumed for the nanoparticles.
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where
neff ; keff ¼
8 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 91=2 < ðeeff V ;xx Þ2 þ ðeeff W ;xx Þ2 Feeff V ;xx = :
2
;
:
ð10Þ
Absolute values of the calculated free-electron off-diagonal component jef,xy(d)j were always much smaller than the bound-electron off-diagonal component jeb,xyj. The off-diagonal components relate with the magnetization, i.e., the delectrons which are itinerant but no more free-electron-like. Then the calculated size dependence is mainly given from the diagonal parts, i.e., the size-dependent complex refractive index of Ni:SiO2 composite. It should be noted that the heff,K and geff,K depend not only on the off-diagonal eeff,xy but also on neff and keff as shown in Eq. (9). Calculated Kerr rotation and ellipticity spectra of SiO2 including Ni nanoparticles (diameters = 1, 3 and 10 nm) are plotted in Fig. 5, with keeping a volume fraction p = 0.10. The spectra calculated without the size effect are also shown. Since the calculated spectra of 10 nm in diameter almost coincide with the spectra calculated without the size effect, the size effects are negligible in the nanoparticles larger than 10 nm in diameter. With decreasing the diameter, the calculated peak becomes broader. However, the experimental peaks in the Kerr spectra are always sharper than the corresponding peaks calculated. Moreover, while the experimental spectra qualitatively agree with the calculated results, the experimental peaks always locate at the lower energy side comparing with the calculated ones. Since the MFPC effect gives the peak broadening only, the narrow peak may be an evidence of the QSE [21]. However, it is not easy to explain the low energy shift from the QSE. The lowenergy shift and the narrowing of the experimental Kerr peaks may be explained by inadequate values of dielectric constants of SiO2, because the sample is in as-implanted state, i.e., containing a lot of defects. Another candidate origin is the two-layer structure of the implanted sample, i.e., the nanoparticle-dispersed SiO2 layer ( f 100 nm thick) on a pure SiO2 substrate may play an important role. In fact, an enhancement of Kerr effect is reported in multi-layer structure [22].
5. Conclusion Using the optical-retardation modulation technique, Kerr rotation and ellipticity of Ni nanoparticles in SiO2 fabricated by implantation of Ni negative ions of 60 keV were studied in the wavelength region of 200– 900 nm under magnetic fields up to f 21 kOe at room temperature. Kerr spectra of Ni nanoparticles in SiO2 were fairly different from those of Ni film of f 120-nm thick, indicating a composite nature of Ni nanoparticles in SiO2. Kerr spectra of Ni nanoparticles
in SiO2 were calculated using the improved LS theory, which is an extension of Maxwell-Garnett (MG) theory to magnetic composites with inclusion of the size-dependent Drude free-electron term and the size-independent boundelectron term. The experimental spectra qualitatively agree with the calculated ones, except shifts to the lower energy side and sharper peaks. Possible origins are the QSE, damaged SiO2 media and/or the two-layer structure of the implanted sample.
Acknowledgements A part of this study was financially supported by the Budget for Nuclear Research of the MEXT, based on the screening and counseling by the Atomic Energy Commission.
