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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 8 — Apr. 22, 2013
  • pp: 9906–9914
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Optical property study of FePt-C nanocomposite thin film for heat-assisted magnetic recording

Z. H. Cen, B. X. Xu, J. F. Hu, J. M. Li, K. M. Cher, Y. T. Toh, K. D. Ye, and J. Zhang  »View Author Affiliations


Optics Express, Vol. 21, Issue 8, pp. 9906-9914 (2013)
http://dx.doi.org/10.1364/OE.21.009906


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Abstract

Optical properties of the FePt-C nanocomposite thin film that was synthesized by sputtering with MgO/NiTa underlayer on glass substrate have been determined by an approach combining spectroscopic ellipsometry and transmission over the wavelength range of 380 – 1700 nm. It was observed that the refractive index is larger than the extinction coefficient, indicating that free electron absorption is not the dominant optical transition in the FePt-C thin film. Compared with FePt thin film, the FePt-C thin film has smaller optical constants, which lead to better optical performance including smaller optical spot on recording media and higher transducer efficiency for heat assisted magnetic recording.

© 2013 OSA

1. Introduction

FePt nanocomposite thin films with good L10 FePt (100) texture have been regarded as one of the most promising candidates for ultra-high density magnetic recording media, because of their large magnetocrystalline anisotropy, Ku (7 × 107 erg/cm3) that can suppress superparamagnetism at room temperature at a small particle size even below 10 nm [1

1. T. Suzuki, H. Muraoka, Y. Nakamura, and K. Ouchi, “Design and recording properties of FePt perpendicular media,” IEEE Trans. Magn. 39(2), 691–696 (2003). [CrossRef]

3

3. K. F. Dong, H. H. Li, Y. G. Peng, G. Ju, G. M. Chow, and J. S. Chen, “Well-isolated L10 FePt-SiNx-C nanocomposite films with large coercivity and small grain size,” J. Appl. Phys. 111(7), 07A308 (2012). [CrossRef]

]. Up till now, much study has been focused on the material synthesis and its structural and magnetic properties [4

4. J. S. Chen, B. C. Lim, Y. F. Ding, J. F. Hu, G. M. Chow, and G. Ju, “Granular L10 FePt-X (X=C, TiO2, Ta2O5) (001) nanocomposite films with small grain size for high density magnetic recording,” J. Appl. Phys. 105(7), 07B702 (2009). [CrossRef]

,5

5. S. D. Granz and M. H. Kryder, “Granular L10 FePt (001) thin films for Heat Assisted Magnetic Recording,” J. Magn. Magn. Mater. 324(3), 287–294 (2012). [CrossRef]

]. It has been demonstrated that a monolayer of L10 FePt nanoparticles with good magnetic properties embedded in a nonmagnetic material matrix has been successfully fabricated by chemical synthesis method and sputtering technique, separately [3

3. K. F. Dong, H. H. Li, Y. G. Peng, G. Ju, G. M. Chow, and J. S. Chen, “Well-isolated L10 FePt-SiNx-C nanocomposite films with large coercivity and small grain size,” J. Appl. Phys. 111(7), 07A308 (2012). [CrossRef]

6

6. T. Song, T. J. Zhou, C. L. Chen, and H. Gong, “XPS study of thermal effects on FePt and FePtAg nanoparticles,” IEEE Trans. Magn. 41(10), 3367–3369 (2005). [CrossRef]

]. However, existing magnetic recording heads cannot provide a magnetic field large enough to write FePt nanocomposite thin films with such high Ku using conventional writing schemes. To address this problem, heat-assisted magnetic recording (HAMR) has been proposed [7

7. M. H. Kryder, E. C. Gage, T. W. McDaniel, W. A. Challener, R. E. Rottmayer, G. P. Ju, Y. T. Hsia, and M. F. Erden, “Heat Assisted Magnetic Recording,” Proc. IEEE 96(11), 1810–1835 (2008). [CrossRef]

]. In HAMR, the recording medium is heated up to its Curie temperature by light locally and temporarily to lower the magnetic anisotropy during the recording process. Because of the interaction between light and recording media in HAMR, optical properties of FePt nanocomposite thin films are indispensable for HAMR system design and modeling.

