# Unusual magneto-optical behavior induced by local dielectric variations under localized surface plasmon excitations

- Juan B González-Díaz
^{1}Email author, - Antonio García-Martín†
^{1}and - Gaspar Armelles Reig†
^{1}

**6**:408

https://doi.org/10.1186/1556-276X-6-408

© González-Díaz et al; licensee Springer. 2011

**Received: **4 November 2010

**Accepted: **2 June 2011

**Published: **2 June 2011

## Abstract

We study the effect of global and local dielectric variations on the polarization conversion *r*
_{ps} response of ordered nickel nanowires embedded in an alumina matrix. When considering local changes, we observe a non-monotonous behavior of the *r*
_{ps}, its intensity unusually modified far beyond to what it is expected for a monotonous change of the whole refractive index of the embedding medium. This is related to the local redistribution of the electromagnetic field when a localized surface plasmon is excited. This finding may be employed to develop and improve new biosensing magnetoplasmonic devices.

During the last years, a great effort has been devoted to the study of metallic nanoparticles due to their distinct optical properties with respect to that of the bulk material [1]. These differences arise mainly from their ability to uphold charge density oscillations known as localized surface plasmons (LSPs). These spatially localized modes may appear at a metal/dielectric interface, manifesting themselves as optical resonances in the transmission and reflection spectra, being their most significant feature the local enhancement of the electromagnetic (EM) field at the metal/dielectric interface [2]. The spectral position, width, and intensity of the optical resonances are extremely dependent on the size, shape, particle inter-distance, embedding environment, or material components of the nanoparticles. In a number of works, the influence of such parameters has been thoroughly studied putting forward the possibility of tailoring their optical response through the morphology of the particles [3–6].

More recently, the optical response arising from the combination of both surface plasmon resonances and magneto-optical (MO) properties that takes place in ferromagnetic nanoparticles is under intensive study. Different theoretical and experimental works [7–11] have pointed out that LSPs affect the MO response, finding an enhancement of the signal that has been usually ascribed to a pure optical effect related to the plasmonic excitation [10, 12–14]. However, the MO activity defines in terms of the reflectivity coefficients as *Φ* = *r*
_{ps}/*r*
_{pp}, being *r*
_{ps} the polarization conversion and *r*
_{pp} the optical response (when the magnetic field is applied perpendicular to the sample plane). Therefore, the MO response may also be enhanced by modifying *r*
_{ps}. This was first shown in [11], where the authors suggested as a possible origin the strong localization of the EM field in the MO active material due to the LSP excitation. The scope of this work is to study more in detail the correspondence between the polarization conversion and the EM field under LSP excitations. To do so, we will theoretically analyze the *r*
_{ps} dependence to global and local dielectric changes of the surrounding media in periodic ferromagnetic nanowire arrays. We will show that the different dielectric environments affect the EM field distribution when the LSP is excited, consequently changing the spectral position and intensity of the *r*
_{ps} peak. Moreover, we will prove that variations of the refractive index in the close vicinity of the wires extremely affect the *r*
_{ps}, making its intensity much larger and/or smaller than that obtained if the whole embedding matrix is replaced. This is a consequence of the local redistribution of the EM field induced by the plasmon excitation at the metal/dielectric interface.

*r*

_{ps}response, we considered an ordered hexagonal array of nickel nanowires embedded in a dielectric matrix and oriented along the

*z*-axis. The diameter of the wires was set to 80 nm, with a lattice parameter of 180 nm and a height of 15 μm (a schematic view of the model system can be seen on top of Figure 1a). The spectral dependence of the absolute value of the polarization conversion |

*r*

_{ps}| was obtained by means of a scattering matrix method (SMM), modified to allow MO activity in the polar configuration [15]. The diagonal and off-diagonal dielectric constants of nickel were taken from [16, 17], respectively, whereas the refractive index of the dielectric matrix remained energy independent. Calculations were performed for different embedding mediums (from

*n*= 1.7 to

*n*= 1.4), shown in Figure 1a. A peak can be observed in all the spectra, blue-shifting and increasing its intensity, as the refractive index decreases. This peak is originated by an LSP excitation in the wires, as it was pointed out in [10, 11], being its spectral position related to the variation of the plasmon resonance condition introduced by the modification of the dielectric background. We also performed additional calculations replacing the hexagonal array of nanowires with an effective layer. Since the dimensions of the nanostructure are much smaller than the wavelength of light, the optical properties of the nanowires and the embedding matrix can be merged by means of an effective medium approximation (EMA) [18]. The results are shown in Figure 1b. As it can be observed, the spectra show the LSP-induced peak, but contrary to the SMM results, its intensity decreases with the refractive index.

*z*-axis (just its intensity). The circle delimits the nanowire section. As it can be observed, the EM field tends to localize at the interface between the dielectric and the nanowire. When the refractive index of the matrix decreases, it appears less localized at the metal/dielectric interface, which is the expected for a plasmonic behavior. As a consequence, the EM field increases within the nanowires. Figure 2 shows this evolution with the refractive index, where we plot the average EM field spectra for different embedding matrices within the nanowires. The curves reproduce the same trend observed for the |

*r*

_{ps}| calculations, i.e., the intensity increases as the refractive index decreases, thus pointing out that the strong relation between the polarization conversion and the amount of EM field within the nanowires induced by LSP excitations.

*n*= 1.4 (

*n*= 1.7 for the matrix) and (b)

*n*= 1.7 (

*n*= 1.4 for the matrix). Figure 3a, b shows the spectral position and intensity of the |

*r*

_{ps}| peak as a function of the shell thickness for the different (a) and (b) dielectric environments (dots and circles, respectively). The black and dotted horizontal lines correspond to the values for the

*n*= 1.7 and

*n*= 1.4 uniform dielectric backgrounds, respectively. For both dielectric environments, the spectral position of the |

*r*

_{ps}| peak (see Figure 3a) shifts almost linearly with the shell thickness. On the contrary, the evolution of its intensity does not appear to happen in a linear way. For example, if we restrict to the first case (a), a 5-nm shell around the wires implies a strong decrease of the intensity for the |

*r*

_{ps}| peak. A 20-nm shell leads to the maximum decrease, and beyond this thickness, the value of |

*r*

_{ps}| approaches gradually to that of the uniform dielectric medium. On the other hand, case (b) shows that the intensity increases above the values for the two uniform backgrounds, being the 15-nm thick shell the one that leads to the maximum |

*r*

_{ps}|. It is worth noticing that in both cases, there is a range of shell thicknesses in which the value of |

*r*

_{ps}| exceeds that obtained if the whole embedding matrix had the same refractive index of the shell. In particular, if we assume that replacing the whole refractive index of the matrix represents a 100% variation of the |

*r*

_{ps}|, then the optimum shell thicknesses for cases (a) and (b) represent more than a 200% variation of the |

*r*

_{ps}|. It is also remarkable that employing other materials presenting a larger difference in their refractive indexes might provide a much intense variation of the |

*r*

_{ps}|. However, in our case, we have tried to remain as realistic as possible, employing refractive indexes that have already measured in the fabrication of alumina templates [20].

*n*= 1.7 (

*n*= 1.4) shell is depicted at the energies where the LSP is excited. As it can be observed, when the shell presents a smaller refractive index (bottom) than the embedding matrix, the EM field within the nanowires decreases. Moreover, as the shell thickness increases, the EM field reaches a minimum that matches with that observed in the |

*r*

_{ps}| calculations. This can be better seen in the graph of Figure 4, where we present the intensity of the average EM field within the nanowires for the (a) dielectric environments (dots). On the other hand, when the shell has a larger refractive index than the embedding matrix (b), the EM field increases within the nanowires. The average EM field for this system (circles) shows (see Figure 4) a maximum that again coincides with that obtained for the polarization conversion. This lead us to conclude that the origin of the enhanced or reduced |

*r*

_{ps}| response in the shelled nanowires system can be ascribed to the redistribution of the EM field at the metal/dielectric interface induced by the LSP excitation, i.e., any variation of the refractive index in the vicinity of the wires affects the EM field, thus inducing a larger perturbation of the MO response.

In summary, we have theoretically analyzed the relation between the LSP-induced enhancement of the EM field and the polarization conversion in hexagonally ordered ferromagnetic nanowires. We have shown that local variations of the refractive index extremely affect the |*r*
_{ps}| response, which is the consequence of the local EM field redistribution at the LSP resonance within the MO active material. We expect these results may find important applications in biosensing and novel magnetoplasmonic devices.

## Notes

## Declarations

### Acknowledgements

This work was supported by the EU (NMP3-SL-2008-214107-Nanomagma), the Spanish MICINN ("MAGPLAS" MAT2008-06765-C02-01/NAN and "FUNCOAT" CONSOLIDER INGENIO 2010 CSD2008-00023), the Comunidad de Madrid ("NANOBIOMAGNET" S2009/MAT-1726 and "MICROSERES-CM" S2009/TIC-1476), and CSIC ("CRIMAFOT" PIF08-016-4).

## Authors’ Affiliations

## References

- Kelly KL, Coronado E, Zhao LL, Schatz GC: The optical properties of metal nanoparticles: the influence of size, shape and dielectric environment.
*J Phys Chem B*2003, 107: 668. 10.1021/jp026731yView ArticleGoogle Scholar - Maier SA, Atwater HA: Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structure.
*J Appl Phys*2005, 98: 011101. 10.1063/1.1951057View ArticleGoogle Scholar - Miller MM, Lazarides AA: Sensitivity of metal nanoparticle surface plasmon resonance to the dielectric environment.
*J Phys Chem B*2005, 109: 21556. 10.1021/jp054227yView ArticleGoogle Scholar - Haes AJ, Zou S, Schatz GC, Van Duyne RP: Nanoscale optical biosensor: short range distance dependence of the localized surface plasmon resonance of noble metal nanoparticles.
*J Phys Chem B*2004, 108: 6961. 10.1021/jp036261nView ArticleGoogle Scholar - Lee KS, El-Sayed MA: Gold and silver nanoparticles in sensing and imaging: sensitivity of plasmon response to size, shape, and metal composition.
*J Phys Chem B*2006, 110: 19220. 10.1021/jp062536yView ArticleGoogle Scholar - Liz-Marzan L: Tailoring surface plasmons through the morphology and assembly of metal nanoparticles.
*Langmuir*2006, 22: 32. 10.1021/la0513353View ArticleGoogle Scholar - Hui PM, Stroud D: Theory of Faraday rotation by dilute suspensions of small particles.
*Appl Phys Lett*1987, 50: 950. 10.1063/1.97996View ArticleGoogle Scholar - Abe M, SuWa T: Surface plasma resonance and magneto-optical enhancement in composites containing multicore-shell structured nanoparticles.
*Phys Rev B*2004, 70: 235103.View ArticleGoogle Scholar - Smith DA, Stokes K: Discrete dipole approximation for magneto-optical scattering calculations.
*Opt Exp*2006, 14: 5746. 10.1364/OE.14.005746View ArticleGoogle Scholar - Melle S, Menéndez JL, Armelles G, Navas D, Vázquez M, Nielsch K, Wehrspohn RB, Gösele U: Magneto-optical properties of nickel nanowire arrays.
*Appl Phys Lett*2003, 83: 4547. 10.1063/1.1630840View ArticleGoogle Scholar - González-Díaz JB, García-Martín A, Armelles G, Navas D, Vázquez M, Nielsch K, Wehrspohn RB, Gösele U: Enhanced magneto-optics and size effects in ferromagnetic nanowire arrays.
*Adv Mat*2007, 19: 2643. 10.1002/adma.200602938View ArticleGoogle Scholar - Hermann C, Kosobukin VA, Lampel G, Peretti J, Safarov VI, Bertrand P: Surface-enhanced magneto-optics in metallic multilayer films.
*Phys Rev B*2001, 64: 235422.View ArticleGoogle Scholar - Richard N, Dereux A, David T, Bourillot E, Goudonnet JP, Scheurer F, Beaurepaire E, Garreau G: Magneto-optical effects in multilayers illuminated by total internal reflection.
*Phys Rev B*1999, 59: 5936. 10.1103/PhysRevB.59.5936View ArticleGoogle Scholar - Safarov VI, Kosobukin VA, Hermann C, Lampel G, Peretti J, Marliere C: Magneto-optical effects enhanced by surface plasmons in metallic multilayer films.
*Phys Rev Lett*1994, 73: 3584. 10.1103/PhysRevLett.73.3584View ArticleGoogle Scholar - García-Martín A, Armelles G, Pereira S: Light transport in photonic crystals composed of magneto-optically active materials.
*Phys Rev B*2005, 71: 205116.View ArticleGoogle Scholar - Weaver JH, Krafka C, Lynch DW, Koch EE:
*Optical properties of metals*.*Volume 18–1*. Karlsruhe: Fachinformationszentrum; 1981.Google Scholar - Visnovsky S, Parizek V, Nyvlt M, Kielar P, Prosser V, Krishman R: Magneto-optical Kerr spectra of nickel.
*J Magn Magn Mater*1993, 127: 135. 10.1016/0304-8853(93)90206-HView ArticleGoogle Scholar - Ahn JS, Kim KH, Noh TW, Riu DH, Boo KH, Kim HE: Effective-medium theories for spheroidal particles randomly oriented on a plane: application to the optical properties of SiC whisker-Al
_{ 2 }O_{ 3 }composite.*Phys Rev B*1995, 52: 15244. 10.1103/PhysRevB.52.15244View ArticleGoogle Scholar - Sepúlveda B, Calle A, Lechuga LM, Armelles G: Highly sensitive detection of biomolecules with the magneto-optic surface-plasmon-resonance sensor.
*Opt Lett*2006, 31: 1085. 10.1364/OL.31.001085View ArticleGoogle Scholar - Choi J, Luo Y, Wehrspohn RB, Hillebrand R, Schilling J, Gösele U: Perfect two-dimensional porous alumina photonic crystals with duplex oxide layers.
*J Appl Phys*2003, 94: 4757. 10.1063/1.1609033View ArticleGoogle Scholar

## Copyright

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.