Article
pubs.acs.org/journal/apchd5
Far- and Near-Field Broad-Band Magneto-Optical Functionalities
Using Magnetoplasmonic Nanorods
Gaspar Armelles,*,† Alfonso Cebollada,† Fernando García,† Antonio García-Martín,*,†
and Nuno de Sousa‡,§
†
IMM-Instituto de Microelectrónica de Madrid (CNM-CSIC), Isaac Newton 8, PTM, Tres Cantos, E-28760 Madrid, Spain
Departamento de Física de la Materia Condensada, Universidad Autónoma de Madrid, 28049 Madrid, Spain
§
Donostia International Physics Center (DIPC), Paseo Manuel Lardizabal 4, 20018 Donostia-San Sebastian, Spain
‡
ABSTRACT: We have performed a systematic study of magnetoplasmonic
Au/Co/Au nanorods with different long/short axes ratio arranged in a
disordered fashion but with the same spatial orientation of their axes. We
show that the magneto-optical response can be tuned from the visible to the
near-infrared range by changing the long/short axes ratio. Moreover, the
analysis of the magnetic field induced polarization conversion indicates a
different behavior for the far field and for the near field. In particular, the farfield polarization conversion of the nanorod does not depend on the incident
polarization, whereas the near field does. This anticipates direct consequences
for near-field interactions, since the interacting elements at different spatial
positions could give rise to different magneto-optical responses.
KEYWORDS: magnetoplasmonics, polarization conversion, active nanoantennas
P
polarized along the two principal axes of the rod, giving rise to
resonances whose spectral position can be tailored on demand
by simply acting over the shape and dimensions of the
nanorod.12,13 Adding MO activity to such building blocks may
pave the way to a new kind of active metasurfaces, with
enhanced optical functionalities, such as active polarizers or
image devices such as controlled holographic plates or MO
spatial light modulators.14,15 In similar structures such as
nanodisks, the MO effect can be viewed as the magnetic field
induced rotation of the electric dipole; that is, an electric dipole
active control is produced by an external magnetic field.16,17
In this work we present a simple magnetoplasmonic element
that can be used as the essential building block for the
development of complex planar optical systems with externally
modulated polarization conversion capabilities. This element is
a Au/Co/Au nanorod, whose properties will be analyzed by
performing a systematic study of the optical and magnetooptical response for different long/short axes ratios. The
analysis will be carried out in both the far and near field. The
near-field case is of paramount importance here since
interactions are essential to develop the collective response of
the nanorod antenna array.
The analyzed nanorods will be around 35 nm thick (H ≈ 35
nm) and 130−150 nm wide (W ≈ 130−150 nm), and the
length will go from a disk-like shape to 310 nm to display an
elongated rod shape (L ≈ 130−310 nm). See Methods for a
lasmonic antenna-based optical planar devices are among
the most versatile systems in nanophotonics. These
devices are formed by the adequate arrangement of individual
building blocks with tuned sizes and shapes tailored in the
nanoscale. The structures conformed this way provide a large
range of functionalities, allowing the design and fabrication of
novel elements such as holographic optical devices,1 metalenses,2,3 or polarization devices.4,5
As a general rule, the specific characteristics of such elements
are predefined by the selection of the working dimensions and
spatial configuration. In this aspect, the possibility to endow
them with an active tunable character is of obvious interest. For
this purpose, it becomes necessary that some factor that
determines the final global optical properties of the system may
be switched or tuned in an external way. In this sense, magnetooptically (MO) active elements are excellent candidate
components, as they precisely modify the optical response of
a system under the action of an external magnetic field.6 Even
more, it has recently been put forward that the combined
plasmonic and magneto-optical action in novel magnetoplasmonic systems of a large variety of configurations actually
allows enhancing the global MO response by the antenna effect
of the plasmonic part.7−11 If one considers ferromagnetic
metals as the MO active element, the dimensions of the
plasmonic structure remain virtually unaltered, allowing the
development of active planar optical devices. Regarding this
type of devices, one of the favored plasmonic building blocks
within the planar optical structure is a metallic nanorod. The
reason lies in that they respond differently to light that is
© 2016 American Chemical Society
Received: September 8, 2016
Published: November 10, 2016
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detailed description of the fabrication. The thicknesses of the
different layers is (from top-to-bottom) 20 nm Au/5 nm Co/8
nm Au/2 nm Ti. Let us begin with the more common case of
the far-field optical and magneto-optical responses. This will
serve to characterize the system and to verify the numerical
techniques that will be used to perform the near-field analysis.