Unlike the structural and magnetic properties of FePt nanocomposite thin films, its optical properties have seldom been studied [8

8. S. J. Lee, A. C. C. Yu, C. C. H. Lo, and M. Fan, “Optical properties of monodispersive FePt nanoparticle films,” Phys. Status Solidi 201(13), 3031–3036 (2004) (a). [CrossRef]

,9

9. S. L. Lee, C. C. H. Lo, A. C. C. Yu, and M. Fan, “Spectroscopic ellipsometry study of FePt nanoparticle films,” Phys. Status Solidi 203(15), 3801–3804 (2006) (a). [CrossRef]

]. A chemically synthesized FePt nanoparticle thin film with coupling layers on SiO2/Si substrate has been characterized by spectroscopic ellipsometry (SE), and it was shown that optical properties of the FePt nanoparticle film are different from those of the bulk and thin film counterparts [8

8. S. J. Lee, A. C. C. Yu, C. C. H. Lo, and M. Fan, “Optical properties of monodispersive FePt nanoparticle films,” Phys. Status Solidi 201(13), 3031–3036 (2004) (a). [CrossRef]

]. To the best of our knowledge, optical properties of FePt nanocomposite films fabricated by sputtering that is preferred for industrial manufacturing have not been fully investigated yet. In addition, optical properties of FePt nanocomposite films could strongly depend on the fabrication condition and technique [9

9. S. L. Lee, C. C. H. Lo, A. C. C. Yu, and M. Fan, “Spectroscopic ellipsometry study of FePt nanoparticle films,” Phys. Status Solidi 203(15), 3801–3804 (2006) (a). [CrossRef]

]. In this paper, study of optical properties of a FePt nanocomposite thin film doped with C (FePt-C) is reported. The thin film with MgO/NiTa underlayer on glass substrate was fabricated by sputtering. Due to the transparent substrate used in samples, SE together with transmission was employed to determine optical functions (i.e., refractive index n and extinction coefficient k as functions of wavelength) of the FePt-C thin film over the visible and near-infrared (near-IR) spectrum. Using the extracted FePt-C optical constants for the recording layer in a HAMR system, optical field distribution in the recording layer was simulated by finite-difference time-domain (FDTD) method. By comparing with the FePt film without doping C, it is shown that doping C into FePt thin film changes the thin film optical properties, which results in better optical performance as the HAMR recording layer.

2. Experimental details and modeling

SE measurement was conducted on samples at room temperature over a wavelength range from 380 to 1700 nm with a step of 5 nm at 3 incident angles (i.e., 65°, 70° and 75°), using a variable angle spectroscopic ellipsometer. Transmission (T) at normal incidence was also measured on the samples over the same wavelength range. Simultaneous analysis of the data obtained from both measurement techniques (i.e., SE and T) can improve accuracy of the extracted SE results, because correlation effect between thickness and optical constants of absorbing thin films can be alleviated [11

11. G. K. Pribil, B. Johs, and N. J. Ianno, “Dielectric function of thin metal films by combined in situ transmission ellipsometry and intensity measurements,” Thin Solid Films 455–456, 443–449 (2004). [CrossRef]

]. An optical multilayer model consisting of seven phases (i.e., Ambient/FePt-C/MgO/NiTa/Glass Substrate/NiTa/Ambient) as shown in Fig. 1(a) was used in spectral analysis of the measured ellipsometric angles (i.e., Ψ and Δ) and the transmission intensity. Optical functions of the NiTa and MgO layers as well as those of the glass substrate were measured from the corresponding control samples and a clean glass substrate, respectively. Thicknesses of the NiTa and MgO layers were determined to be 34.8 and 6.6 nm. The glass substrate thickness was measured by Vernier caliper, and it is 635 µm. The thicknesses of the NiTa and MgO layers and the substrate were fixed during spectral analysis for the FePt-C sample. Surface roughness of the FePt-C film, whose root mean square roughness Rq is 0.9 nm in this study, is not included in the optical model here. As a result, the retrieved optical constants are effective optical properties of the FePt-C film, and are not exactly reflective of all detailed thin film structures.

