OSA's Digital Library

Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 8 — Apr. 22, 2013
  • pp: 9875–9889

Polarizability and magnetoplasmonic properties of magnetic general nanoellipsoids

Nicolò Maccaferri, Juan B. González-Díaz, Stefano Bonetti, Andreas Berger, Mikko Kataja, Sebastiaan van Dijken, Josep Nogués, Valentina Bonanni, Zhaleh Pirzadeh, Alexandre Dmitriev, Johan Åkerman, and Paolo Vavassori  »View Author Affiliations


Optics Express, Vol. 21, Issue 8, pp. 9875-9889 (2013)
http://dx.doi.org/10.1364/OE.21.009875


View Full Text Article

Enhanced HTML    Acrobat PDF (2526 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

An approach to compute the polarizability tensor of magnetic nanoparticles having general ellipsoidal shape is presented. We find a surprisingly excellent quantitative agreement between calculated and experimental magneto-optical spectra measured in the polar Kerr configuration from nickel nanodisks of large size (exceeding 100 nm) with circular and elliptical shape. In spite of its approximations and simplicity, the formalism presented here captures the essential physics of the interplay between magneto-optical activity and the plasmonic resonance of the individual particle. The results highlight the key role of the dynamic depolarization effects to account for the magneto-optical properties of plasmonic nanostructures.

© 2013 OSA

OCIS Codes
(160.1190) Materials : Anisotropic optical materials
(160.3820) Materials : Magneto-optical materials
(290.5850) Scattering : Scattering, particles

ToC Category:
Scattering

History
Original Manuscript: February 5, 2013
Revised Manuscript: March 13, 2013
Manuscript Accepted: March 28, 2013
Published: April 12, 2013

Citation
Nicolò Maccaferri, Juan B. González-Díaz, Stefano Bonetti, Andreas Berger, Mikko Kataja, Sebastiaan van Dijken, Josep Nogués, Valentina Bonanni, Zhaleh Pirzadeh, Alexandre Dmitriev, Johan Åkerman, and Paolo Vavassori, "Polarizability and magnetoplasmonic properties of magnetic general nanoellipsoids," Opt. Express 21, 9875-9889 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-8-9875