θp + iϵp =
rpp
,
θs + iϵs =
rsp
rss
(1)
where θp,s and ϵp,s are the Kerr rotation and ellipticity when the
incident light is p- or s-polarized, respectively.
In Figure 2a, d, and g we show the spectral dependence of
the modulus of the complex Kerr rotation for p- and s-polarized
■
RESULTS AND DISCUSSION
In Figure 1 we present the transmission spectra at normal
incidence for polarized light along the short axis (black curve)
Figure 2. (a, d, g) Spectral dependence of the modulus of the complex
Kerr rotation for light impinging at normal incidence with respect to
the sample plane for polarized light along the short axis, s-polarized
(black curve) and long axis, p-polarized (red curve) and for the three
structures shown in Figure 1. (b, e, and h) Corresponding reflectivity
* ) and s (Rss = rssrss*) polarization. (c, f, and i)
for p (Rpp = rpprpp
Corresponding polarization conversion values.
Figure 1. Optical transmission spectra at normal incidence for
polarized light along the short axis (black curve) and long axis (red
curve) for three structures: (a) a nanodisk and two nanorods (b) 290
and (c) 305 nm long, accompanied by the corresponding AFM images.
and long axis (red curve) of the nanorods for three structures, a
nanodisk and two nanorods 290 and 305 nm long. As it can be
observed, each spectrum presents one well-defined minimum.
In the spectra for light polarized along the short axis the
minima are located at basically the same wavelength, whereas
for those where the light is polarized along the long axis the
minimum appears red-shifted as the length of the nanorod
increases. These features relate themselves immediately to
localized surface plasmon resonances (LSPRs), since the
spectral position of LSPRs depends on the size of the particle
along the polarization direction, red-shifting as the size
increases. In our case the size of the short axis is the same
for all cases, and hence the minimum stays at virtually the same
position; however, when exploring the polarization along the
long axis, the resonance position red-shifts as the length
increases. This basically means that we are able to generate
nanorod antenna arrays with optical anisotropies whose
magnitude can be finely tuned by varying the rods L/W aspect
ratio.
By virtue of the ferromagnetic component of the nanorod,
the layers also show MO activity, which allows the modification
of the optical properties (dielectric tensor) of the layer in the
presence of an external magnetic field. In particular, if the
magnetic field is applied perpendicular to the sample plane
(polar configuration), the resulting effect on the optical
response appears as a change in the polarization state of the
reflected light (polar Kerr effect). This change in the
polarization state of the reflected light can be related to the
r rsp
Fresnel coefficients of the reflectivity matrix rpp
as
ps rss
(
rps
light impinging at normal incidence with respect to the sample
plane (also called magneto-optical activity, MOA) for a
magnetic field of 1.2 T (high enough to reach a saturation
state) for the three structures shown in Figure 1. It would be
possible to reduce the field needed to magnetically saturate the
structure using a more complex fabrication scheme that
involves substituting the actual individual Au and Co layers
by Au/Co multilayers with an equivalent Co vs Au ratio but
with thinner (1.1 nm thick) Co layers. This strategy has
previously been employed to obtain layers with perpendicular
magnetic anisotropy, therefore allowing magnetic saturation
along the surface normal with relatively small magnetic
fields.18,19
In optically isotropic systems the two polarizations are
degenerated at normal incidence, and thus the MOA should be
independent of polarization (as for the disk-like shape). Since
our system presents optical anisotropy, this will no longer be
the case.20−22 For the sake of simplicity, we establish that the
wave is p-polarized when the polarization is along the long axis
of the nanorods (red) and s-polarized when the polarization is
along the short axis (black). As the rod length increases, two
different effects can be observed. The first is that the MOA
evolves from a narrow peak for the disks case (Figure 2a), with
no difference between p and s as mentioned before, to a broad
structured band for the longest rods (Figure 2g). The second is
that the difference between p- and s-MOAs is increased as the
rod length increases (in the same direction as the optical
anisotropy does, as seen in Figure 1). The most noticeable
difference between MOAp and MOAs occurs in the low-energy
region, where not only is the broadening different but the shape
)
follows:
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of the spectra reflects two peaks rather than one (more
noticeable for s-polarization). This difference between the two
MO activities has an optical origin related to the in-plane
anisotropy of the nanorod, which gives rise to a difference in
the complex Fresnel elements for p (rpp) and s (rss) polarized
light. In Figure 2b, e, and h we present the reflectivity for p (Rpp
= rpprpp
* ) and s (Rss = rssrss*) polarization for increasing rod
length. These spectra follow the same trend as the transmission
shown in Figure 1: the presence of a peak that changes position
and intensity for the p-polarized wave (i.e., along the long axis).