In order to evaluate optical performance of the FePt-C thin film as the recording layer in HAMR systems, the extracted FePt-C and FePt optical functions were employed for the recording layer in FDTD simulation of a simple HAMR system. In the HAMR system, a C-shape aperture transducer in gold (Au) film on a glass substrate and the recording medium were included in simulation [14

14. N. Zhou, E. C. Kinzel, and X. F. Xu, “Nanoscale ridge aperture as near-field transducer for heat-assisted magnetic recording,” Appl. Opt. 50(31), G42–G46 (2011). [CrossRef] [PubMed]

]. A light source at 780 nm with a Gaussian intensity distribution normally shining on the Au film was used to excite plasmons of the transducer. The Gaussian beam is focused to a diameter of 2 µm by a lens with numerical aperture (NA) of 0.33. The field magnitude of the light source was set at 1 V/m. The simulation boundaries were set to be perfectly matched layers to absorb the electromagnetic energy incident upon them. The whole FDTD simulation was conducted by using commercial software, Lumerical FDTD Solutions.

3. Results and discussion

The spectral fittings for the FePt-C and FePt samples are shown in Fig. 2
Fig. 2 (a) SE and (b) transmission spectral fittings for FePt-C and FePt thin films.
. As can be seen in Fig. 2(a), the SE spectra are well fitted by the point-by-point fitting approach, which have an average SE MSE around 1.5 for all fitting wavelengths. In addition, a good fitting with transmission MSE smaller than 1 is also achieved in the transmission spectra over the whole measured wavelength range as shown in Fig. 2(b). The thickness of the FePt-C thin film yielded from the fittings is 7.8 nm, which agrees with the TEM measurement result. The slight difference of the FePt-C film thickness from the height of FePt nanoparticles in the FePt-C film revealed in Fig. 1(b) could result from the FePt-C film roughness, and the FePt-C film thickness yielded by the optical model shown in Fig. 1(a) is an average thickness.

Figure 3
Fig. 3 (a) Refractive index and (b) extinction coefficient of FePt-C and FePt thin films as functions of wavelength. Smoothing optical functions using polynomial fitting is given also.
shows the yielded optical functions of the FePt-C thin film, as well as those of the FePt thin film for comparison. There is no prominent peak shown in the FePt-C optical functions. The refractive index of the FePt-C thin film increases with wavelength, while the corresponding extinction coefficient is around 1.75 over the wavelength range between 380 and 1300 nm, but increases with wavelength at the near-IR wavelengths longer than 1300 nm, which could be attributed to free electron absorption. However, the FePt-C refractive index is larger than the extinction coefficient at near-IR wavelengths, which is different from metallic characteristics. In addition, a similar result between refractive indexes and extinction coefficients at near-IR wavelengths can also be observed for the FePt thin film in the present study, showing that C with small extinction coefficients in the FePt-C film is not the only cause of the experimental result. Therefore, the dielectric-like FePt-C optical functions at near-IR wavelengths indicate that free electron absorption does not dominate FePt-C optical transitions. And it can be explained by the intrinsic scattering inside FePt nanoparticles, such as scattering by FePt crystal defects, and the scattering on the surfaces of FePt nanoparticles [9

9. S. L. Lee, C. C. H. Lo, A. C. C. Yu, and M. Fan, “Spectroscopic ellipsometry study of FePt nanoparticle films,” Phys. Status Solidi 203(15), 3801–3804 (2006) (a). [CrossRef]

], which would increase with decreasing the nanoparticle size.