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. M. Sandtke and L. Kuipers, “Slow guided surface plasmons at telecom frequencies,” Nat. Photonics 1(10), 573–576 (2007). [CrossRef]
  2. V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett. 8(12), 4391–4397 (2008). [CrossRef] [PubMed]
  3. S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,” Nat. Photonics 1(11), 641–648 (2007). [CrossRef]
  4. B. Sepúlveda, A. Calle, L. M. Lechuga, and G. Armelles, “Highly sensitive detection of biomolecules with the magneto-optic surface-plasmon-resonance sensor,” Opt. Lett. 31(8), 1085–1087 (2006). [CrossRef] [PubMed]
  5. G. Armelles, A. Cebollada, A. García-Martín, J. M. García-Martín, M. U. González, J. B. González-Díaz, E. Ferreiro-Vila, and J. F. Torrado, “Magnetoplasmonic nanostructures: systems supporting both plasmonic and magnetic properties,” J. Opt. A, Pure Appl. Opt. 11(11), 114023 (2009). [CrossRef]
  6. G. Armelles, A. Cebollada, A. García-Martín, and M. U. González, “Magnetoplasmonics: combining magnetic and plasmonic functionalities,” Adv. Opt. Mater. 1, 10–35 (2013).
  7. S. Melle, J. L. Menéndez, G. Armelles, D. Navas, M. Vázquez, K. Nielsch, R. B. Wehrspohn, and U. Gösele, “Magneto-optical properties of nickel nanowire arrays,” Appl. Phys. Lett. 83(22), 4547–4549 (2003). [CrossRef]
  8. V. I. Belotelov, L. L. Doskolovich, and A. K. Zvezdin, “Temporal coherence of photons emitted by single nitrogen-vacancy defect centers in diamond using optical Rabi-oscillations,” Phys. Rev. Lett. 98(7), 077401 (2007). [CrossRef] [PubMed]
  9. Z. Liu, L. Shi, Z. Shi, X. H. Liu, J. Zi, S. M. Zhou, S. J. Wei, J. Li, X. Zhang, and Y. J. Xia, “Magneto-optical Kerr effect in perpendicularly magnetized Co/Pt films on two-dimensional colloidal crystals,” Appl. Phys. Lett. 95(3), 032502 (2009). [CrossRef]
  10. G. Ctistis, E. Papaioannou, P. Patoka, J. Gutek, P. Fumagalli, and M. Giersig, “Optical and magnetic properties of hexagonal arrays of subwavelength holes in optically thin cobalt films,” Nano Lett. 9(1), 1–6 (2009). [CrossRef] [PubMed]
  11. V. Bonanni, S. Bonetti, T. Pakizeh, Z. Pirzadeh, J. Chen, J. Nogués, P. Vavassori, R. Hillenbrand, J. Åkerman, and A. Dmitriev, “Designer magnetoplasmonics with nickel nanoferromagnets,” Nano Lett. 11(12), 5333–5338 (2011). [CrossRef] [PubMed]
  12. J. Chen, P. Albella, Z. Pirzadeh, P. Alonso-González, F. Huth, S. Bonetti, V. Bonanni, J. Åkerman, J. Nogués, P. Vavassori, A. Dmitriev, J. Aizpurua, and R. Hillenbrand, “Plasmonic nickel nanoantennas,” Small 7(16), 2341–2347 (2011). [CrossRef] [PubMed]
  13. T. Katayama, Y. Suzuki, H. Awano, Y. Nishihara, and N. Koshizuka, “Enhancement of the magneto-optical Kerr rotation in Fe/Cu bilayered films,” Phys. Rev. Lett. 60(14), 1426–1429 (1988). [CrossRef] [PubMed]
  14. J. B. González-Díaz, A. García-Martín, J. M. García-Martín, A. Cebollada, G. Armelles, B. Sepúlveda, Y. Alaverdyan, and M. Käll, “Plasmonic Au/Co/Au nanosandwiches with enhanced magneto-optical activity,” Small 4(2), 202–205 (2008). [CrossRef] [PubMed]
  15. J. B. González-Díaz, B. Sepulveda, A. García-Martín, and G. Armelles, “Cobalt dependence of the magneto-optical response in magnetoplasmonic nanodisks,” Appl. Phys. Lett. 97(4), 043114 (2010). [CrossRef]
  16. J. C. Banthí, D. Meneses-Rodríguez, F. García, M. U. González, A. García-Martín, A. Cebollada, and G. Armelles, “High magneto-optical activity and low optical losses in metal-dielectric Au/Co/Au-SiO2 magnetoplasmonic nanodisks,” Adv. Mater. 24(10), OP36–OP41 (2012). [CrossRef] [PubMed]
  17. V. V. Temnov, G. Armelles, U. Woggon, D. Guzatov, A. Cebollada, A. García-Martín, J. M. García-Martín, T. Thomay, A. Leitenstorfer, and R. Bratschitsch, “Active magneto-plasmonics in hybrid metal–ferromagnet structures,” Nat. Photonics 4(2), 107–111 (2010). [CrossRef]