In this difference in the reflectivity coefficients lies the
anisotropy of the MO activity. This is clearly confirmed in
Figure 2c, f, and i, where we present the corresponding spectral
dependence of the absolute values of the polarization
conversion coefficients rps and rsp obtained through eq 1
using the data from the spectra of the first and second columns
of Figure 2. Within experimental error, and for all rod lengths,
both curves, rps and rsp, are identical, pointing to a pure optical
origin of the anisotropy of the MO activity.
Remarkably, here comes the first important result regarding
the polarization conversion coefficients themselves, rps and rsp,
which is that the polarization conversion efficiency, p-to-s (rps)
or s-to-p (rsp), does not depend on the polarization state of the
impinging light.
Additionally, as the length of the rods increases, the spectral
dependence of these magnitudes evolves from a single, welldefined peak for disks (s- and p-resonances appear at the same
spectral position) to a broad peak due to the big but not total
overlap of the two resonances, to finally reflect a double-peak
structure for the longest rods where the two resonances are
clearly separated. These two peaks reveal that the polarization
conversion coefficient will show enhancements, or resonant
behavior, whenever any of the resonant states, either the initial
s (p) or the final state p (s), involved in the polarization
conversion process rsp (rps) are excited, widening therefore the
bandwidth at which plasmon-enhanced MO activity is achieved.
To verify these statements, we have performed theoretical
calculations of the electromagnetic response of isolated
nanorods (see inset in Figure 3) upon illumination from a
linearly polarized plane wave by using the discrete dipole
approximation.23
The nanorods are basically a half-cylinder of ellipsoidal crosssection (whose length will be varied to mimic the fabricated
rods) capped with two quarters of an ellipsoid (one at each
end). The radius of the cylinder, as well as the capping quarterellipsoid, is 65 nm (leading to a short axis of the nanorod of
130 nm), whereas the height is 35 nm. The length of the
cylinder will vary from 0 (disk-like, 130 nm in diameter, no
anisotropy) to 180 nm (giving rise to a long axis of 310 nm,
similar to the experimental case). In Figure 3a−c we can see the
normalized far-field intensity (R|Eff|, where R is the far-field
point location) in the backward direction for the component
along the polarization direction (R|Ess|, black lines; R|Epp|, red
lines) for different lengths of the long axes: (a) 130 nm, disklike geometry, (b) 220 nm, and (c) 310 nm. This quantity is
equivalent to the experimental Fresnel coefficients |rss| and |rpp|.
As we can see, the behavior is very similar to the experimental
one depicted in Figure 2. For polarization along the short axis
we obtain a fixed position for the resonance location, whereas
for the long axis the spectral position is a function of the length
of the axis. In Figure 3d−f we present the polarization
conversion, i.e., the normalized far-field intensity in the
backward direction for the component along the converted
Figure 3. Far-field electromagnetic intensity in the backscattered
direction, normalized by the distance of the observation point. The
left-hand panel (a−c) displays the normalized fields for the same
polarization as the incident one, p-polarized in red lines while spolarized in black open dots, for bars with 130 nm width and different
lengths of the long axis, namely, 130 nm (a), 220 nm (b), and 310 nm
(c). The red shift experienced by the resonance for p-polarization as
the length of the long axis increases is clearly captured. (d−f)
Polarization conversion for p-polarized incidence in red lines and for spolarized in black open dots. As seen, the spectral shape is the same
irrespective of the incidence polarization. The red shift experienced by
the resonance along the long axis can be seen first as a broadening of
the peak (e) and then as a second, low-frequency peak. The overlap
between the two resonances gives rise to a broad-band almost uniform
polarization conversion region.
direction (s-to-p R|Esp|, black lines; p-to-s R|Eps|, red lines) for
the same length of the long axes. Again the agreement with the
Fresnel coefficients rsp and rps is remarkable. The curves for the
two incident polarizations appear overlaid on one another
since, and as mentioned before, the polarization conversion in
the far field does not depend on the initial polarization state.
The modification of the spectral position for the long axis
resonance is responsible for the broadening and final splitting
of the initial single peak for the isotropic structure.
