# Direction-sensitive magnetophotonic surface crystal

###### Abstract

Nanometer-thin rare-earth-transition metal (RE-TM) alloys with precisely
controlled compositions and out-of-plane magnetic anisotropy are currently in
the focus for ultrafast magnetophotonic applications. However, achieving
lateral nanoscale dimensions, crucial for potential device downscaling, while
maintaining designable optomagnetic functionality and out-of-plane magnetic
anisotropy is extremely challenging. Here we integrate nanosized Tb18Co82
ferrimagnetic alloys, having strong out-of-plane magnetic anisotropy, within a
gold plasmonic nanoantenna array to design micrometer-scale a magnetophotonic
crystal that exhibit abrupt and narrow magneto-optical spectral features that
are both magnetic field and light incidence direction controlled. The narrow
Fano-type resonance arises through the interference of the individual
nanoantenna’s surface plasmons and a Rayleigh anomaly of the whole nanoantenna
array, in both optical and magneto-optical spectra, which we demonstrate and
explain using Maxwell-theory simulations. This robust magnetophotonic crystal
opens the way for conceptually new high-resolution light incidence direction
sensors, as well as for building blocks for plasmon-assisted all-optical
magnetization switching in ferrimagnetic RE-TM alloys.

###### keywords:

magnetoplasmonics, rare-earth–transition-metal ferrimagnets, all-optical
switching, magnetophotonic crystal, Fano resonance

Richard M. Rowan-Robinson* Jérome Hurst Agne Ciuciulkaite Ioan-Augustin Chioar
Merlin Pohlit Mario Zapata Paolo Vavassori Alexandre Dmitriev* Peter M.
Oppeneer Vassilios Kapaklis*

R. M. Rowan-Robinson
Department of Material Science and Engineering, University of Sheffield,
Sheffield, United Kingdom
Email<EMAIL_ADDRESS>
J. Hurst
Univ. Grenoble Alpes, CNRS, CEA, Grenoble INP, IRIG-Spintec, F-38000 Grenoble,
France
R. M. Rowan-Robinson, J. Hurst, A. Ciuciulkaite, I-A. Chioar, M. Pohlit, Prof.
P. M. Oppeneer, Prof. V. Kapaklis
Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20
Uppsala, Sweden
Email<EMAIL_ADDRESS>
I-A. Chioar
Department of Applied Physics, Yale University, New Haven 06511, CT, USA
M. Zapata, Prof. P. Vavassori
CIC nanoGUNE BRTA, E-20018 Donostia-San Sebastian, Spain
M. Zapata, Prof. P. Vavassori
IKERBASQUE, Basque Foundation for Science, E-48013 Bilbao, Spain
Prof. A. Dmitriev
Department of Physics, University of Gothenburg, SE-412 96 Göteborg, Sweden
Email<EMAIL_ADDRESS>

##  1 Introduction

Nanoscale magnetophotonics merges magnetism with nanophotonics [1], combining
seamlessly magneto-optical (MO) effects with surface plasmons, thus being
capable of delivering ultra-high performance biological and chemical sensors
[2, 3], active tunability in nano-optics by external magnetic fields [1, 4, 5,
6, 7, 8, 9, 10, 11, 12], and setting a platform for ultrafast opto-magnetism
and spintronic [13] devices on the nanoscale. Pure ferromagnetic plasmonic
systems were earlier considered unfeasible for these purposes due to the high
ohmic losses associated with the transition-metal ferromagnets. However, to a
large extent, these can be overcome through nanopatterning [14, 15], materials
engineering and fabrication of hybrid noble metal-ferromagnetic nanostructures
[16, 17, 18, 19, 20]. The enhancement of various MO effects is typically
achieved in these systems through near-field light concentration at the
nanoscale, boosting light-magnetism interactions that relate to the MO Voigt
parameter of the ferromagnet [21, 22]. Importantly, by exploiting magnetic
anisotropy control, the magnetization can be stabilized in a desired direction
and MO effects can be recorded at zero external magnetic field. Linewidth
engineering [17, 23, 24] wherein high Q-factor resonances are achieved, can
furthermore be employed in ordered arrays of magnetoplasmonic nanoantennas
with surface lattice resonances.

The use of rare-earth–transition-metal alloys is of paramount interest for
future nanoscale magnetophotonic and magnetoplasmonic systems for several key
reasons. Firstly, they are known to exhibit very large MO effects [25, 26]
potentially permitting very high real-time active tunability of light
polarization. Secondly, they can exhibit strong perpendicular magnetic
anisotropy, yet with an amorphous texture [27, 28, 29, 30, 31]. For instance,
carefully engineered Co/Pt multilayered nanodots having large interfacial
spin-orbit coupling with perpendicular magnetic anisotropy, demonstrate
tenfold enhancements in MO activity and demonstrate the great potential of
out-of-plane magnetic anisotropy materials for magnetoplasmonics [32]. The
amorphous texture of RE-TM alloys greatly simplifies the otherwise stringent
requirements on material microstructure for obtaining these highly desired
magnetic properties. As such, they can be grown on noble metals like Au with
minimal residual stresses, and with highly smooth interfaces, thereby
maintaining much of their original magnetic properties even after patterning
[27]. Importantly, with perpendicular magnetic anisotropy the remanent
magnetization state of the magnetic nanostructures can be designed to be
parallel to the light propagation direction for normal light incidence,
greatly simplifying potential practical applications of magnetoplasmonic
crystals. This allows one to explore their MO functionality (such as, tunable
Faraday effect) directly, i.e., without the need of external magnetic fields
in order to stabilize the magnetization along the out-of-plane axis. Thirdly,
ferrimagnetic alloys such as Tb18Co82, have recently experienced extensive
interest due to the demonstration of enhanced spin-orbit torques [33, 34, 35]
and all-optical switching [35, 36, 37, 27], allowing for zero-field magnetic
switching, on picosecond timescales, with the use of pulsed lasers. Thus,
demonstrating the compatibility of these materials with nanoantennas is
essential for the development of nanoscale (i.e., sub-diffraction) all-optical
switching technologies [13].