By comparing the optical functions of FePt-C and FePt thin films, significant decrease in optical constants, particularly in extinction coefficient, can be observed after doping C. According to the effective medium approximation theory [15

15. D. A. G. Bruggeman, “Calculation of various physics constants in heterogenous substances I. Dielectricity constants and conductivity of mixed bodies from isotropic substances,” Ann. Phys. (Leipzig) 24(7), 636–664 (1935).

], inclusion of C into FePt can reduce the thin film effective optical constants, because C has lower optical constants with respect to FePt [16

16. S. Logothetidis, M. Gioti, S. Lousinian, and S. Fotiadou, “Haemocompatibility studies on carbon-based thin films by ellipsometry,” Thin Solid Films 482(1-2), 126–132 (2005). [CrossRef]

]. On the other hand, because of the increasing importance of the atom layer on nanoparticle surface and the limited particle size relative to the electron mean free path [17

17. E. S. Kooij, H. Wormeester, E. A. M. Brouwer, E. van Vroonhoven, A. van Silfhout, and B. Poelsema, “Optical characterization of thin colloidal gold films by spectroscopic ellipsometry,” Langmuir 18(11), 4401–4413 (2002). [CrossRef]

,18

18. C. Q. Sun, “Size dependence of nanostructures: Impact of bond order deficiency,” Prog. Solid State Chem. 35(1), 1–159 (2007). [CrossRef]

], FePt nanoparticles could have smaller optical constants as compared with the bulk counterpart [9

9. S. L. Lee, C. C. H. Lo, A. C. C. Yu, and M. Fan, “Spectroscopic ellipsometry study of FePt nanoparticle films,” Phys. Status Solidi 203(15), 3801–3804 (2006) (a). [CrossRef]

]. As a result, the FePt-C thin film shows optical constants distinct from those of the FePt thin film. Moreover, they can be tuned by adjusting the volume fraction ratio between FePt nanoparticles and the C matrix in the FePt-C film.

In order to employ the extracted optical properties of FePt-C and FePt thin films in HAMR system simulation, the FePt-C and FePt optical functions were smoothed by polynomial fitting as shown in Fig. 3. The simulation model of the HAMR system with the recording medium is shown in Fig. 4(a)
Fig. 4 (a) Simulation model of HAMR system. (b) Structure of C-aperture transducer.
, and the structure of the C-aperture transducer in the HAMR system is given in Fig. 4(b). The recording medium consists of a 10 nm recording layer, a 6 nm MgO layer, a 6 nm NiTa layer, and a 50 nm Au layer on a glass substrate. Here, the Au layer acts as a heat sink layer to improve the medium thermal property in practical case. FePt-C and FePt were used as the recording layer, respectively. The polarization of the incident light is along y direction. A 4 nm air gap between the transducer and the top surface of the recording medium was set in the simulation. Optical constants of the used materials at wavelength of 780 nm are listed in Table 1

Table 1. Optical constants (at 780 nm) of materials used in FDTD simulation

table-icon
View This Table
.

Figure 5(a)
Fig. 5 (a) Electric field intensity distribution on the recording layer top surface in FePt-C and FePt cases. (b) Electric field intensity distribution in recording layer.
shows the electric field intensity distribution on the top surface of the recording layer for the FePt-C and FePt cases, respectively. Similar optical spots with close values of maximum field enhancement were obtained in both cases. The optical spot size (full width at half maximum, FWHM) along x direction is nearly the same at 42.6 nm, while the spot size (FWHM) along y direction is 29 nm in the FePt-C case, which is 1 nm smaller than that in the FePt case. Although the difference of the optical spot size along the C-aperture ridge (i.e. along y direction) is not prominent, which is just close to the simulation mesh size (1 nm), it indicates that the propagation length of the surface plasmon along the Au/air interface is affected by the recording layer [14

14. N. Zhou, E. C. Kinzel, and X. F. Xu, “Nanoscale ridge aperture as near-field transducer for heat-assisted magnetic recording,” Appl. Opt. 50(31), G42–G46 (2011). [CrossRef] [PubMed]

], and it is shorter when the optical constants of the recording layer are smaller.

