Shayegan
et al
.,
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, eabm4308 (2022) 6 May 2022
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APPLIED PHYSICS
Nonreciprocal infrared absorption via resonant
magneto-optical coupling to
InAs
Komron J.
Shayegan
1
, Bo
Zhao
2
, Yonghwi
Kim
1
, Shanhui
Fan
2
, Harry A.
Atwater
1
*
Nonreciprocal elements are a vital building block of electrical and optical systems. In the infrared regime, there is
a particular interest in structures that break reciprocity because their thermal absorptive (and emissive) proper-
ties should not obey the Kirchhoff thermal radiation law. In this work, we break time-reversal symmetry and reci-
procity in n-type–doped magneto-optic InAs with a static magnetic field where light coupling is mediated by a
guided-mode resonator structure, whose resonant frequency coincides with the epsilon-near-zero resonance of
the doped indium arsenide. Using this structure, we observe the nonreciprocal absorptive behavior as a function
of magnetic field and scattering angle in the infrared. Accounting for resonant and nonresonant optical scatter-
ing, we reliably model experimental results that break reciprocal absorption relations in the infrared. The ability
to design these nonreciprocal absorbers opens an avenue to explore devices with unequal absorptivity and emis-
sivity in specific channels.
INTRODUCTION
There has been great interest and numerous theoretical proposals for
nonreciprocal absorbers on the grounds that they do not obey the
Kirchhoff thermal radiation law (
1
–
4
). Interest in this phenomenon
stems from fundamental considerations and applications ranging
from infrared (IR) spectroscopy, sensing, and thermal energy con-
version efficiency (
5
,
6
). For IR sensing applications, the amount of
light absorbed in each channel is something that could be controlled
in a nonreciprocal device, where the absorptivity can be tuned from
strong in one channel and weak in another and vice versa (
7
,
8
). As
we review in the coming section, nonreciprocal absorption achieved
through an external magnetic field necessitates that the emission is
channeled through the opposite channel. Nonreciprocal absorption is
a required functionality to enable thermal energy harvesting exceed-
ing the conversion efficiency constrained by the Shockley-Queisser
limit (
9
) and reaching higher theoretical efficiency limits, such as
the Landsberg limit (
10
–
12
).
The Kirchhoff thermal radiation law can be expressed as an
equality of the absorptivity and emissivity at a given wavelength (
),
polarization, and angle of incidence (
i
) (
13
–
15
)
(
i
,
) =
e
(
i
,
)
(1)
This equality between the angular and spectral distributions of
the emissivity and absorptivity is a direct consequence of reciprocity,
which, in a scattering context, takes the form
r
(
i
,
) =
r
(−
i
,
)
(2)
where
r
(
i
,
) is the incident radiation from
i
that is not absorbed
by the absorber/emitter and reflected through the −
i
channel and
vice versa for
r
(−
i
,
). The above relationships, however, assume
that the emitter/absorber obeys Lorentz reciprocity and does not
transmit any of the incident radiation (
16
). In a nonreciprocal sys-
tem, the equality in Eq. 2 is broken, and the Kirchhoff law is violated
(
17
). The nonreciprocal behavior of the reflection directly relates
to the nonreciprocal thermal radiation. This relation is visualized in
Fig. 1 (A and B).
Achievement of nonreciprocity for IR radiation is a subject of
widespread investigation. Reciprocity can be broken with linear time–
invariant, nonlinear, and linear time–varying platforms (
18
–
21
).
The use of magneto-optical materials, e.g., ferrites, in basic optical
elements such as isolators and circulators has been a fundamental
building block in integrated photonics for many decades. The use of
bare magneto-optical materials to observe free-space radiation from
coupled plasmon-phonon modes has been demonstrated; however
the wavelength regimes are limited to the far IR, and the dependence
on magnetic field was not measured (
22
). Prior experimental work
on free-space magneto-optical elements has investigated coupling
to surface plasmon resonances at a fixed incidence angle in the Otto
configuration in the far-IR regime (
23
) and polarization rotation in
the Faraday geometry (
24
,
25
). Pairing magneto-optical semicon-
ductors with photonic crystals and examining the magnetic field and
angular dependence in the IR have not yet been experimentally
explored. Furthermore, to date, there has not been a measurement
of the interaction of thermal radiation with materials that break
reciprocal relations in the far and mid-IR despite an abundance of
theoretical designs reporting free-space propagation with magneto-
optical elements in this wavelength regime (
5
,
26
,
27
). Here, we ex-
perimentally demonstrate strong nonreciprocal behavior, breaking
the reflectivity relationship in Eq. 2 over a wide range of incident
angles in an IR thermal photonic absorber that incorporates
magneto-optic InAs with a static external magnetic field (
28
). To
apply the external magnetic field, we use a Halbach array consisting
of three permanent magnets with their fields oriented toward a pole
piece (Fig. 1C) (
29
). The pole piece is made of a soft ferromagnetic
alloy, which focuses the field so that it is uniform over the sample.