Here we devise a magnetophotonic crystal composed of nanocone Au plasmonic
nanoantenna arrays incorporating an amorphous RE-TM ferrimagnetic alloy,
Tb18Co82, with perpendicular magnetic anisotropy [27]. We show that this
hybrid Au/Tb18Co82 system provides high-Q MO resonances, overcoming the losses
associated with ferrimagnetic alloys. By Maxwell-theory modelling we show that
this is achieved through the resonant collective excitation of surface lattice
modes that exhibit a particularly strong angular dispersion. This is a result
of the interference of a Rayleigh anomaly with the individual nanoantennas’
plasmons, giving rise to surface lattice resonance resonances with
characteristic Fano-type asymmetric lineshape in both the optical and MO
spectra. We demonstrate an exceptionally strong tunability of the spectral
position of such resonances by varying the angle of incidence (incident
direction) of the incoming light, exemplifying the potential of
magnetophotonic crystals for high-resolution mechanical tilt-angle sensors
and, more broadly, for actively-controlled optical systems [38, 39].

##  2 Results and Discussion

Nanocone antennas were previously shown to exhibit a very strong field
enhancement [40], with the electromagnetic field concentrated at the tip [40,
41]. We build large rectangular lattice arrays of Au/Tb18Co82 truncated
nanocone antennas (Fig. 1a) [27] with two selected base diameters (179 $\pm$ 5
nm and 227 $\pm$ 4 nm (see SEM insets in Fig. 1f and h respectively). The
light incidence angle ($\alpha_{\mathrm{i}}$) is varied with respect to the
lattice plane, directed along either one or the other of the array periodicity
(Fig. 1b). We first use finite-element Maxwell-theory simulations (COMSOL
Multiphysics, see Supporting Information) to pinpoint the emerging resonances’
linewidth narrowing and high incidence-angle sensitivity. The magnetophotonic
crytstal is built of Au(80 nm)/Tb18Co82(15 nm) truncated nanocones (base
diameter, $D_{\mathrm{B}}$ = 179 nm), arranged in a rectangular array with 340
nm $\times$ 425 nm periodicity (Fig. 1c). The light incidence direction angle
(using the optical convention) defines a scattering plane which is parallel to
one (340 nm) or the other (425 nm) of the array periodicity axes with
azimuthal angles $\varphi_{\mathrm{i}}$ = 0 or $\varphi_{\mathrm{i}}$ = 90∘,
respectively.

Figure 1:  Magnetophotonic crystals composed of arrays of truncated nanocone
hybrid antennas, with tunable optical transmission response. (a) Schematic of
a single Au-TbCo nanoantenna featuring PMA (left) and scanning electron
micrograph view of a magnetophotonic crystal (right). (b) Magnetophotonic
crystal illumination with resulting Faraday rotation ($\theta_{\mathrm{F}}$),
ellipticity ($\eta_{\mathrm{F}}$) of the transmitted light, and the Rayleigh
anomaly associated with the passing-off of the diffraction order. (c)
Magnetophotonic crystal illumination with two azimuthal orientations
($\varphi_{\mathrm{i}}$ = 0 and 90∘) with respect to the incident light
polarisation ($E_{\mathrm{i}}$) and scattering plane, with $p_{\mathrm{E}}$
denoting the orientation of the electric dipolar plasmon in the nanoantennas.
The reciprocal lattice vectors $[1,0]$ and $[0,1]$ are shown to illustrate the
90∘ rotation of the reciprocal lattice vectors with respect the real space
lattice. (d, e) Calculated transmission spectra for incidence angles
$\alpha_{\mathrm{i}}$ between 0 and 20 degrees, for the $\varphi_{\mathrm{i}}$
= 0 (d) and the $\varphi_{\mathrm{i}}$ = 90∘ (e) configurations, respectively.
(f, g) Measured transmission spectra for incidence $\alpha_{\mathrm{i}}$
angles 0 - 20 degrees for the magnetophotonic crystal built on
$D_{\mathrm{B}}$ = 179 nm nanoantennas for the $\varphi_{\mathrm{i}}$ = 0 (f,
inset – SEM of nanoantennas in this magnetophotonic crystal) and the
$\varphi_{\mathrm{i}}$ = 90∘ (g). (h, i) Same as (f, g) but for the
magnetophotonic crystal with $D_{\mathrm{B}}$ = 227 nm nanoantennas (inset in
(h) – nanoantennas SEM).