  18. G. Armelles, J. B. González-Díaz, A. García-Martín, J. M. García-Martín, A. Cebollada, M. Ujué González, S. Acimovic, J. Cesario, R. Quidant, and G. Badenes, “Localized surface plasmon resonance effects on the magneto-optical activity of continuous Au/Co/Au trilayers,” Opt. Express 16(20), 16104–16112 (2008). [CrossRef] [PubMed]
  19. F. Wang, A. Chakrabarty, F. Minkowski, K. Sun, and Q. Wei, “Polarization conversion with elliptical patch nanoantennas,” Appl. Phys. Lett. 101(2), 023101 (2012). [CrossRef]
  20. J. B. González-Díaz, A. García-Martín, G. Armelles, D. Navas, M. Vázquez, K. Nielsch, R. B. Wehrspohn, and U. Gösele, “Enhanced magneto-optics and size effects in ferromagnetic nanowire arrays,” Adv. Mater. 19(18), 2643–2647 (2007). [CrossRef]
  21. J. B. González-Díaz, J. M. García-Martín, A. García-Martín, D. Navas, A. Asenjo, M. Vázquez, M. Hernández-Vélez, and G. Armelles, “Plasmon-enhanced magneto-optical activity in ferromagnetic membranes,” Appl. Phys. Lett. 94(26), 263101 (2009). [CrossRef]
  22. P. K. Jain, Y. Xiao, R. Walsworth, and A. E. Cohen, “Surface plasmon resonance enhanced magneto-optics (SuPREMO): Faraday rotation enhancement in gold-coated iron oxide nanocrystals,” Nano Lett. 9(4), 1644–1650 (2009). [CrossRef] [PubMed]
  23. E. Th. Papaioannou, V. Kapaklis, P. Patoka, M. Giersig, P. Fumagalli, A. García-Martín, E. Ferreiro-Vila, and G. Ctistis, “Magneto-optic enhancement and magnetic properties in Fe antidot films with hexagonal symmetry,” Phys. Rev. B 81(5), 054424 (2010). [CrossRef]
  24. L. Wang, C. Clavero, Z. Huba, K. J. Carroll, E. E. Carpenter, D. Gu, and R. A. Lukaszew, “Plasmonics and enhanced magneto-optics in core-shell Co-Ag nanoparticles,” Nano Lett. 11(3), 1237–1240 (2011). [CrossRef] [PubMed]
  25. M. Rubio-Roy, O. Vlasin, O. Pascu, J. M. Caicedo, M. Schmidt, A. R. Goñi, N. G. Tognalli, A. Fainstein, A. Roig, and G. Herranz, “Magneto-optical enhancement by plasmon excitations in nanoparticle/metal structures,” Langmuir 28(24), 9010–9020 (2012). [CrossRef] [PubMed]
  26. D. R. Fredkin and I. D. Mayergoyz, “Resonant behavior of dielectric objects (electrostatic resonances),” Phys. Rev. Lett. 91(25), 253902 (2003). [CrossRef] [PubMed]
  27. I. D. Mayergoyz, D. R. Fredkin, and Z. Zhang, “Electrostatic (plasmon) resonances in nanoparticles,” Phys. Rev. B 72(15), 155412 (2005). [CrossRef]
  28. A. F. Stevenson, “Electromagnetic scattering by an ellipsoid in the third approximation,” J. Appl. Phys. 24(9), 1143–1151 (1953). [CrossRef]
  29. A. Wokaun, J. P. Gordon, and P. F. Liao, “Radiation damping in surface-enhanced Raman scattering,” Phys. Rev. Lett. 48(14), 957–960 (1982). [CrossRef]
  30. M. Meier and A. Wokaun, “Enhanced fields on large metal particles: dynamic depolarization,” Opt. Lett. 8(11), 581–583 (1983). [CrossRef] [PubMed]
  31. M. Meier, A. Wokaun, and P. F. Liao, “Enhanced fields on rough surfaces: dipolar interactions among particles of sizes exceeding the Rayleigh limit,” J. Opt. Soc. Am. B 2(6), 931–949 (1985). [CrossRef]
  32. A. Moroz, “Depolarization field of spheroidal particles,” J. Opt. Soc. Am. B 26(3), 517–527 (2009). [CrossRef]
  33. A. Lakhtakia, “Rayleigh scattering by bianisotropic ellipsoid in a biisotropic medium,” Int. J. Electron. 71(6), 1057–1062 (1991). [CrossRef]
  34. A. Lakhtakia, “Strong and weak forms of the method of moments and the coupled dipole method for scattering of time-harmonic electromagnetic fields,” Int. J. Mod. Phys. C 3(3), 583–603 (1992).
  35. R. Landauer, “The electrical resistance of binary metallic mixtures,” J. Appl. Phys. 23(7), 779–784 (1952). [CrossRef]
  36. D. Stroud, “Generalized effective-medium approach to the conductivity of an inhomogeneous material,” Phys. Rev. B 12(8), 3368–3373 (1975). [CrossRef]