We control the strength of the field through the sample by tuning
the length of the gap,
l
, between the two pole pieces (Fig. 1, C and D).
The maximum field used in this paper is limited by the sample
size, 5 mm.
1
Thomas J.
Watson Laboratory of Applied Physics, California Institute of Technology,
Pasadena, CA 91125, USA.
2
Department of Electrical Engineering, Ginzton Labora-
tory, Stanford University, Stanford, CA 94305, USA.
*Corresponding author. Email: haa@caltech.edu
Copyright © 2022
The Authors, some
rights reserved;
exclusive licensee
American Association
for the Advancement
of Science. No claim to
original U.S. Government
Works. Distributed
under a Creative
Commons Attribution
NonCommercial
License 4.0 (CC BY-NC).
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, eabm4308 (2022) 6 May 2022
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RESULTS
Experiment
Our device consists of a low-loss, amorphous silicon (
-Si) guided
mode resonance (GMR) waveguide structure fabricated on the
surface of a 500-
m-thick, degenerately n-type–doped InAs wafer
(Fig. 1, D and E) serving as our magneto-optical material resonantly
excited in the Voigt geometry. The patterned
-Si structure on the
InAs gives a clear angle-dependent guided mode dispersion relation
with distinct resonances for both the zero and nonzero magnetic
field cases. While most of the modal field of a guided mode is con-
fined within the low-loss
-Si resonator, some of the modal field
penetrates the magneto-optic InAs layer below, which produces the
nonreciprocal effect in the presence of a magnetic field (Fig. 1F).
Optical characterization of
InAs and
resonant IR device design
The doping concentration of the InAs is chosen such that the GMR
wavelength coincides with the epsilon-near-zero (ENZ) wavelength
(17.3
m) in the IR.
The degenerately doped InAs exhibits a Drude-
like optical response with nonzero off-diagonal permittivity values
in an applied magnetic field
(
) =
[
xx
xy
0
yx
yy
0
0
0
zz
]
(3)
xx
=
yy
=
∞
−
p
2
(
+
i
)
───────────
[ (
+
i
)
2
−
c
2
]
(4)
xy
= −
yx
=
i
p
2
c
───────────
[ (
+
i
)
2
−
c
2
]
(5)
zz
=
∞
−
p
2
─
(
+
i
)
(6)
In Eqs. 4 to 6, the plasma and cyclotron frequencies are
p
=
√
_
n
e
2
/ (
m
e
0
) and
c
=
eB
/
m
e
, respectively. Four-point probe
measurements of the InAs wafer in conjunction with ellipsometry
fits of the values
and
, the complex ratio amplitude and phase
responses, give a relaxation rate
= 4.5 THz, a high-frequency limit
dielectric constant
∞
= 12.3, a carrier concentration
n
= 1.5 × 10
18
cm
−3
,
and an effective electron mass
m
= 0.033
m
e
, where
m
e
= 9.109 × 10
−31
kg
(
30
). The Drude model fit to the experimental values is shown in
Fig. 2A. Furthermore, our designs targeted the ENZ wavelength
regime (17.3
m) since the off-diagonal terms of the dielectric func-
tion (
xy
,
yx
) are largest relative to the on-diagonal terms when
a magnetic field is applied to the InAs at this wavelength (Fig. 2B).
We focused on controlling the nonreciprocal response around
17.3
m since it corresponds to the portion of the electromagnetic
spectrum exhibiting thermal radiation at or below room temperature.
Fig. 1. Overview of nonreciprocal absorber/emitter theory, design, and implementation.
(
A
and
B
) Reciprocal and nonreciprocal relations for an absorber/emitter.