4. Summary

In summary, optical properties of the FePt-C nanocomposite thin film fabricated by sputtering with MgO/NiTa underlayer on glass substrate have been studied using SE and transmission. The FePt-C thin film have dielectric-like optical functions, where refractive index is larger than extinction coefficient at near-IR wavelengths, indicating that free electron absorption is not the dominant optical transition in FePt-C. As compared with the FePt thin film, significant reduction in optical constants can be observed in the FePt-C thin film. The extracted optical constants were used for the recording layer in FDTD simulation of a HAMR system. Better HAMR optical performance including smaller optical spot size and higher transducer efficiency can be obtained in the case of FePt-C film as compared with the case of FePt film, and it is owed to the smaller optical constants of the FePt-C thin film. Results in this study show that besides the widely studied improvement in magnetic and thermal properties, doping C into FePt to fabricate FePt-C nanocomposite thin film can achieve better HAMR optical performance.

References and links

1.

T. Suzuki, H. Muraoka, Y. Nakamura, and K. Ouchi, “Design and recording properties of FePt perpendicular media,” IEEE Trans. Magn. 39(2), 691–696 (2003). [CrossRef]

2.

J. S. Chen, J. F. Hu, B. C. Lim, Y. F. Ding, G. M. Chow, and G. Ju, “Development of L10 FePt:C (001) thin films with high coercivity and small grain size for ultra-high-density magnetic recording media,” IEEE Trans. Magn. 45(2), 839–844 (2009). [CrossRef]

3.

K. F. Dong, H. H. Li, Y. G. Peng, G. Ju, G. M. Chow, and J. S. Chen, “Well-isolated L10 FePt-SiNx-C nanocomposite films with large coercivity and small grain size,” J. Appl. Phys. 111(7), 07A308 (2012). [CrossRef]

4.

J. S. Chen, B. C. Lim, Y. F. Ding, J. F. Hu, G. M. Chow, and G. Ju, “Granular L10 FePt-X (X=C, TiO2, Ta2O5) (001) nanocomposite films with small grain size for high density magnetic recording,” J. Appl. Phys. 105(7), 07B702 (2009). [CrossRef]

5.

S. D. Granz and M. H. Kryder, “Granular L10 FePt (001) thin films for Heat Assisted Magnetic Recording,” J. Magn. Magn. Mater. 324(3), 287–294 (2012). [CrossRef]

6.

T. Song, T. J. Zhou, C. L. Chen, and H. Gong, “XPS study of thermal effects on FePt and FePtAg nanoparticles,” IEEE Trans. Magn. 41(10), 3367–3369 (2005). [CrossRef]

7.

M. H. Kryder, E. C. Gage, T. W. McDaniel, W. A. Challener, R. E. Rottmayer, G. P. Ju, Y. T. Hsia, and M. F. Erden, “Heat Assisted Magnetic Recording,” Proc. IEEE 96(11), 1810–1835 (2008). [CrossRef]

8.

S. J. Lee, A. C. C. Yu, C. C. H. Lo, and M. Fan, “Optical properties of monodispersive FePt nanoparticle films,” Phys. Status Solidi 201(13), 3031–3036 (2004) (a). [CrossRef]

9.

S. L. Lee, C. C. H. Lo, A. C. C. Yu, and M. Fan, “Spectroscopic ellipsometry study of FePt nanoparticle films,” Phys. Status Solidi 203(15), 3801–3804 (2006) (a). [CrossRef]

10.

J. F. Hu, J. S. Chen, B. C. Lim, and B. Liu, “Underlayer diffusion-induced enhancement of coercivity in high anisotropy FePt thin films,” J. Magn. Magn. Mater. 320(22), 3068–3070 (2008). [CrossRef]

11.