  37. M. Schubert, T. E. Tiwald, and J. A. Woollam, “Explicit solutions for the optical properties of arbitrary magneto-optic materials in generalized ellipsometry,” Appl. Opt. 38(1), 177–187 (1999). [CrossRef] [PubMed]
  38. J. Zak, E. R. Mook, C. Liu, and S. D. Bader, “Universal approach to magneto-optics,” J. Magn. Magn. Mater. 89(1–2), 107–123 (1990). [CrossRef]
  39. Š. Višňovský, R. Lopusnik, M. Bauer, J. Bok, J. Fassbender, and B. Hillebrands, “Magnetooptic ellipsometry in multilayers at arbitrary magnetization,” Opt. Express 9(3), 121–135 (2001). [CrossRef] [PubMed]
  40. H. Fredriksson, Y. Alaverdyan, A. Dmitriev, C. Langhammer, D. S. Sutherland, M. Zäch, and B. Kasemo, “Hole–mask colloidal lithography,” Adv. Mater. 19(23), 4297–4302 (2007). [CrossRef]
  41. R. A. de la Osa, J. F. Saiz, M. Moreno, P. Vavassori, and A. Berger, “Transverse magneto-optical effects in nanoscale disks,” Phys. Rev. B 85(6), 064414 (2012). [CrossRef]
  42. D. Y. K. Ko and J. C. Inkson, “Matrix method for tunnelling in heterostructures: resonant tunnelling in multilayer systems,” Phys. Rev. B 38(14), 9945–9951 (1988). [CrossRef]
  43. D. M. Whittaker and I. S. Culshaw, “Scattering-matrix treatment of patterned multilayer photonic structures,” Phys. Rev. B 60(4), 2610–2618 (1999). [CrossRef]
  44. B. Caballero, A. Garcia Martin, and J. C. Cuevas, “Generalized scattering-matrix approach for magneto-optics in periodically patterned multilayer systems,” Phys. Rev. B 85(24), 245103 (2012). [CrossRef]
  45. Z. J. Yang and M. R. Scheinfein, “Combined three-axis surface magneto-optical Kerr effects in the study of surface and ultrathin-film magnetism,” J. Appl. Phys. 74(11), 6810–6823 (1993). [CrossRef]
  46. H. Kang and G. W. Milton, “Solutions to the Pólya–Szegö conjecture and the weak Eshelby conjecture,” Arch. Ration. Mech. Anal. 188(1), 93–116 (2008). [CrossRef]
  47. W. L. Bragg and A. B. Pippard, “The form birefringence of macromolecules,” Acta Crystallogr. 6(11), 865–867 (1953). [CrossRef]
  48. One should consider also the phase difference due to the incoming light hitting a finite size body. There are several ways to account for this phase difference reported in literature [30, 32, 49]. Although, we verified that inclusion of these corrections have negligible effects, and therefore for sake of clarity we neglect them. We point out, in addition, that for the particular geometry used in our experiments, namely perpendicular incidence over flat disks, this phase difference effects are rigorously zero.
  49. H. Kuwata, H. Tamaru, K. Esumi, and K. Miyano, “Resonant light scattering from metal nanoparticles: practical analysis beyond Rayleigh approximation,” Appl. Phys. Lett. 83(22), 4625–4627 (2003). [CrossRef]
  50. K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The optical properties of metal nanoparticles: the influence of size, shape, and dielectric environment,” J. Phys. Chem. B 107(3), 668–677 (2003). [CrossRef]
  51. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, 1957).
  52. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  53. V. G. Farafonov, V. B. Il’in, and M. S. Prokop’eva, “Light scattering by homogeneous and multilayer ellipsoids in the quasi-static approximation,” Opt. Spectrosc. 92(4), 567–576 (2002). [CrossRef]
  54. V. Myroshnychenko, J. Rodríguez-Fernández, I. Pastoriza-Santos, A. M. Funston, C. Novo, P. Mulvaney, L. M. Liz-Marzán, and F. J. García de Abajo, “Modelling the optical response of gold nanoparticles,” Chem. Soc. Rev. 37(9), 1792–1805 (2008). [CrossRef] [PubMed]
  55. L. Landau and E. M. Lifschitz, Electrodynamics of Continuous Media, (Ed. Pergamon, 1984)
