Supplemental Material for
Polar magneto-optical effects in magnetoplasmonic thin films
illuminated by attenuated total reflection
Cunji Yan (闫存极),1 Li Han(韩立), 1 Jinbo Yang(杨金波)2 and
Wenqi Gu(顾文琪) 1
1
Institute of Electrical Engineering, Chinese Academy of Sciences (CAS), Beijing 100190,
People’s Republic of China
2
State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing
100871, China
(1) Measurements of the Kerr hysteresis loops.
To experimentally confirm the direction of the magnetic easy axis of each of the samples, the
Kerr hysteresis loops in both the polar and longitudinal configurations have been measured, with
results in the form shown in Fig. S1. The experiments show a longitudinal loop with a low saturation
field and high remanent magnetization and a polar loop with a high saturation field (which exceeds
the maximum strength of the magnetic field produced by the electromagnet used in the experiments)
and low remanent magnetization. Therefore, the in-plane magnetic easy axis for the film used in
this study is determined.
FIG. S1. Kerr loops of the Co(10 nm)/Au(5 nm) film measured in (a) longitudinal and (b)
polar configurations. In the experiments, a linearly polarized 632.8nm light beam was
incident on the film through an air atmosphere. The longitudinal Kerr loop was recorded at
a 45° angle of incidence with the applied magnetic field in the film plane, and the polar
Kerr loop was recorded at normal incidence with the applied magnetic field perpendicular
to the film plane.
(2) Calculations of the reflectivities and the electromagnetic field distributions of the Co/Au films
under p excitation.
The angular dependence of the p-polarized reflectivity and the electromagnetic field distribution
in the Co/Au films in the attenuated total reflection configuration have been calculated using a
transfer matrix formalism (as shown in Fig. S2). The optical constants of the Co and Au layers were
2.2126+i4.1702 and 0.18377+i3.4313, respectively, with reference to www.refractiveindex.info.
For the Co(10 nm)/Au(5 nm) film, a relatively high electromagnetic field intensity can be found
over a wide range of angle of incidence above the critical angle, corresponding to the wide
absorption peak in the reflectivity curve. This is related to a large degree to the relatively lowefficiency coupling of light to the surface plasmon polaritons at the Au/air interface because of the
non-optimum film thickness. The relatively thin gold layer (5 nm) means that the electromagnetic
field that results from the excitation of surface plasmon polaritons has a considerable effect on the
Co layer and also affects the magneto-optical response. For the Co(10 nm)/Au(15 nm) film, the
surface plasmon polaritons are excited more efficiently at the Au/air interface. The position of the
maximum electromagnetic field occurs near the angle of incidence of 43° and is somewhat different
to the position of the minimum reflectivity (at approximately 45°). This shows that the absorption
peak is not only related to the excitation of surface plasmon polaritons, but is also connected to other
factors, such as the ohmic loss in the Co layer. Because of the moderate Au layer thickness, the
electromagnetic fields of the surface plasmon polaritons can still penetrate into the Co layer and
affect the magneto-optical activity. For the Co(10 nm)/Au(30 nm) film, the position of the maximum
electromagnetic field, which is found near the angle of incidence of approximately 44° at the Au/air
interface, is identical to the absorption peak position in the reflectivity spectrum. This means that
the optical absorption is mainly a result of the highly efficient excitation of surface plasmon
polaritons. However, because the gold layer is relatively thick, the influence of the surface plasmon
polaritons on the Co layer is small, and thus no relevant magneto-optical activity occurs.
FIG. S2. (a) Calculated angular reflectivity spectra for various Co/Au films under p
excitation. (b)-(d) The calculated electromagnetic field distributions of various Co/Au films
in the attenuated total reflection configuration under p excitation as a function of the angle
of incidence and the distance to the glass-Co interface.
（3）Influence of the polarization azimuth of the incident linearly polarized light on the polarization
azimuth of the reflected light in the attenuated total reflection configuration.
FIG. S3. Influence of the polarization azimuth of the incident linearly polarized light on
the polarization azimuth of the reflected light for the (a) Co(10 nm)Au(5 nm), (b) Co(10
nm)Au(15 nm) and (c) Co(10 nm)Au(30 nm) films in the attenuated total reflection
configuration when the polarization azimuth of the incident linearly polarized light changes
near the p plane. The x-axis θ represents the incident angle, and the y-axis α represents
the polarization azimuth of the reflected light with respect to the p plane, and the angular
spectra with the different polarization azimuth angles (-1°, -0.75°, -0.5°, -0.25°, 0°, 0.25°,
0.5°, 0.75°, 1°) of the incident linearly polarized light relative to the p plane are presented
for each film.
FIG. S4. Influence of the polarization azimuth of the incident linearly polarized light on
the polarization azimuth of the reflected light for the (a) Co(10 nm)Au(5 nm), (b) Co(10
nm)Au(15 nm) and (c) Co(10 nm)Au(30 nm) films in the attenuated total reflection
configuration when the polarization azimuth of the incident linearly polarized light changes
near the s plane. The x-axis θ represents the incident angle, and the y-axis β represents
the polarization azimuth of the reflected light with respect to the s plane, and the angular
spectra with the different polarization azimuth angles (-1°, -0.75°, -0.5°, -0.25°, 0°, 0.25°,
0.5°, 0.75°, 1°) of the incident linearly polarized light relative to the s plane are presented
for each film.
(4) Coupling between the Faraday rotations in the glass materials under the polar magnetic fields
and the rotations caused by the attenuated total reflection.
FIG. S5. Influence of the polar magnetic field on the polarization azimuth of the reflected
light for various Co/Au films in the attenuated total reflection configuration under p
excitation. The x-axis θ represents the angle of incidence, and the y-axis γ represents the
polarization azimuth of the reflected light with respect to the p plane, and the angular
spectra under the different polar magnetic field (-3 kOe, 0 kOe and 3 kOe) are presented
for each film.
FIG. S6. Influence of the polar magnetic field on the polarization azimuth of the reflected
light for various Co/Au films in the attenuated total reflection configuration under s
excitation. The x-axis θ represents the angle of incidence, and the y-axis δ represents the
polarization azimuth of the reflected light with respect to the s plane, and the angular spectra
under the different polar magnetic field (-3 kOe, 0 kOe and 3 kOe) are presented for each
film.
(5) Methods for measurement of the glass Faraday rotations of the incident and reflected light beams
in the attenuated total reflection configuration.
To simplify these measurements, the glass Faraday rotation in the incident process was required
to be equal to the rotation in the reflected process over the entire angle of incidence range involved.
To meet this requirement in the attenuated total reflection system when using a right-angle prism,
the rotation equipment was designed to guarantee that incident and reflected light beams of equal
lengths would propagate in the glass materials during the scanning of the angle of incidence; also,
the polar magnetic field was applied symmetrically around the reflection point, because the strength
of the magnetic field generated by the magnet decays quickly along the direction perpendicular to
the surfaces of the magnetic poles. In addition, to remove the influence of the film, we used a gold
film (120 nm), which has very small magneto-optical effects and has no effect on the plane of
polarization of the incident linearly-polarized light beam upon total internal reflection, to measure
the glass Faraday rotation in the experimental attenuated total reflection system. Because the
magneto-optical effect is non-reciprocal, the total amount of the glass Faraday rotation in the
attenuated total reflection configuration with the gold film was experimentally obtained by
subtracting the reflected polarization azimuth angles before and after application of the magnetic
field. Finally, the Faraday rotations of the incident and reflected light beams were determined and
both of them were found to be the half of the measured total amount. The slightly uneven surface
magnetic field distribution of the magnet could not affect the measurements, because the effects of
the small changes in the magnetic field on both the incident and reflected light beams were almost
identical and could be removed in the measurements.
(6) Polar Kerr rotation spectra of the 10 nm Co film under p excitation
FIG. S7. Angular reflectivity spectrum and angular Kerr rotation spectra of the 10 nm Co
film under p excitation. (a) shows the reflectivity spectrum. (b) and (c) show the polar Kerr
rotation spectra under polar magnetic fields with different polarities.
(7) Polar Kerr rotation spectra of the Au films.
FIG. S8. Angular reflectivity spectra and angular Kerr rotation spectra of various Au films
under p excitation. (a) shows the reflectivity spectra. (b) and (c) show the polar Kerr rotation
spectra under polar magnetic fields with different polarities.
Fig. S9 Angular reflectivity spectra and angular Kerr rotation spectra of various Au films
under s excitation. (a) shows the reflectivity spectra. (b) and (c) show the polar Kerr rotation
spectra under polar magnetic fields with different polarities.