G. K. Pribil, B. Johs, and N. J. Ianno, “Dielectric function of thin metal films by combined in situ transmission ellipsometry and intensity measurements,” Thin Solid Films 455–456, 443–449 (2004). [CrossRef]

12.

Y. H. Yang and J. R. Abelson, “Spectroscopic ellipsometry of thin films on transparent substrates: A formalism for data interpretation,” J. Vac. Sci. Technol. A 13(3), 1145–1149 (1995). [CrossRef]

13.

B. Harbecke, “Coherent and incoherent reflection and transmission of multilayer structures,” Appl. Phys. B 39(3), 165–170 (1986). [CrossRef]

14.

N. Zhou, E. C. Kinzel, and X. F. Xu, “Nanoscale ridge aperture as near-field transducer for heat-assisted magnetic recording,” Appl. Opt. 50(31), G42–G46 (2011). [CrossRef] [PubMed]

15.

D. A. G. Bruggeman, “Calculation of various physics constants in heterogenous substances I. Dielectricity constants and conductivity of mixed bodies from isotropic substances,” Ann. Phys. (Leipzig) 24(7), 636–664 (1935).

16.

S. Logothetidis, M. Gioti, S. Lousinian, and S. Fotiadou, “Haemocompatibility studies on carbon-based thin films by ellipsometry,” Thin Solid Films 482(1-2), 126–132 (2005). [CrossRef]

17.

E. S. Kooij, H. Wormeester, E. A. M. Brouwer, E. van Vroonhoven, A. van Silfhout, and B. Poelsema, “Optical characterization of thin colloidal gold films by spectroscopic ellipsometry,” Langmuir 18(11), 4401–4413 (2002). [CrossRef]

18.

C. Q. Sun, “Size dependence of nanostructures: Impact of bond order deficiency,” Prog. Solid State Chem. 35(1), 1–159 (2007). [CrossRef]

19.

B. X. Xu, Z. H. Cen, Y. T. Toh, J. M. Li, K. D. Ye, and J. Zhang, “Efficiency analysis of near field optical transducer used in heat-assisted magnetic recording,” IEEE Trans. Magn. (to be published).

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(050.1755) Diffraction and gratings : Computational electromagnetic methods
(160.4236) Materials : Nanomaterials
(240.2130) Optics at surfaces : Ellipsometry and polarimetry

ToC Category:
Optics at Surfaces

History
Original Manuscript: December 12, 2012
Revised Manuscript: March 10, 2013
Manuscript Accepted: March 12, 2013
Published: April 15, 2013

Citation
Z. H. Cen, B. X. Xu, J. F. Hu, J. M. Li, K. M. Cher, Y. T. Toh, K. D. Ye, and J. Zhang, "Optical property study of FePt-C nanocomposite thin film for heat-assisted magnetic recording," Opt. Express 21, 9906-9914 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-8-9906