References [1] For example, C.B. Murray, S. Sun, H. Doyle, T. Betley, MRS Bull. 26 (2001) 985. [2] J.I. Gittleman, Y. Goldstein, S. Bozowski, Phys. Rev., B 5 (1972) 3609. [3] J. Ishikawa, H. Tsuji, Y. Toyota, Y. Gotoh, K. Matsuda, M. Tanjyo, S. Sakaki, Nucl. Instrum. Methods Phys. Res., B Beam Interact. Mater. Atoms 96 (1995) 7. [4] H. Amekura, N. Umeda, Y. Takeda, H. Kitazawa, N. Kishimoto, Trans. Mater. Res. Soc. Jpn. 28 (2003) 465. [5] H. Amekura, H. Kitazawa, T. Mochiku, N. Umeda, Y. Takeda, N. Kishimoto, Proc.-SPIE 4936 (2002) 1. [6] R. Ruppin, J. Appl. Phys. 59 (1986) 1355. [7] J.C. Maxwell-Garnett, Philos. Trans. R. Soc., A 203 (1904) 358. [8] U. Kreibig, M. Vollmer, Optical Properties of Metal Clusters, Springer-Verlag, Berlin, 1995, p. 81. [9] P.H. Lissberger, P.W. Saunders, Thin Solid Films 34 (1976) 323. [10] N. Kishimoto, Y. Takeda, V.T. Gritsyna, E. Iwamoto, T. Saito, in: J. Matsuo, G. Takaoka, I. Yamada (Eds.), IEEE Transactions from 1998 International Conference on Ion Implantation Technology Proceedings, IEEE, Piscataway, 1999, p. 342. [11] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, Pergamon Press, New York, 1985, http://www.srim.org/. [12] K. Sato, H. Hongu, H. Ikekame, Y. Tosaka, M. Watanabe, K. Takanashi, H. Fujimori, Jpn. J. Appl. Phys. 32 (1993) 989. [13] K. Sato, H. Hongu, H. Ikekame, J. Watanabe, K. Tsuzukiyama, Y. Togami, M. Fujisawa, T. Fukuzawa, Jpn. J. Appl. Phys. 31 (1992) 3603. [14] IEEE Standard Dictionary of Electrical and Electronical Terms, 3rd ed., IEEE, Piscataway, 1984, pp. 483 – 789. [15] S. Visnovsky, V. Parizek, M. Nyvlt, P. Kielar, V. Prosser, R. Krishnan, J. Magn. Magn. Mater. 127 (1993) 135. [16] A. Delin, O. Eriksson, B. Johansson, S. Auluck, J.M. Wills, Phys. Rev., B 60 (1999) 14105. [17] J. Kunes, P. Novak, J. Phys., Condens. Matter 11 (1999) 6301. [18] For example, D.L. Leslie-Pelecky, R.D. Rieke, Chem. Mater. 8 (1996) 1770. [19] For example, K. Sato, Light and Magnetism, 2nd ed., Asakura Pub, Tokyo, 2001, in Japanese. [20] E.D. Palik (Ed.), Handbook of Optical Constants of Solids, vol. 1, Academic Press, San Diego, 1998, p. 313. [21] A. Kawabata, R. Kubo, J. Phys. Soc. Jpn. 21 (1966) 1765. [22] T. Chen, D. Cheng, G.B. Chrlan, IEEE Trans. Mag. 16 (1980) 1194.
Magneto-optical Kerr spectra of nickel nanoparticles in silica glass fabricated by negative-ion implantation H. Amekura *, Y. Takeda, N. Kishimoto Nanomaterials Laboratory, National Institute for Materials Science, 3-13 Sakura, Tsukuba, Ibaraki 305-0003, Japan Available online 17 July 2004
Abstract Magneto-optical Kerr effects, i.e., Kerr rotation and ellipticity, of nickel nanoparticles in silica glasses (SiO2) fabricated by implantation of Ni negative ions of 60 keV were studied in the wavelength region of 200 – 900 nm under a magnetic field up to f 21 kOe at room temperature. Experimental results of the Kerr spectra of the Ni nanoparticles were compared with calculations using the improved Lissberger – Saunders theory which is an extension of Maxwell-Garnett theory to magnetic composites including the size-dependent Drude free-electron function and the size-independent bound-electron term. Although the calculated spectra qualitatively agree with the experimental results, quantitative agreements were not good. Possible origins of the discrepancy are discussed. D 2004 Elsevier B.V. All rights reserved. PACS: 33.55.-b; 75.75.+a; 78.67.Bf; 78.20.Bh Keywords: Magnetic nanoparticle; Magneto-optical Kerr effect; Extended Maxwell-Garnett theory; Ion implantation