This can be seen as consistent with a description based on
the behavior of a sole dipole in the far field. This has already
been successfully employed by Maccaferri and co-workers,22
where they considered the MO response of a collection of
ellipsoidal ferromagnetic nanoparticles, each described as a
single dipole. They showed that the MO response presented a
marked dependence on the polarization of the incident beam,
with features similar to those presented in Figure 2g. However,
the properties of the polarization conversion itself were not
explicitly discussed. Indeed, from the static polarizability α0 (the
actual polarizability α0 including radiative corrections is given
by α = (α0−1 − Iik3/(6π))−1) of a prolate ellipsoid,12,23 it is
possible to already infer that the polarization conversion does
not depend on the incident polarization. For that case, the
static polarization of one of these particles is described by
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⎞
⎛
(ϵ − 1)[1 + Ly(ϵ − 1)] + Ly ϵ2MO
ϵMO
⎟
⎜
0
⎟
⎜ [1 + Lx(ϵ − 1)][1 + Ly(ϵ − 1)] + (Lx ϵMO)(Ly ϵMO) [1 + Lx(ϵ − 1)][1 + Ly(ϵ − 1)] + (Lx ϵMO)(Ly ϵMO)
⎟
⎜
⎟
V⎜
(ϵ − 1)[1 + Lx(ϵ − 1)] + Lx ϵ2MO
−ϵMO
α0 = ⎜
⎟
0
3 ⎜ [1 + Lx(ϵ − 1)][1 + Ly(ϵ − 1)] + (Lx ϵMO)(Ly ϵMO) [1 + Lx(ϵ − 1)][1 + Ly(ϵ − 1)] + (Lx ϵMO)(Ly ϵMO)
⎟
⎟
⎜
(ϵ − 1)
⎟
⎜
0
0
⎟
⎜
[1 + Lz(ϵ − 1)] ⎠
⎝
where Lx, Ly, and Lz are the geometrical factors of the particle in
each direction, V is the volume of the nanoparticle, ϵ is the
diagonal element of the dielectric tensor, and ϵMO is the offdiagonal (magneto-optically induced) element. Notice that we
have chosen the s-polarization to be aligned with the xdirection and the p-polarization to be aligned with the ypolarization, so we can now refer to the orientation axes of the
nanorod. It can be readily seen that the absolute value of the
polarization conversion is independent of the incidence since
αyx = −αxy, as evidenced by the experimental and theoretical
findings.
Let us now verify that the far field can be seen indeed as an
effective single dipole. Within our approach, the far-field
intensities are obtained from the contributions of all the dipoles
involved in the discretization, using Eexact
= (k2/ε0)∑pGff(rff, rp)
ff
Pp, where the Green function at the far field is given by
Gff (rff , rp) =
(2)
polarized, ΔPyx, and in the x-direction when the incoming wave
is y-polarized, ΔPxy), normalized to its highest value.
As ΔPyx = −ΔPxy we show only one of them (red line). It can
be seen that this dipole has two defined peaks at the same
spectral locations as the polarization conversion curve shown in
Figure 3 for the same geometry. In blue we show the
corresponding far field generated by that averaged dipole
located at r0, also normalized to its highest value. This far field
is basically the polarization conversion factor presented above.
Notice that the spectral shape is identical to that of the exact far
field generated by the sum of the contribution of all dipoles
Eexact
=
ff
k2
ϵ0
∑p Gff (rff , rp).
However, the different spatial distributions of the dipole
intensities for each polarization are already suggesting that the
effective dipole view cannot be valid for the entire range of
distances. We present here the third important result, showing
e ikR p
[ − u R p ⊗ u R p], R p = rff − rp,
4πR p
R p = |R p|
where ff indicates the observation point (at the far field) and p
the location of the given dipole. In order to get insight on the
origin of the far-field features, it would be useful to visualize the
intensities of the magneto-optically induced contribution for
the individual dipoles forming the nanorod.
In Figure 4b,c we present the real part of the magnetooptically induced dipoles for all point-like elements that
compose the nanorod, for the most elongated one (see sketch
in (a)) showing the internal layers of the rods for each
polarization incidence.
We show the cross-induced dipoles (i.e., the half-difference
upon magnetic inversion +M to −M, where M is the
magnetization at saturation). In Figure 4b the incident wave
is polarized in the x-direction and thus Δpyx = 0.5(py(+M) −
py(−M)) is represented, while in Figure 4c the incident wave is
polarized in the y-direction and Δpxy = 0.5(px(+M) − px(−M))
is represented. Although not shown, it is important to mention
that Δpxx and Δpzx, when the incidence is in x, or Δpyy and
Δpzy, when the incidence is in y, are not vanishing quantities,
but do not contribute to the far field.