Surface lattice resonances are the result of the coupling between a broad
lossy resonance, in this case the localised plasmon resonances of individual
nanoantennas, and diffracted waves in the plane of the nanoantenna array (a
detailed description is provided in the supporting information). This
condition is generally observed close to a Rayleigh anomaly, where for a given
$\alpha_{\mathrm{i}}$ and lattice periodicity, a Rayleigh anomaly exists where
a diffracted wave is directed parallel to the grating [42]. This Rayleigh
anomaly represents the passing-off of a diffraction order through a laterally
excited beam. There can exist a large number of these diffraction orders,
which are labeled by two integers $n$ and $m$. The allowed waves are obtained
by imposing the condition that the component of the light wave-vector normal
to the lattice surface is real, through the expression

$k_{\perp}=\sqrt{k_{s}^{2}-\left(\bm{k_{\parallel}}+m\bm{G_{1}}+n\bm{G_{2}}\right)^{2}}\in\Re.$
(1)

In the above formula, $k_{\mathrm{s}}=2\pi n_{\mathrm{sub}}/\lambda$
corresponds to the light wave-vector in the substrate, where
$n_{\mathrm{sub}}$ is the refractive index of the fused silica substrate
($n_{\mathrm{sub}}$ = 1.45), $\lambda$ the light wavelength,
$\bm{k_{\parallel}}=k_{0}\left[\sin(\alpha_{i})\cos(\varphi_{i})~{}\bm{u_{x}}+\sin(\alpha_{i})\sin(\varphi_{i})~{}\bm{u_{y}}\right]$
corresponds to the wave-vector component of the incident radiation (in
air/vacuum) parallel to the lattice surface, $k_{0}=2\pi/\lambda$ is the light
wave-vector in air and $\bm{G_{1}}=(2\pi/a)~{}\bm{u_{x}}$,
$\bm{G_{2}}=(2\pi/b)~{}\bm{u_{y}}$ are the reciprocal lattice vectors, with
$~{}\bm{u_{x}}$, $~{}\bm{u_{y}}$ being the reciprocal lattice unit vectors and
$a$ = 340 nm, $b$ = 425 nm, being the lattice parameters. The number of
diffracted waves depends on the lattice parameters, the angle of incidence,
the refractive index of the substrate and the light wavelength. For
wavelengths greater than 600 nm, Equation (1) indicates that only the
diffracted waves ($n=0~{};~{}m=-1$) for $\varphi_{i}=0$ and ($n=-1~{};~{}m=0$)
for $\varphi_{i}=90^{\circ}$ can be obtained by varying the incidence angle
between 0 - 20∘ (see Supporting Information).

We use reciprocal vector notation, such that the Rayleigh anomaly occurs at
wavelengths $\lambda_{\mathrm{R}}^{[n,m]}$ with wave-vector orientated along
the reciprocal lattice vectors $[n,m]$. Fig. 1c demonstrates how the
reciprocal lattice vectors are orientated with respect to the real-space
lattice. The analytical expressions for the two allowed substrate waves
($[0,-1],[-1,0]$) from Equation (1), are given by

$\lambda_{\mathrm{R}}^{[0,-1]}=a\left[n_{\mathrm{sub}}+n_{\mathrm{air}}\sin\left(\alpha_{\mathrm{i}}\right)\right]~{}~{}\textrm{for}~{}\varphi_{\mathrm{i}}=0,$
(2)
$\lambda_{\mathrm{R}}^{[-1,0]}=b\left[n_{\mathrm{sub}}+n_{\mathrm{air}}\sin\left(\alpha_{\mathrm{i}}\right)\right]~{}~{}\textrm{for}~{}\varphi_{\mathrm{i}}=90^{\circ},$
(3)

where $n_{\mathrm{air}}=1$ is the refractive index of air.

We first calculate the spectral transmission through the array for
$p$-polarised light (i.e., incident electric field is in the scattering plane)
(Fig. 1d, e). Individual nanoantenna dipole-type plasmons are excited in the
respective scattering planes at 690 nm at normal incidence
($\alpha_{\mathrm{i}}$ = 0). For the $\varphi_{\mathrm{i}}$ = 0 configuration
(scattering plane along 340 nm array periodicity, Fig. 1d) the surface lattice
resonances from Eq. (2) are at $\lambda_{\mathrm{R}}^{[0,-1]}$ = 493 nm, 552
nm, 581 nm and 609 nm for $\alpha_{\mathrm{i}}$ = 0, 10, 15, and 20 degrees,
respectively, and therefore not spectrally overlapping with the nanoantennas’
individual plasmons. For $\varphi_{\mathrm{i}}$ = 90∘ (scattering plane along
425 nm array periodicity, Fig. 1e), Eq. (3) gives
$\lambda_{\mathrm{R}}^{[-1,0]}$ = 616 nm, 690 nm, 726 nm and 762 nm, strongly
overlapping with the nanoantennas’ plasmon, resulting in a very substantial
tuning of the spectrally abrupt transmission spectrum by changing
$\alpha_{\mathrm{i}}$ (see Fig. 1e).