1. Introduction Magnetic nanoparticles dispersed in insulators draw much attention, because of their applicability for super high-density data storage [1] and tunneling magneto-resistance (TMR) devices [2], etc. High-flux negative-ion implantation is one of the most promising methods to fabricate metal nanoparticles in insulators, without heat treatment, with good controllability inherent in ion implantation and without surface charge accumulation [3]. Up to now, we have implanted Ni negative-ions of 60 keV to silica glasses (SiO2), and confirmed the Ni nanoparticles formation in SiO2 using cross-sectional transmission electron microscopy (TEM) [4] and the SQUID magnetometry [5]. In this paper, magneto-optical Kerr spectra of the Ni nanoparticles in SiO2 are studied. The Kerr spectra are determined from not only diagonal components of the dielectric tensor, e.g., exx, but also the off-diagonal components, e.g., exy. As for optical absorption, Ruppin [6] has succeeded in describing the spectra of non-magnetic Cu nanoparticles in glasses using the Maxwell-Garnett (MG) * Corresponding author. Tel.: +81-29-863-5479; fax: +81-29-863-5599. E-mail address: [email protected] (H. Amekura). 0040-6090/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2004.06.007
theory [7] with the mean-free-path confinement (MFPC) effect [8]. He assumed that the dielectric constants of metal nanoparticle em,xx were described as a sum of a sizesensitive free-electron contribution ef,xx(d) and a size-insensitive bound-electron contribution eb,xx; em;xx ðdÞ ¼ ef ;xx ðdÞ þ eb;xx :
ð1Þ
The free-electron contribution was approximated by the Drude model as, ef ;xx ðdÞ ¼ 1
x2p x2 þ ifx=sðdÞg
ð2Þ
where xp, s and d denote the bulk plasmon frequency, the relaxation time and the nanoparticle diameter, respectively. The size effect was introduced to the free-electron part ef,xx(d) only through the size-dependent relaxation time s(d) as, 1 1 2vF ¼ þ ð3Þ sðdÞ s0 d where so and vF denote the relaxation time of the bulk metal and the Fermi velocity, respectively. The size effect on the bound-electron part eb,xx was neglected. The bound-electron
H. Amekura et al. / Thin Solid Films 464 – 465 (2004) 268–272
part eb,xx was determined as a difference between the experimental bulk value and the calculated ef,xx (d ! l) from Eqs. (2) and (3). Then the absorption spectra were derived using the MG theory. On the other hand, Lissberger and Saunders (LS) extended the MG theory with including off-diagonal parts to calculate Kerr spectra of nanoparticles in insulators [9]. However, they approximated the dielectric tensor by the Drude-type of ef,xx and ef,xy only, and neglected the boundelectron parts eb,xx and eb,xy. Since the bound-electron components cannot be neglected in actual metals, their theory failed. We have improved the LS theory by including the bound-electron contributions in both the diagonal part eb,xx and off-diagonal part eb,xy in Ruppin’s way, i.e., size-dependent ef,xx and ef,xy, and independent eb,xx and eb,xy. One of the aims of this paper is to examine to what extent the experimental Kerr spectra of Ni nanoparticles in SiO2 are reproduced by the improved LS theory, i.e., the extended MG theory and the Drude-MFPC effect with Ruppin’s inclusion of the bound-electron contribution.
269
through a hole of the magnetic pole, i.e., the polar Kerr configuration. A wavelength resolution of the monochromator was set in 1 nm. An incident angle of the light to the sample was 7j from normal to the surface. Between the monochromator and the magnet, a polarizer and a PEM were inserted to modulate the optical retardation of the incident light. The modulation frequency was f 42 kHz. The reflected light was collected by a photomultiplier via another polarizer. Polarities of hK and gK were determined from a standard Pt60Co40 alloy film (f50 nm thick) to reproduce results shown in Ref. [13]. This definition is consistent with a proposal by IEEE [14]. However, it is different from that used in a series of studies on experimental results and band calculations of Kerr effect of Ni films [15 –17]. Although the ellipticity signal from SiO2 substrate was negligible, the rotation signal from the substrate was too large to be neglected. Hereafter, the rotation signal is shown after subtracting the linear component due to the substrate.