This could lead to the conclusion that the analogue to the
behavior of one single dipolar element might not be right, or at
least it might be overstretched. However, the geometrical
average of the induced dipole, i.e., ΔP = ∑(Δp), is zero except
for ΔPyx and ΔPxy. What is more, ΔPyx = −ΔPxy for the whole
spectral range. This is the second important result, since this
averaged dipole is ultimately responsible for the point-like
dipolar behavior observed in the far field.
To explore this idea, in Figure 5a we show the spectral
dependence of the modulus of the geometrical average of the
magneto-optically induced dipole for the most elongated bar
(oscillating in the y-direction when the incoming wave is x-
Figure 4. (a) Sketch of the geometry depicting the actual aspect ratio
employed in the calculation. (b, c) Spatial distribution of the real part
of each magneto-optically induced dipole involved in the calculation
(b) along the y-direction for x-polarized incidence (Δpyx) and (c)
along the x-direction for y-polarized incidence (Δpxy) for a wavelength
of 600 nm and for a 130 nm wide by 310 nm long nanorod.
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band region of magneto-optical activity. This magneto-optically
induced polarization conversion presents strong differences
depending on the observation point. The far-field signature is
found to be independent of the orientation of the incoming
field, and thus the polarization conversion is equivalent to
consider the geometrically averaged dipole. The near field,
however, is very sensitive to the details of the excitation of the
individual elements of the nanorod, and thus the spatial profile
of the near field presents a strong dependence on the incoming
polarization, thus allowing tailoring the near-field response by
an adequate design of the nanorods and their orientation with
respect to the incident polarization state.
■
METHODS
Fabrication. The fabrication of the actual nanorods is
carried out by a combination of hole mask colloidal
lithography24 and multiaxial evaporation in ultrahigh vacuum.
This process allows fabricating multicomponent structures of a
wide variety of shapes with nanometer accuracy, on top of
virtually any substrate and uniformly distributed in the range of
cm2 areas.25,26 More importantly, this lithographic process is
inexpensive when compared to other techniques especially
when large areas are required. In the particular process used in
this work a 200 nm poly(methyl methacrylate) (PMMA) resist
layer, deposited on a standard glass substrate and covered with
a sacrificial 30 nm thick Au film, is perforated with overetched
holes of selected diameters. By oscillating the substrate surface
in the direction of the incoming evaporated material, the
projection of the hole on the substrate surface produces a rod
whose length is controlled by the oscillation angle, α (Figure
6a). It is important to notice that there is an inevitable size
distribution in the nanorods due to the intrinsic dispersion in
the size of the nanospheres used to fabricate the templates. At
the same time, the separation between some nanorods might be
sufficiently small to induce interaction effects, but the average
Figure 5. (a) Spectral dependence of the averaged magneto-optically
induced dipole (red) and the corresponding absolute value of the far
field (blue), both normalized to the maximum value for a 130 nm wide
by 310 nm long nanorod. (b) Spatial distribution of the absolute value
of the y-component of the magneto-optically induced electromagnetic
field at a plane 65 nm above the nanorod (Ey component of the
induced near-field pattern) for an incident wave polarized along the
long axis (x-direction) with a wavelength of 600 nm. (c) The same but
depicting the x-component of the magneto-optically induced electromagnetic field (Ex component of the induced near-field pattern) when
the incident polarization is along the short axis (y-direction).
that the single dipole picture breaks down whenever one
abandons the far field and approaches the vicinity of the
nanoparticle. In this near-field range the details do matter. As
an example, in Figure 5b,c we present the spatial distributions
of the module of the magneto-optically induced y-component (|
Ey| in (b)) and x-component ((|Ex| in (b)) of the electric field
at an x−y plane 65 nm above the particle for an incident
wavelength of 600 nm. Although the far-field radiations of the
induced dipole for both incidence directions are indistinguishable (blue curve), the near field is completely different. This
different behavior will have direct consequences when the
nanoparticle interacts with its neighborhood, since, depending
on their relative position, the interacting elements would
experience different fields. Therefore, an adequately tailored
near-field pattern by means of an engineered particle would be
paramount to obtain unprecedented performances in devices
such as sensors, isolators, and modulators, to name a few.