In the Fano-type resonance description [43, 44], the nanoantennas plasmon
represents a continuum of states, whereas the Rayleigh anomaly is a narrow
line-width diffracted wave, which, upon interfering with the continuum,
results in the characteristic asymmetric lineshape of the surface lattice
resonances. A similar behaviour has been seen previously with magnetoplasmonic
Ni nanoantennas arrays [24, 23], where the overlap between
$\lambda_{\mathrm{R}}^{[n,m]}$ and the nanoantenna plasmon was tuned by
varying the lattice periodicity of the magnetoplasmonic crystal. However, a
much simpler alternative method of tuning the surface lattice resonance
spectral position can be obtained using the angular dispersion of
$\lambda_{\mathrm{R}}^{[n,m]}$. This tuning of the spectral position of the
surface lattice resonance opens up applications as mechanical tilt-angle
transducers/sensors, and in contrast with previously observed
transmission/reflectance angular dependence in pure plasmonic arrays [45],
this magnetoplasmonic crystal allows one to fully explore angular MO
tunability.

The dipolar radiation field is strongest transverse to the dipolar plasmon
oscillation given by $p_{\mathrm{E}}$ (Fig. 1c). In our simulations we used
$p$-polarised light and hence the electric dipole excitation within individual
nanocone antennas is orientated within the scattering plane and parallel to
the diffraction anomaly. This dipole cannot radiate along the oscillation
direction, hence there must exist an additional mechanism for light to be
scattered along the other periodicity direction for the excitation of the
Rayleigh anomaly. We show this to be the result of an out-of-plane component
to the electric dipole due to the illumination at oblique incidence (see
Supporting Information), which would radiate in all directions within the
plane of the lattice [46] providing the excitation for all
$\lambda_{\mathrm{R}}^{[n,m]}$, e.g. [-1, 0], [0, -1], [-1, -1] waves for
$p$-polarised light.

The measured transmission spectra are shown in Fig. 1f-i. In agreement with
the electromagnetic simulations above, for the $\varphi_{i}$ = 0 configuration
(Fig. 1f, h) the transmission spectra show very little dependence on
$\alpha_{\mathrm{i}}$. The nanoantenna plasmon is red-shifted and spectrally
broadened as compared to the simulations though, which is likely a result of
the thin Al2O3 isolation layer (see Methods) and oxidation of the exposed
Tb18Co82 side-walls on the fabricated nanocones and also the size and shape
distribution of the nanoantenna ensemble. There is a spectral feature between
500 - 600 nm (Fig. 1f, h) that migrates to longer wavelengths as
$\alpha_{\mathrm{i}}$ increases that is most likely due to
$\lambda_{\mathrm{R}}^{[0,-1]}$, since it occurs at the same spectral
positions for both the $D_{\mathrm{B}}$ = 179 nm (Fig. 1f) and 227 nm (Fig.
1h) nanoantennas, suggesting its origin relates to the lattice and not the
individual nanoantenna plasmon resonance.

When rotated into the $\varphi_{\mathrm{i}}$ = 90∘ configuration (Fig. 1g and
i), the strong variations in the transmission spectra are observed, in
excellent agreement with the simulations, in both spectral position and
lineshape, albeit with reduced amplitude. For both $D_{\mathrm{B}}$ = 179 nm
(Fig. 1g) and 227 nm (Fig. 1i) nanoantennas, the $\alpha_{\mathrm{i}}$ = 0
incidence shows a small blue shift of the plasmon for the $\varphi_{i}$ = 90∘
configuration relative to the $\varphi_{i}$ = 0 configuration. As shown in the
inset scanning electron microscopy images, the nanocones are not perfectly
circular and this discrepancy is likely a result of this asymmetry. Markedly,
the broad spectral distribution with the $D_{\mathrm{B}}$ = 227 nm nanocone
antennas allows for a larger tuning bandwidth, such that there exists a larger
range of $\alpha_{\mathrm{i}}$ for which $\lambda_{\mathrm{R}}^{[-1,0]}$
overlaps with the nanoantenna plasmon.

While we readily earn high incidence direction tunability of optical
transmission with the designed magnetophotonic crystals, resonances in MO
spectra can yield much larger Q-factors [47]. Maccaferri et al. [48] showed
that an out-of-plane magnetization in the presence of the electric dipolar
plasmon gives rise to an in-plane MO dipolar plasmon ($p_{\mathrm{MO}}$) which
is orientated orthogonal to $p_{\mathrm{E}}$ and is induced in the
ferromagnetic layer. The magnitude of $p_{\mathrm{MO}}$ is proportional to the
magnitude of $p_{\mathrm{E}}$. Given that a material’s optical constants are
typically much larger than their MO constants, even lossy broad localised
plasmon resonances can give rise to large enhancements in MO activity as
compared to ferrimagnets without plasmonic integration. This transverse
oscillation is induced via spin-orbit coupling, generating an oscillation of
conduction electrons in-the-plane but orthogonal to $p_{\mathrm{E}}$. With the
use of p-polarised light, the pure optical dipole is orientated along
$p_{\mathrm{E}}$ and the transverse MO dipole is aligned along
$p_{\mathrm{MO}}$ (Fig. 2a). Hence, the use of $p$-polarised light results in
the MO dipole induced in the Tb18Co82 layer which radiates strongly in the
scattering plane, and is therefore expected to be most sensitive to the
angular dispersion of the surface lattice resonances as the crystal is tilted
by $\alpha_{\mathrm{i}}$.