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References

  1. T. Suzuki, H. Muraoka, Y. Nakamura, and K. Ouchi, “Design and recording properties of FePt perpendicular media,” IEEE Trans. Magn.39(2), 691–696 (2003). [CrossRef]
  2. J. S. Chen, J. F. Hu, B. C. Lim, Y. F. Ding, G. M. Chow, and G. Ju, “Development of L10 FePt:C (001) thin films with high coercivity and small grain size for ultra-high-density magnetic recording media,” IEEE Trans. Magn.45(2), 839–844 (2009). [CrossRef]
  3. K. F. Dong, H. H. Li, Y. G. Peng, G. Ju, G. M. Chow, and J. S. Chen, “Well-isolated L10 FePt-SiNx-C nanocomposite films with large coercivity and small grain size,” J. Appl. Phys.111(7), 07A308 (2012). [CrossRef]
  4. J. S. Chen, B. C. Lim, Y. F. Ding, J. F. Hu, G. M. Chow, and G. Ju, “Granular L10 FePt-X (X=C, TiO2, Ta2O5) (001) nanocomposite films with small grain size for high density magnetic recording,” J. Appl. Phys.105(7), 07B702 (2009). [CrossRef]
  5. S. D. Granz and M. H. Kryder, “Granular L10 FePt (001) thin films for Heat Assisted Magnetic Recording,” J. Magn. Magn. Mater.324(3), 287–294 (2012). [CrossRef]
  6. T. Song, T. J. Zhou, C. L. Chen, and H. Gong, “XPS study of thermal effects on FePt and FePtAg nanoparticles,” IEEE Trans. Magn.41(10), 3367–3369 (2005). [CrossRef]
  7. M. H. Kryder, E. C. Gage, T. W. McDaniel, W. A. Challener, R. E. Rottmayer, G. P. Ju, Y. T. Hsia, and M. F. Erden, “Heat Assisted Magnetic Recording,” Proc. IEEE96(11), 1810–1835 (2008). [CrossRef]
  8. S. J. Lee, A. C. C. Yu, C. C. H. Lo, and M. Fan, “Optical properties of monodispersive FePt nanoparticle films,” Phys. Status Solidi201(13), 3031–3036 (2004) (a). [CrossRef]
  9. S. L. Lee, C. C. H. Lo, A. C. C. Yu, and M. Fan, “Spectroscopic ellipsometry study of FePt nanoparticle films,” Phys. Status Solidi203(15), 3801–3804 (2006) (a). [CrossRef]
  10. J. F. Hu, J. S. Chen, B. C. Lim, and B. Liu, “Underlayer diffusion-induced enhancement of coercivity in high anisotropy FePt thin films,” J. Magn. Magn. Mater.320(22), 3068–3070 (2008). [CrossRef]
  11. G. K. Pribil, B. Johs, and N. J. Ianno, “Dielectric function of thin metal films by combined in situ transmission ellipsometry and intensity measurements,” Thin Solid Films455–456, 443–449 (2004). [CrossRef]
  12. Y. H. Yang and J. R. Abelson, “Spectroscopic ellipsometry of thin films on transparent substrates: A formalism for data interpretation,” J. Vac. Sci. Technol. A13(3), 1145–1149 (1995). [CrossRef]
  13. B. Harbecke, “Coherent and incoherent reflection and transmission of multilayer structures,” Appl. Phys. B39(3), 165–170 (1986). [CrossRef]
  14. N. Zhou, E. C. Kinzel, and X. F. Xu, “Nanoscale ridge aperture as near-field transducer for heat-assisted magnetic recording,” Appl. Opt.50(31), G42–G46 (2011). [CrossRef] [PubMed]
  15. D. A. G. Bruggeman, “Calculation of various physics constants in heterogenous substances I. Dielectricity constants and conductivity of mixed bodies from isotropic substances,” Ann. Phys. (Leipzig)24(7), 636–664 (1935).
  16. S. Logothetidis, M. Gioti, S. Lousinian, and S. Fotiadou, “Haemocompatibility studies on carbon-based thin films by ellipsometry,” Thin Solid Films482(1-2), 126–132 (2005). [CrossRef]
  17. E. S. Kooij, H. Wormeester, E. A. M. Brouwer, E. van Vroonhoven, A. van Silfhout, and B. Poelsema, “Optical characterization of thin colloidal gold films by spectroscopic ellipsometry,” Langmuir18(11), 4401–4413 (2002). [CrossRef]
  18. C. Q. Sun, “Size dependence of nanostructures: Impact of bond order deficiency,” Prog. Solid State Chem.35(1), 1–159 (2007). [CrossRef]
  19. B. X. Xu, Z. H. Cen, Y. T. Toh, J. M. Li, K. D. Ye, and J. Zhang, “Efficiency analysis of near field optical transducer used in heat-assisted magnetic recording,” IEEE Trans. Magn. (to be published).

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