■
CONCLUSIONS
In summary, we have explored the optical and magneto-optical
response of optically anisotropic magnetoplasmonic elements
with the shape of elongated nanorods. We have found that the
magneto-optically induced polarization conversion of such
anisotropic entities is independent of the incident wave
polarization, when observed in the far-field range. Thus, when
the resonances of the two main symmetry axes are brought
apart by increasing the length of one of the axes, the overlap
between them gives rise to a broad-band region of high
polarization conversion, which manifests itself as an also broad-
Figure 6. (a) Sketch of the deposition process through PMMA holes
to obtain rods by oscillating the substrate about the surface normal.
(b) Sketch of the obtained Au/Co/Au nanorods. (c) AFM image of a
representative rods’ structure. (d) Incidence angle dependence of the
obtained rods’ L/W aspect ratio, with the corresponding AFM detail
images for three specific cases.
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205419.
(18) Armelles, G.; Caballero, B.; Prieto, P.; García, F.; Cebollada, A.;
González, M. U.; García-Martín, A. Magnetic field modulation of
chirooptical effects inmagnetoplasmonic structures. Nanoscale 2014, 6,
3737.
(19) Armelles, G.; Cebollada, A.; Feng, H. Y.; García-Martín, A.;
Meneses-Rodríguez, D.; Zhao, J.; Giessen, H. Interaction effects
between magnetic and chiral building blocks: A new route for tunable
magneto-chiral plasmonic structures. ACS Photonics 2015, 2, 1272.
(20) Du, G.; Mori, T.; Saito, S.; Takahashi, M. Shape-enhanced
magneto-optical activity: Degree of freedom for active plasmonics.
Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 82, 161403.
(21) Du, G.-X.; Saito, S.; Takahashi, M. The effect of shape
anisotropy on the spectroscopic characterization of the magnetooptical activity of nanostructures. J. Appl. Phys. 2013, 113, 213104.
(22) Maccaferri, N.; Berger, A.; Bonetti, S.; Bonanni, V.; Kataja, M.;
Qin, Q. H.; Van Dijken, S.; Pirzadeh, Z.; Dmitriev, A.; Nogués, J.;
Åkerman, J.; Vavassori, P. Tuning the magneto-optical response of
inter-rod distance is large enough to consider those as rare
events. These two facts may give rise to small broadening
effects in the optical and magneto-optical resonance peaks.
After deposition, sonication for 2 h in an acetone bath
removes the PMMA and the sacrificial gold layer, leaving the
bare multicomponent rods on the substrate. As depicted in
Figure 6b the so-obtained rods are expected to present rounded
edges due to the circular shape of the holes in the template.
The width of the rods (W) is determined by the diameter of the
hole, being thus independent of the oscillation amplitude. The
rod length (L) is determined by the oscillation amplitude and
the geometrical parameters of the template (mainly PMMA
thickness). The height (H) is controlled by the deposition time,
and its homogeneity along the rod is optimized by
compensating the oscillation speed along the different steps
of the oscillation cycle. Typically hundreds of oscillation cycles
are performed in each deposition process to further ensure the
lateral homogeneity of the final structures. A representative
AFM image of rods obtained this way is shown in Figure 6c.
The typical individual layer thicknesses for a 20° incidence
angle are 21 nm Au/5 nm Co/8 nm Au/2 nm Ti. The obtained
length vs width aspect ratios for the different deposition angles
and the corresponding morphology for three specific cases are
also shown in Figure 6d.
Experimental Measurements. The transmission measurements were done using an M-2000 Woollam ellipsometer,
whereas the reflectivity and polar Kerr spectra were obtained
using a homemade polar Kerr spectrometer, where light from a
xenon lamp source is dispersed by a monochromator. The
resulting monochromatic light passes through a polarizer and a
photoelastic modulator before reaching the sample. The
reflected light is then analyzed by a polarizer, whose orientation
can be change to obtain Rpp, Rss, rps, rpp, rsp, and rss.
■
AUTHOR INFORMATION
Corresponding Authors
*E-mail (G. Armelles): [email protected].
́
́ [email protected].
*E-mail (A. Garcia-Marti
n):
ORCID
Antonio García-Martín: 0000-0002-3248-2708
Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS
Funding from the Spanish Ministry of Economy and
Competitiveness through grant AMES MAT2014-58860-P is
acknowledged. N.d.S. is thankful for the financial support from
Spanish Ministerio de Economiá y Competitividad (MINECO)
project FIS2015-69295-C3-3-P.
■
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