In Fig. 2b-j the calculated and experimental Faraday rotation
($\theta_{\mathrm{F}}$), Faraday ellipticity ($\eta_{\mathrm{F}}$) and Faraday
angle
($\Theta_{\mathrm{F}}=\sqrt{\theta_{\mathrm{F}}^{2}+\eta_{\mathrm{F}}^{2}}$)
are presented. The calculated Faraday effect using the experimental
permittivity for a Tb18Co82 thin film is shown in Fig. 2b, e, h for the
$D_{\mathrm{B}}$ = 179 nm nanocone antennas array (see Supporting Information
for details). The $\varphi_{\mathrm{i}}$ = 0 configuration shows no angular
dependence for the Faraday effect (see Supporting information) and through
fitting a Lorentzian to the $\alpha_{\mathrm{i}}$ = 0 transmission and
$\Theta_{\mathrm{F}}$ spectra for the $\varphi_{\mathrm{i}}$ = 0 configuration
we estimate that the MO resonance exhibits a two-fold reduction in linewidth
relative to the pure optical resonance. While for $\varphi_{\mathrm{i}}$ = 0
(no overlap of nanoantennas plasmon with Rayleigh anomaly) a reasonable
spectral feature narrowing is achieved without angular dependence, in the
$\varphi_{\mathrm{i}}$ = 90∘ configuration the experimental Faraday spectra
show strong angular dependence and suggest that sizeable Faraday angles of up
to 0.3∘ are readily available. The simulated spectra prompts that extremely
sharp features exist that coincide with $\lambda_{\mathrm{R}}^{[-1,0]}$ (Fig.
2b, e, h).

Figure 2: Angle-of-incidence spectral dependence of the Faraday effect in the
magnetophotonic crystals. (a) Illumination configuration as in Fig, 1c, with
added MO plasmon dipole of nanoantenna ($p_{\mathrm{MO}}$, green). (b, e, h)
Calculated spectral $\theta_{\mathrm{F}}$ (b), $\eta_{\mathrm{F}}$ (e) and
$\Theta_{\mathrm{F}}$ (h) for incidence angles $\alpha_{\mathrm{i}}$ between 0
and 20 degrees. Measured $\theta_{\mathrm{F}}$ (c, d), $\eta_{\mathrm{F}}$ (f,
g) and $\Theta_{\mathrm{F}}$(i, j) for the $D_{\mathrm{B}}$ = 179 nm and 227
nm nanoantenna arrays respectively. A quadratic polynomial has been fitted to
the $\theta_{\mathrm{F}}$ measurements and subtracted to remove the background
contribution which arises from the Faraday rotation of the fused-silica
substrate, which is strongest for short wavelengths and approaches zero with
increasing wavelength.

The Rayleigh anomaly is strongest through the substrate and the observation of
strong diffractive effects in the Faraday spectra indicates that the MO dipole
induced in the Tb18Co82 layer is transferred to the rest of the nanoantenna
[19]. The experimental MO spectra measured for the nanoantennas with $D_{B}$ =
179 nm (Fig. 2c, f, i) compare well to the calculations. The excellent match
of the measured spectra with simulations demonstrates the suitability of
combining finite-element methods with experimentally measured thin-film
permittivity for the calculated design of magnetophotonic devices. For the
nanoantennas with $D_{B}$ = 227 nm (Fig. 2d, g, j) there is a stronger Faraday
effect, but with broader spectral features, demonstrating the trade-off
between adding more magnetic material in the nanoantenna whilst maintaining
small dimensions for narrow plasmon resonances.

From the above it is clear that it is not possible to measure the MO response
of the Au-Tb18Co82 nanoantennas off-resonance, where $\theta_{\mathrm{F}}$ and
$\eta_{\mathrm{F}}$ quickly drop to values comparable to the measurement
uncertainty. In effect, the nanoantennas plasmons strongly amplify the minute
magnetic signals that ordinarily wouldn’t be resolved. It is possible to
estimate the Tb18Co82 amount in each nanoantenna, corresponding to a nanodisk
with 86 $\pm$ 10 nm diameter and 15 nm height for nanoantennas with base
diameter of 179 nm. This yields Tb18Co82 effective film thickness (i.e. the
thickness of a film made with the same amount of material) of approximately
0.6 nm, of the order of an atomic monolayer, demonstrating the MO
amplification obtained through the nanoantenna’s plasmons.

The experimental $\Theta_{\mathrm{F}}$, $\eta_{\mathrm{F}}$ and
$\theta_{\mathrm{F}}$ curves all show abrupt features that onset with the
excitation of the surface lattice resonance associated with
$\lambda_{\mathrm{R}}^{[-1,0]}$ in the $\varphi_{\mathrm{i}}$ = 90∘
configuration. However, spectrally just prior to this resonance there is the
greatest change in MO activity for the smallest change in wavelength. Since
this feature is dependent on the spectral position of
$\lambda_{\mathrm{R}}^{[-1,0]}$, it can be effectively tuned by varying
$\alpha_{\mathrm{i}}$, indicating the potential use of such magnetophotonic
crystals as light incidence direction/angular sensors. This is explored in
Fig. 3a, where hysteresis loops are recorded through measurements of the
transmitted light ellipticity at a wavelength of 730 nm for the nanoantennas
with base diameter 227 nm for different $\alpha_{\mathrm{i}}$. The
nanoantenna’s Tb18Co82 tops maintain perpendicular magnetic anisotropy even
after the lithography process, which is clear from the large remanent
magnetization observed in the hysteresis loops in Fig. 3a, reducing the
magnetic field strength required to saturate the sample along the out-of-plane
direction. The dynamic tunability of the MO activity by varying
$\alpha_{\mathrm{i}}$ is remarkable in this case, resulting in a dramatic
change in the magnitude of $\eta_{\mathrm{F}}$, where extraordinarily at
$\alpha_{\mathrm{i}}$ = 15∘ the loop is even inverted (see a view of
$\eta_{\mathrm{F}}$ for the spectral region around the surface lattice
resonance in Supporting information; it is clear that this sign change in
$\eta_{\mathrm{F}}$ is associated with the migration of the surface lattice
resonance to the measurement wavelength of 730 nm).