3. Experimental results 2. Experimental Two types of samples, namely Ni thin-films on SiO2 substrates (continuous films) and Ni nanoparticles in SiO2, were used. Optical-grade silica glasses (KU-1: OH 820 ppm) of 15 mm in diameter and 0.5 mm in thickness were used for substrates of both types of the samples. The Ni films were deposited on the SiO2 substrates by resistive heating under a base pressure of less than f 1 10 4 Pa. The film thickness of f 120 nm was determined by a stepheight profiler (DEKTAK V200SI). The Ni nanoparticles were fabricated by implantation of Ni negative-ions of 60 keV to SiO2, using a Cs-assisted plasma-sputter type negative-ion source [10]. The nanoparticles were spontaneously formed in SiO2 without any heat treatments [4]. The ion flux was 56 AA/cm2. The fluence was 3.8 1016 ions/cm2, which was also confirmed by Rutherford Backscattering Spectrometry (RBS) using 2.06 MeV He+. According to Monte-Carlo ion-range simulation code SRIM2000 [11], the projectile range of Ni ions of 60 keV and the averaged volume fraction of Ni over the ion range are 47 nm and f 0.10, respectively, in SiO2. TEM observation showed Ni nanoparticle formation of 2.9 nm in mean diameter without heat treatments [4]. Kerr rotation hK and ellipticity gK were detected using the optical retardation modulation (ORM) method using a photo-elastic modulator (PEM). Principles of the ORM method are given in Ref. [12]. A sample was set between magnetic poles of an iron-core magnet. Magnetic field was applied normal to the sample surface up to f 21 kOe. The sample was illuminated by light (k = 200 –900 nm) from a 150-W Xe lamp via a 30-cm single grating monochromator
Fig. 1 shows magneto-optical hysteresis loops of a Ni film and Ni nanoparticles in SiO2. The film shows a parallelogrammic loop with hysteresis which is characteristic of ferromagnetic materials. The coercive field was f 0.18 kOe. Contrarily, the nanoparticles show a smooth and slow-rising curve characteristic of superparamagnetic particles [5]. Within an experimental error, hysteresis was
Fig. 1. Hysteresis loops of a Ni film on SiO2 substrate and Ni nanoparticles in SiO2 detected by Kerr ellipticity gK. A low field region of the loops in (a) is magnified and shown in (b). The loops of the film are shifted vertically for clarity.
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Fig. 4. Kerr rotation (open circles) and ellipticity (closed circles) spectra of a Ni film (f120 nm thick) on SiO2 substrate determined from the loops at each wavelength at T = 300 K. Solid lines are guide for eyes. In the rotation spectra, linear components from the rotation signal of SiO2 substrate were subtracted.
Fig. 2. Kerr ellipticity loops of Ni nanoparticles in SiO2 detected at several wavelengths at T = 300 K. One division of ordinate corresponds to 0.1 degrees. Horizontal lines indicate offsets of the each loop.
not observed. The curve is well fitted by the Langevin function [18]. Fig. 2 shows Kerr ellipticity loops of Ni nanoparticles in SiO2 at several wavelengths between 200 and 900 nm. The loop changes with the wavelength, not only in magnitude, but also in polarity. All the curves are saturated at H f 21 kOe. Then the wavelength dependences of hK and gK at H = 21 kOe are plotted in Fig. 3. The spectra of rotation and ellipticity should be connected to each other by the Kramers – Kronig relations [19]. In the case of transitions between discrete levels, the S-shaped dispersion in gK corresponds to the bell-type spectral shape of gK. Although it is not always true in metals, this was observed in Fig. 3, where the center of dispersion in gK at f 4 eV coincided with the negative peak of hK. In Fig. 4, Kerr rotation and ellipticity spectra of Ni film were shown. The spectra of Ni film are fairly different from the spectra of Ni nanoparticles in SiO2: Twin peak structures in hK ( f 1.6 and f 3.1 eV) and in gK ( f 2.2 and f 3.6 eV) of the Ni film spectra become one-peak structures ( f 2.8 eV in hK and f 3.4 eV in gK) of Ni nanoparticle spectra. Additional peaks appear in the Ni nanoparticle spectra at f 5.4 eV in hK and f 5.9 eV in gK. The difference is discussed in the next section.