  56. For a proper comparison, it is necessary to establish the association between Dx, Dy and Dz and D|| and D⊥ from Moroz. Based on the definitions of the eccentricities given in the text, our prolate profile is characterized by ax = az < ay, so Dx and Dz are equivalent to D|| and Dy to D⊥, whereas the oblate profile is characterized by ax = az < ay, so that Dx is equivalent this time to D⊥, while Dy and Dz toD||.
  57. http://www.nanogune.eu/en/research/nanomagnetism/polarizability-calculator/.
  58. L. A. Golovan, S. V. Zabotnov, V. Yu. Tinoshenko, and P. K. Kashkarov, “Consideration for the dynamic depolarization in the effective-medium model for description of optical properties for anisotropic nanostructured semiconductors,” Semiconductors 43(2), 218–222 (2009). [CrossRef]
  59. J. C. Maxwell-Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. Lond. B Biol. Sci. 203(359-371), 385–420 (1904). [CrossRef]
  60. A. Lakhtakia, “General theory of Maxwell-Garnett model for particulate composites with bi-isotropic host materials,” Int. J. Electron. 73(6), 1355–1362 (1992). [CrossRef]
  61. M. Abe, “Derivation of non-diagonal effective dielectric-permeability tensors for magnetized granular composites,” Phys. Rev. B 53(11), 7065–7075 (1996). [CrossRef]
  62. M. Abe and T. Suwa, “Surface plasma resonance and magneto-optical enhancement in composites containing multicore-shell structured nanoparticles,” Phys. Rev. B 70(23), 235103 (2004). [CrossRef]
  63. P. M. Hui and D. Stroud, “Theory of Faraday rotation by dilute suspensions of small particles,” Appl. Phys. Lett. 50(15), 950–952 (1987). [CrossRef]
  64. T. K. Xia, P. M. Hui, and D. Stroud, “Theory of Faraday rotation in granular magnetic materials,” J. Appl. Phys. 67(6), 2736–2741 (1990). [CrossRef]
  65. M. J. Freiser, “A survey of magnetooptic effects,” IEEE Trans. Magn. 4(2), 152–161 (1968). [CrossRef]
  66. This value for the embedding medium refractive index is chosen since the nano-disks embedded in air have one side in contact with the glass substrate. In the calculation we don’t account for the dispersion in the disks size, and we assume that the diameters are the average ones, although the dispersion in diameter can be easily included in Eq. (6) (following Ref. [62]), if required.
  67. S. A. Maier, Plasmonics: Fundamentals and Applications, (Springer, 2007).
  68. V. Giannini, A. I. Fernández-Domínguez, S. C. Heck, and S. A. Maier, “Plasmonic nanoantennas: fundamentals and their use in controlling the radiative properties of nanoemitters,” Chem. Rev. 111(6), 3888–3912 (2011). [CrossRef] [PubMed]
  69. C. Fourn and C. Brosseau, “Electrostatic resonances of heterostructures with negative permittivity: homogenization formalisms versus finite-element modeling,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77(1), 016603 (2008). [CrossRef] [PubMed]
  70. A. Mejdoubi and C. Brosseau, “Intrinsic electrostatic resonances of heterostructures with negative permittivity from finite-element calculations: application to core-shell inclusions,” J. Appl. Phys. 102(9), 094104 (2007). [CrossRef]
  71. P. Vavassori, “Polarization modulation technique for magneto-optical quantitative vector magnetometry,” Appl. Phys. Lett. 77(11), 1605–1607 (2000). [CrossRef]
  72. G. S. Krinchik and V. A. Artem’ev, “Magneto-optical properties of Ni, Co, and Fe in the ultraviolet visible, and infrared parts of the spectrum,” Sov. Phys. JTEP 26(6), 1080–1085 (1968).
  73. Š. Višňovský, V. Pařízek, M. Nývlt, P. Kielar, V. Prosser, and R. Krishnan, “Magneto-optical Kerr spectra of nickel,” J. Magn. Magn. Mater. 127(1–2), 135–139 (1993). [CrossRef]
  74. S. Albaladejo, R. Gómez-Medina, L. S. Froufe-Pérez, H. Marinchio, R. Carminati, J. F. Torrado, G. Armelles, A. García-Martín, and J. J. Sáenz, “Radiative corrections to the polarizability tensor of an electrically small anisotropic dielectric particle,” Opt. Express 18(4), 3556–3567 (2010). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited