110
C. de Julián Fernández and F. Pineider
6–8] that solves Maxwell’s equations of propagation of an electromagnetic field in a
metallic sphere. Plasmon resonances can correspond to single-mode or multi-mode
electronic excitations that modify the scattering and the attenuation of the light [1,
6–8]. In the case of nanoparticles with sizes below 30 nm-case that will be mainly
discussed here—the wavelength of the exciting light (for Vis or nIR light, between
275 and 1000 nm) is larger than the particle size. Considering other conditions
such as the absence of interparticle electrical interactions and that the medium is
a pure, non-lossy (i.e. non-absorbing) dielectric, the electrodynamic behavior of a
particle can be described as that of a dipole in which the phase of the incoming
electromagnetic field is constant over the particle volume [1, 3, 8]. The absorption
spectrum is determined by the attenuation phenomenon (scattering is negligible, thus
extinction ≈ absorption) at which corresponds an absorption cross section σ ext of:
σ ext =
24π
2 R
3
ε
3/2
m
λ
ε 2
(ε 1 + 2ε m )
2
+ ε
2
2
(5.1)
Absorption depends on the nanoparticle radius, R, on the light wavelength, λ, on
the dielectric constant of the medium, ε m , and on the real and the complex dielectric
constant of the metal of the nanoparticle, ε 1 + iε 2 , The plasmonic resonance occurs
at the wavelength λ p at which when the denominator of the second part of 5.1 is zero
or minimum, denominated Mie resonant conditions:
ε 1
λ p
+ 2ε m
2 + ε
2
2
λ p
= 0
( 5 . 2 )
The calculated σ ext using 5.1 of selected plasmonic and magnetic nanoparticles
with a R = 5 nm dispersed in silica medium (ε m = 2.16) are represented in Fig. 5.2c,
d.
Figure 5.2a and b represent respectively the wavelength dependence of the dielectric constants of the main plasmonic materials, Au and Ag, as well as the Ni of some
magnetic metals and alloys: Ni, Co, Fe, Fe 80 Ni 20 (Permalloy) and FePt (in L 10 structure). Optical data were obtained from [16–18]. As can be seen in Fig. 5.2c, both
Au and Ag exhibit a very strong increase of absorption at the plasmonic resonance,
followed by a decrease of the absorption in the IR range. In comparison, the SPR
peak of the Ni is quite weak (observe that Fig. 5.2c is in powers of ten scale), while
absorption is almost constant toward the IR spectral region. Figure 5.2d shows that
Fe and FePt exhibit broader SPR peaks, while the SPR of Co and Fe 80 Ni 20 should be
at lower wavelength. The differences in strength and energy for the excitation of the
SPR between the plasmonic and magnetic materials can be correlated to their electronic structures. In first instance, considering the dielectric functions of the metals in
terms of the Drude-Sommerfeld model of free electrons [1, 9, 20], plasmon resonance
of magnetic metals should be strongly damped and blue shifted with respect to the
plasmonic metals. This is due to the larger density of electrons at the Fermi level [20]
that shift the bulk plasmon resonance to high energies and to higher relaxation times
[9, 10] of the magnetic metals. A more realistic approach to describe the dielectric
C. de Julián Fernández and F. Pineider
6–8] that solves Maxwell’s equations of propagation of an electromagnetic field in a
metallic sphere. Plasmon resonances can correspond to single-mode or multi-mode
electronic excitations that modify the scattering and the attenuation of the light [1,
6–8]. In the case of nanoparticles with sizes below 30 nm-case that will be mainly
discussed here—the wavelength of the exciting light (for Vis or nIR light, between
275 and 1000 nm) is larger than the particle size. Considering other conditions
such as the absence of interparticle electrical interactions and that the medium is
a pure, non-lossy (i.e. non-absorbing) dielectric, the electrodynamic behavior of a
particle can be described as that of a dipole in which the phase of the incoming
electromagnetic field is constant over the particle volume [1, 3, 8]. The absorption
spectrum is determined by the attenuation phenomenon (scattering is negligible, thus
extinction ≈ absorption) at which corresponds an absorption cross section σ ext of:
σ ext =
24π
2 R
3
ε
3/2
m
λ
ε 2
(ε 1 + 2ε m )
2
+ ε
2
2
(5.1)
Absorption depends on the nanoparticle radius, R, on the light wavelength, λ, on
the dielectric constant of the medium, ε m , and on the real and the complex dielectric
constant of the metal of the nanoparticle, ε 1 + iε 2 , The plasmonic resonance occurs
at the wavelength λ p at which when the denominator of the second part of 5.1 is zero
or minimum, denominated Mie resonant conditions:
ε 1
λ p
+ 2ε m
2 + ε
2
2
λ p
= 0
( 5 . 2 )
The calculated σ ext using 5.1 of selected plasmonic and magnetic nanoparticles
with a R = 5 nm dispersed in silica medium (ε m = 2.16) are represented in Fig. 5.2c,
d.
Figure 5.2a and b represent respectively the wavelength dependence of the dielectric constants of the main plasmonic materials, Au and Ag, as well as the Ni of some
magnetic metals and alloys: Ni, Co, Fe, Fe 80 Ni 20 (Permalloy) and FePt (in L 10 structure). Optical data were obtained from [16–18]. As can be seen in Fig. 5.2c, both
Au and Ag exhibit a very strong increase of absorption at the plasmonic resonance,
followed by a decrease of the absorption in the IR range. In comparison, the SPR
peak of the Ni is quite weak (observe that Fig. 5.2c is in powers of ten scale), while
absorption is almost constant toward the IR spectral region. Figure 5.2d shows that
Fe and FePt exhibit broader SPR peaks, while the SPR of Co and Fe 80 Ni 20 should be
at lower wavelength. The differences in strength and energy for the excitation of the
SPR between the plasmonic and magnetic materials can be correlated to their electronic structures. In first instance, considering the dielectric functions of the metals in
terms of the Drude-Sommerfeld model of free electrons [1, 9, 20], plasmon resonance
of magnetic metals should be strongly damped and blue shifted with respect to the
plasmonic metals. This is due to the larger density of electrons at the Fermi level [20]
that shift the bulk plasmon resonance to high energies and to higher relaxation times
[9, 10] of the magnetic metals. A more realistic approach to describe the dielectric