4. Calculations and discussion Fig. 3. Kerr rotation (open circles) and ellipticity (closed circles) spectra of Ni nanoparticles in SiO2 determined from the loops at each wavelength at T = 300 K. Solid lines are guide for eyes. In the rotation spectra, linear components from the rotation signal of SiO2 substrate were subtracted.
To understand the Kerr spectra of Ni nanoparticles in SiO2 and those of Ni film, we have improved the LS theory with the inclusion of the bound-electron contributions, and
H. Amekura et al. / Thin Solid Films 464 – 465 (2004) 268–272
calculated the spectra of the nanoparticles in SiO2 from the literature spectra of Ni film [15]. Although dielectric tensor of isotropic media at zero field is given by only diagonal part exx, the magnetic field induces off-diagonal component exy as, 1 1 0 0 exx 0 0 exx exy 0 C C B B C C B B C C: B ð4Þ e¼B 0 e e 0 ! e 0 xx C Hp0 B xy xx C B A A @ @ 0 0 exx 0 0 ezz Real and imaginary parts of the off-diagonal exy V and exyU are given from the Kerr rotation hK and ellipticity gK as, exyV ¼ nð1 n2 þ 3k 2 ÞhK kð1 3n2 þ k 2 ÞgK exyW ¼ kð1 3n2 þ k 2 ÞhK þ nð1 n2 þ 3k 2 ÞgK :
271
value of 2.33 108 cm/s was used [11] for the Fermi velocity vF. Effective dielectric tensors of SiO2 including Ni nanoparticles (Ni:SiO2 composite) are derived from the extension of MG theory [9] as, eeff ;xx ¼ ed;xx
em;xx ð1 þ 2pÞ þ 2ed;xx ð1 pÞ em;xx ð1 pÞ þ ed;xx ð2 þ pÞ
eeff ;xy ¼ pem;xy
3ed;xx em;xx ð1 pÞ þ ed;xx ð2 þ pÞ
2 ð8Þ
where p and ed,xx denote volume fraction of the nanoparticles and a diagonal dielectric component of SiO2. From the effective dielectric tensor (eeff)ij, Kerr rotation heff,K and ellipticity geff,K of the composite are given [19] as,
ð5Þ
where n and k denote refractive index and extinction coefficient, respectively [19]. From the Kerr rotation and ellipticity spectra in Ref. [15], the off-diagonal components em,V xy and em, W xy of pure Ni metal are derived using Eq. (5). Values of n and k are obtained from literature [20]. The diagonal and off-diagonal components of Ni nanoparticles, em,xx(d) and em,xy(d), are assumed to be described as a sum of size-sensitive free-electron contribution ef,ij (d) and size-insensitive bound-electron contribution eb,ij;
heff ;K ¼
2 2 nð1 n2eff þ 3keff Þeeff V ;xy þ kð1 3n2eff þ keff Þeeff W ;xy 2 2 2 2 2 ðneff þ keff Þfð1 neff keff Þ þ 4keff g
geff ;K ¼
2 2 kð1 3n2eff þ keff Þeeff V ;xy þ nð1 n2eff þ 3keff Þeeff W ;xy 2 2 2 2 2 ðneff þ keff Þfð1 neff keff Þ4keff g
ð9Þ
em;xx ðdÞ ¼ ef ;xx ðdÞ þ eb;xx em;xy ðdÞ ¼ ef ;xy ðdÞ þ eb;xy
ð6Þ
The diagonal and off-diagonal free-electron contributions are approximated by the Drude model as shown in Eq. (2) and, ef ;xy ðdÞ ¼ i
xxc x2p fx2 þ i½x=sðdÞ g2 x2 x2c
ð7Þ
where xc = eB/m denotes the cyclotron frequency [19]. Values of 4.23 eV and 83.8 meV were determined for ¯hxp and ¯h/s, respectively, so that the Eq. (2) fits the bulk literature values of n(x) and k(x) [20]. Two kinds of size effects are known in metallic nanoparticles, i.e., the classical MFPC effect [8] and the quantum size effect (QSE) [21]. In this paper, only the MFPC effect is taken into account, which has given a success in the absorption calculation of noble metal nanoparticles in insulators [6]. The MFPC effect is introduced through the size-dependent relaxation time s(d) described in Eq. (3). Only the free-electron components ef,xx(d) and ef,xy(d) suffer the size effect. A
Fig. 5. Kerr rotation (upper half) and ellipticity (lower half) spectra of Ni nanoparticles in SiO2 calculated by the improved LS theory. The dottedbroken, broken and dotted lines indicate the results of the nanoparticle diameters of 1, 3 and 10 nm, respectively. The spectra calculated without the size effect are also shown by solid lines. Open and closed circles indicate the experimental results. A volume fraction of p = 0.10 is assumed for the nanoparticles.