This is explored further in Fig. 3b where the change in Faraday ellipticity
($\delta\eta_{\mathrm{F}}$) between successive wavelength increments
($\delta\lambda$ = 5 nm) is plotted. Since the gradient of this feature is
positive when it coincides with $\lambda_{\mathrm{R}}^{[-1,0]}$ (see inset of
Fig. 3a), the $\delta\eta_{\mathrm{F}}$ $<$ 0 data has been excluded from the
fits. It is evident that $\eta_{\mathrm{F}}$ undergoes a sign change, which in
turn is tunable by varying $\alpha_{\mathrm{i}}$. This active tuning modality
was previously envisioned for refractive index biochemosensing, where the
spectral region of maximum sensitivity can be tuned by varying the angle of
incidence, thereby allowing to operate in a spectral region where the analyte
solution is minimally absorbing [49]. Here we foresee that the deviations from
a set angle, i.e., a mechanical tilt, could be employed in high-precision
tilt-control systems and detected with high accuracy, simply as reduced MO
activity in transmittance. The latter feature starkly differentiates this
approach from the currently employed optical systems where reflection is
captured by a complex system of mirrors/detectors often with the need of a
microelectromechanical (MEMS) array of actuators. Lorentzian functions have
been fitted to the $\delta\eta_{\mathrm{F}}$ data, in order to estimate the
spectral width of the abrupt transition in $\eta_{\mathrm{F}}$. Due to the
limited number of data points on this abrupt spectral transition, a full
estimate of the full-width at half-maximum (FWHM) is difficult to obtain from
these fits. However, all values are within the $5-10$ nm range (which is
comparable to the wavelength resolution of the setup) with the exception of
the $\alpha_{\mathrm{i}}$ = 10∘ where a FWHM of 24 $\pm$ 10 nm is obtained due
to the anomalously large error on this particular measurement.

Crucially, the perpendicular magnetic anisotropy in this magnetophotonic
crystal allows for the measurement of the magnetic differential absorption of
circularly polarised light, underpinning $\eta_{\mathrm{F}}$, without the need
for an out-of-plane magnetic field to stabilize the magnetization along the
propagation direction of light. When circularly polarized light beam, with a
time-varying helicity is incident on the sample, we can measure the ratio,
$C_{\mathrm{\omega}}^{q}/C_{\mathrm{\circ}}^{q}$ which is proportional to the
differential absorption of circularly polarised light (see Methods) for the
two opposite polar magnetization states. Here, $C_{\mathrm{\omega}}^{q}$ is
the amplitude of the $\omega/2\pi$ = 50 kHz signal from the modulation of the
light circular polarization (see Methods), for a fixed polar magnetization
$q=\pm M_{\mathrm{z}}$, while $C_{\mathrm{\circ}}^{q}$ is the DC signal
intensity, which contains the helicity independent absorption contribution.
Fig. 4a shows several spectra for the nanoantennas with base diameter of 227
nm for different values of $\alpha_{\mathrm{i}}$, in the
$\varphi_{\mathrm{i}}$ = 90∘ configuration and in zero external magnetic
field. The spectral minima strongly depend on $\alpha_{\mathrm{i}}$. If we
include an external field, the amplitude of
$C_{\mathrm{\omega}}^{q}/C_{\mathrm{\circ}}^{q}$ can be further modulated by
reversing the magnetization ($q$ = $+M_{\mathrm{z}}\rightarrow-
M_{\mathrm{z}}$, and vice versa), as indicated by the variation between the
dashed and solid curves. The magnetophotonic crystal then exhibits active
transmission tunability, whereby absolute transmission can be enhanced or
attenuated with the use of a magnetic field. Similar active magnetic
transmission tunability has been devised with magnetoplasmonic chiral
nanoantennas [16], however, an external field was required to orient the
magnetization out-of-plane throughout the measurement, whereas here the
external field is only required to set the magnetic state. An additional
tuning knob is implemented through the light incidence direction/angle
$\alpha_{\mathrm{i}}$, whereby the spectral location of this maximum for
magnetic modulation can be tuned with the surface lattice resonance.

Figure 3: Dynamic Faraday ellipticity in the magnetophotonic crystal. (a)
Hysteresis loops under externally-applied magnetic field recorded from the
magnetophotonic crystal with $D_{\mathrm{B}}=227$ nm, at a wavelength of 730
nm demonstrating how the magnitude and sign of the Faraday ellipticity
($\eta_{\mathrm{F}}$) can be controlled through the illumination incidence
angle ($\alpha_{\mathrm{i}}$), varying between 0 and 20 degs. (b) The change
in Faraday ellipticity ($\delta\eta_{\mathrm{F}}$) measured at different
wavelengths. Following the onset of the surface lattice resonance, there is an
abrupt change in light ellipticity at various illumination angles (0-20
degrees), which is associated with a maximum in $\delta\eta_{\mathrm{F}}$. The
peaks at different incidence angles have been fitted with Lorentzians.