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where
neff ; keff ¼
8 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 91=2 < ðeeff V ;xx Þ2 þ ðeeff W ;xx Þ2 Feeff V ;xx = :
2
;
:
ð10Þ
Absolute values of the calculated free-electron off-diagonal component jef,xy(d)j were always much smaller than the bound-electron off-diagonal component jeb,xyj. The off-diagonal components relate with the magnetization, i.e., the delectrons which are itinerant but no more free-electron-like. Then the calculated size dependence is mainly given from the diagonal parts, i.e., the size-dependent complex refractive index of Ni:SiO2 composite. It should be noted that the heff,K and geff,K depend not only on the off-diagonal eeff,xy but also on neff and keff as shown in Eq. (9). Calculated Kerr rotation and ellipticity spectra of SiO2 including Ni nanoparticles (diameters = 1, 3 and 10 nm) are plotted in Fig. 5, with keeping a volume fraction p = 0.10. The spectra calculated without the size effect are also shown. Since the calculated spectra of 10 nm in diameter almost coincide with the spectra calculated without the size effect, the size effects are negligible in the nanoparticles larger than 10 nm in diameter. With decreasing the diameter, the calculated peak becomes broader. However, the experimental peaks in the Kerr spectra are always sharper than the corresponding peaks calculated. Moreover, while the experimental spectra qualitatively agree with the calculated results, the experimental peaks always locate at the lower energy side comparing with the calculated ones. Since the MFPC effect gives the peak broadening only, the narrow peak may be an evidence of the QSE [21]. However, it is not easy to explain the low energy shift from the QSE. The lowenergy shift and the narrowing of the experimental Kerr peaks may be explained by inadequate values of dielectric constants of SiO2, because the sample is in as-implanted state, i.e., containing a lot of defects. Another candidate origin is the two-layer structure of the implanted sample, i.e., the nanoparticle-dispersed SiO2 layer ( f 100 nm thick) on a pure SiO2 substrate may play an important role. In fact, an enhancement of Kerr effect is reported in multi-layer structure [22].
5. Conclusion Using the optical-retardation modulation technique, Kerr rotation and ellipticity of Ni nanoparticles in SiO2 fabricated by implantation of Ni negative ions of 60 keV were studied in the wavelength region of 200– 900 nm under magnetic fields up to f 21 kOe at room temperature. Kerr spectra of Ni nanoparticles in SiO2 were fairly different from those of Ni film of f 120-nm thick, indicating a composite nature of Ni nanoparticles in SiO2. Kerr spectra of Ni nanoparticles
in SiO2 were calculated using the improved LS theory, which is an extension of Maxwell-Garnett (MG) theory to magnetic composites with inclusion of the size-dependent Drude free-electron term and the size-independent boundelectron term. The experimental spectra qualitatively agree with the calculated ones, except shifts to the lower energy side and sharper peaks. Possible origins are the QSE, damaged SiO2 media and/or the two-layer structure of the implanted sample.
Acknowledgements A part of this study was financially supported by the Budget for Nuclear Research of the MEXT, based on the screening and counseling by the Atomic Energy Commission.
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