We define a magnetic asymmetry ratio
$(C_{\mathrm{\omega}}^{-M_{\mathrm{z}}}-C_{\mathrm{\omega}}^{+M_{\mathrm{z}}})/(C_{\mathrm{\circ}}^{-M_{\mathrm{z}}}+C_{\mathrm{\circ}}^{+M_{\mathrm{z}}})$,
which represents the available helicity-dependent transmission modulation
between the two antiparallel magnetization states (see Methods) which is
plotted in Fig. 4b. The dispersion of the surface lattice resonance calculated
from equation (3) is given by the dashed lines. Here, it is clear that the
latter dictates the onset wavelength for the magnetic modulation of the
differential circular transmission, meaning that the peak sensitivity can be
tuned to arbitrary wavelength between 650 nm - 800 nm. This tunability range
is governed by the FWHM of the magnetophotonic crystal transmission spectra. A
maximum magnetic asymmetry ratio of around 0.5% can be obtained, however, we
believe there is enormous scope for improvement through composition
optimisation of the RE-TMs and the noble metal thicknesses in the
nanoantennas, including exploring new geometries sustaining plasmon optically
dark modes, which result in a stronger plasmonic enhancement of the MO
activity than achieved with the here-used strongly scattering dipolar plasmons
[50]. The essential operation of a simple mechanical tilt-control/light
incidence optical sensor can be further envisioned as in Fig. 4c. The
differential chiral transmission
($C_{\mathrm{\omega}}^{q}/C_{\mathrm{\circ}}^{q}$) reports the mechanical
tilt/change of light incidence direction angle on the pre-magnetized
magnetophotonic crystal by having sharp spectral dips at various wavelengths.
We can also envision that by using materials exhibiting all-optical
magnetization switching [27] such as the TbCo family of alloys employed here,
the need for the external magnetic field to setup the magnetic state of the
magnetophotonic crystal or for magnetic transmission modulation can be
entirely removed, whereby the transmission would be modulated purely optically
at the ultrafast (fs) timescale and allowing for sub-wavelength (nanoscale)
miniaturization [35, 51].

Figure 4: Angle-controlled chiral transmittance and mechanical tilt-angle
sensing. (a) Spectral dependence of the
$C_{\mathrm{\omega}}^{q}/C_{\mathrm{\circ}}$ signals, where $q$ =
+$M_{\mathrm{z}}$ or -$M_{\mathrm{z}}$ for the solid and dashed curves
respectively. $C_{\mathrm{\omega}}^{q}$ is related to the total circular
dichroism for a particular magnetization state, containing both magnetic and
non-magnetic contributions. (b) The amplitude of the magnetic modulation of
the helicity dependent transmission as function of both wavelength and
$\alpha_{\mathrm{i}}$, which relates to the difference between the solid and
dashed curves in (a). The dashed white line indicates the expected location of
the Rayleigh anomaly calculated from Eq. (3). (c) Schematics of the tilt-angle
sensing device, where the difference in left- and right- circularly-polarized
light, passing through the pre-magnetized magnetophotonic crystal, is detected
as spectrally-resolved differential chiral transmission, having sharp spectral
dips at distinct wavelengths, depending on the light’s angle of incidence.

##  3 Conclusion

In conclusion, our work demonstrates the seamless integration of a rare-
earth–transition-metal into magnetophotonic crystals. A strong angular
dispersion is engineered through the interference of the Rayleigh anomaly and
the nanoantenna’s plasmons, producing a sharp surface lattice resonance in
both the optical and MO responses. We showcase dynamic tunability of
magnetophotonic crystals using the light’s incidence direction angle, which
strongly modifies the MO response, as rationalized using finite-element method
electromagnetic simulations. Further, we have shown the magnetic modulation of
the differential circular transmission of a magnetophotonic crystal, with
measurements performed in zero external magnetic field, exploiting the
perpendicular magnetic anisotropy of the magnetic nanoantennas. More
generally, the integration of rare-earth–transition-metals within plasmonic
nanoantennas offers an exciting platform for highly tunable, ultrafast all-
optical switching active magnetophotonic devices [51, 1]. Such architectures
could also find further application scope where the optical response from
magnetophotonic crystals can be tuned by the angle of incidence [38, 39] in
combination with the reconfigurable magnetic structure [52] steered by all-
optical ultrafast magnetization switching or by external magnetic fields.

##  4 Experimental Section

Sample Fabrication

The plasmonic nanoantennas are fabricated using a top-down approach, based on
the method outlined by Horrer et al. [40]. Au(80 nm) films were deposited
using electron-beam evaporation onto fused-silica substrates. Later, Al2O3(3.5
nm)/Tb18Co82(15 nm)/Al2O3(2 nm) films were sputter deposited onto these films.
The Tb18Co82 layer was deposited through co-sputtering, with the complete
structure being Au(80 nm)/Al2O3(3.5 nm)/Tb18Co82(15 nm)/Al2O3(2 nm). The
additional thin Al2O3 layers were used as capping and isolating layers for the
Tb18Co82. Here, the composition of the film can be varied by adjusted the
relative power of the Co and Tb magnetrons. Calibration films were made with
different power ratios on the two magnetrons and compositions were verified
using Rutherford back scattering. Electron beam lithography was used to define
disk shaped apertures in a MicroChem 496PMMA A4 electron-beam resist.
Electron-beam evaporation was used to deposit an Al mask through the resist
followed by removal of the PMMA mask with Acetone. The resulting structure was
then milled at a 5 deg incidence angle with sample rotation, removing all
material unprotected by the Al mask. Any remaining Al mask was then removed
with the photoresist developer Microdeposit 351, which in this case was used
as a selective etcher to target the Al. A conical profile is induced through a
combination of the small lateral component of the milling which depends to
some extent on the small milling incidence angle [53]. In our samples, this
results in a constant slope profile of approximately 62 degrees for all
nanoantenna arrays. Therefore, by varying the diameter of the Al mask, the
resulting structures can be tuned from truncated to conical profiles.

Magneto-optical characterisation

The experimental values of $\theta_{\mathrm{F}}$, $\eta_{\mathrm{F}}$ and
$\Theta_{\mathrm{F}}$ were measured using the photoelastic modulator
methodology with an applied field of 450 mT along the light propagation
direction, which is described in the Supporting Information. A quadratic
polynomial was fitted to the raw $\theta_{\mathrm{F}}$ data in order to
subtract the background contribution which arises from the Faraday rotation of
the fused-silica substrate, which is strongest for short wavelengths and
decreases for longer wavelengths [54]. For the differential absorption of
circularly polarised light measurement, a time varying light polarisation,
which alternates between left and right circularly polarised light states at
50 kHz was generated using a photoelastic modulator (PEM) and directed at the
sample at normal incidence. This is achieved by passing linearly polarised
light orientated at 45∘ to the fast axis of the PEM, with the PEM retardation
set to 0.25 wavelengths. Any mechanism in the TNC array which results in a
difference in absorption for opposite helicities (including magnetic circular
dichroism) will contribute to an oscillating light intensity at the detector
at the photoelastic modulator frequency. It is common to express this
measurement as the ratio $C_{\mathrm{\omega}}^{q}/C_{\mathrm{\circ}}^{q}$,
where $C_{\mathrm{\omega}}^{q}$ is the amplitude of the $\omega$ = 50 kHz
signal for a fixed polar magnetization $q=\pm M_{\mathrm{z}}$, and
$C_{\mathrm{\circ}}^{q}$ is the DC signal intensity, which contains the
helicity independent absorption contribution. Prior to the measurement, a
saturating magnetic field was used to initialise the magnetization along the
light propagation direction ($q=+M_{\mathrm{z}}$) and then removed. For the
subsequent measurement, the magnetization was saturated in the opposite polar
direction ($q=-M_{\mathrm{z}}$) and the measurement repeated.

It is important to note that the spectra in Fig. 4a contain additional fake CD
contributions, which arise from leaking-in of the large linear dichroism
signal as a result of the rectangular array with which the nanostructures are
arranged. By observing the difference between the antiparallel magnetization
states, these effects, which are independent of the magnetization orientation,
can be subtracted out, yielding the available magnetic modulation. We define
this magnetic modulation of the helicity dependent transmission as
$(C_{\mathrm{\omega}}^{-M_{\mathrm{z}}}-C_{\mathrm{\omega}}^{+M_{\mathrm{z}}})/(C_{\mathrm{\circ}}^{-M_{\mathrm{z}}}+C_{\mathrm{\circ}}^{+M_{\mathrm{z}}})$,
and this quantity is plotted in Fig. 4b as a function of both
$\alpha_{\mathrm{i}}$ and wavelength.

Supporting Information

Supporting Information is available from the Wiley Online Library or from the
author.

Acknowledgements

The authors would like to express their gratitude towards Prof. Bengt Lindgren
of Uppsala University, Sweden, for fruitful discussions and support with the
ellipsometric characterization of TbCo thin film materials. The excellent
support and infrastructure of the MyFab facility at the Ångström Laboratory of
Uppsala University is also highly appreciated. The authors acknowledge support
from the Knut and Alice Wallenberg Foundation project “Harnessing light and
spins through plasmons at the nanoscale” (Project No. 2015.0060), the Swedish
Research Council (Project No. 2019-03581), the Swedish Foundation for
International Cooperation in Research and Higher Education (Project No.
KO2016-6889), and the Swedish National Infrastructure for Computing (SNIC).
This work is part of a project which has received funding from the European
Union’s Horizon 2020 research and innovation programme under grant agreement
no. 737093, “femtoterabyte”. P.V. acknowledges funding from the Spanish
Ministry of Science and Innovation under the Maria de Maeztu Units of
Excellence Programme (MDM-2016-0618) and the project RTI2018-094881-B-I00
(MICINN/FEDER).

Author Contributions

R.M.R-R. and V.K. designed the material and nanofabrication processing, with
input from A.D. concerning the nanocone design approach. R.M.R-R. and A.C.
carried out the thin film deposition and magnetic characterization. R.M.R-R.,
A.C., I.-A.C. and M.P. performed all magneto-optical characterization of the
nanoarrays. J.H., R.M.R-R., M.Z., P.V. and P.M.O. did the electromagnetic
modelling and simulations. R.M.R-R. and V.K. wrote the manuscript with input
from J.H., P.V., A.D. and P.M.O. All authors discussed the results and
commented on the manuscript.

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