(
C
) Schematic of the Halbach array used in the measurement. The poles of the magnets on each side of the system are rotated by 90° relative to one another to increase
the magnitude of the magnetic field through the pole pieces (gray). The pole pieces provide a focused and uniform magnetic field across the sample, which is shown in
the gap. We tune the magnetic field strength by changing the gap length,
l
, between the pole pieces. (
D
) Schematic of the measurement scheme. A silicon carbide Globar
is used as the thermal source inside of a Fourier transform IR (FTIR) spectrometer. The sample is mounted on a rotating stage, which controls the angle of incidence,
i
,
from the source onto the sample. The detector is mounted on a rotating arm to collect the specular reflected light. Polarizers at the source output and detector input allow
polarization-dependent measurements. (
E
) Scanning electron microscope (SEM) images of the
-Si photonic crystal slab with no tilt (top) and 45° tilt (bottom). (
F
) Simu-
lation showing the electric field intensity for 50° incident radiation at 17.3
m with the measured
-Si parameters from the SEM images.
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We implemented this control with a GMR structure, which is com-
monly used to enhance absorption/reflection by critical coupling in
IR applications (
31
–
34
). We designed the GMR structure to critically
couple to p-polarized free-space radiation (i.e., electric field oscillating
in the
x-y
plane) near the ENZ wavelength over a range of angles,
with the guided resonance in the thermal emitter. Because the
resonator has been designed around the ENZ wavelength, we see a
strong detuning of a resonant peak with a magnetic field. If no
patterned
-Si was used, then the plasma edge of the InAs would
have no distinct resonance that could be detuned with a magnetic
field. This effect is discussed in more detail in the following section.
The optimal dimensions for the GMR structure are found on the
basis of an analysis of the guided mode in a uniform
-Si slab atop
n
-InAs. In this approximation of the periodic
-Si, the uniform
-Si
has a thickness
t
=
d
1
/2 +
d
2
, where
d
1
is the periodic element depth
and
d
2
is the supporting layer thickness of the
-Si. The dispersion
relation,
(
k
x
), of the fundamental guided mode is then found by
solving the equation (
26
,
35
,
36
)
tan(
k
Si
t
) =
k
Si
Si
[
k
air
+
k
InAs,
xx
]
──────────
─
k
Si
2
−
Si
2
k
air
k
InAs,
xx
(7)
where
k
Si
=
√
_______________
Re
(
Si
) (
/
c
)
2
−
k
x
2
,
k
air
=
√
_
k
x
2
− (
/
c
)
2
,
k
InAs
=
√
________________
k
x
2
− (
/
c
)
2
Re
(
InAs
) ,
xx
= 1/
Re
(
InAs
), and
k
x
is the wave vector
along the direction of propagation. In this derivation, we focus on
the reciprocal case to get a sense of matching the slab waveguide to
the Drude-like resonance of the InAs and neglect the off-diagonal
terms of the InAs, which are zero when there is no applied magnet-
ic field. In (
26
), the derivation for the nonzero magnetic field case
shows that
(
k
x
) ≠
(−
k
x
) and the symmetry of the dispersion rela-
tion are broken.
A plot of the symmetric angular dispersion for varying slab
thicknesses of the
-Si waveguide is provided in fig. S1. In the calcu-
lations, we used the fitted dielectric constant values of the
n
-InAs
from ellipsometry.
We chose a periodicity (
) of 7
m such that the guided mode
can be folded in the light cone and couple with the free-space radi-
ation. We fine-tuned the other dimensions and used a GMR struc-
ture depth
d
1
= 0.72
m and supporting layer thickness
d
2
= 2.1
m.
Since the periodicity of the GMR structure itself is much smaller
than the wavelength of interest, we expect to see only specular re-
flection in the considered wavelength range (
37
). We note that the
linewidth of the resonance created by the GMR structure is sensitive
to both the patterned area widths (
/2) and the scattering rate of the
n
-InAs underneath (
38
).
Magnetic field–dependent absorption tuning in
magneto-optic GMR structure
The Voigt geometry used in these experiments means that the non-
reciprocal behavior of electromagnetic radiation inside of the InAs
will be confined to p-polarized scattering, where the electric field
oscillates perpendicular to the applied magnetic field (Fig. 3A).
Conversely, we expect reciprocal behavior for s-polarized scattering,
as the applied magnetic field is aligned with the oscillations in the
electric field, and the cross product of the electric and magnetic
fields is zero. The reciprocal behavior for s-polarized light is shown
in Fig. 3B, where the absorptivity maxima for all magnetic field val-
ues are marked with a dashed gray line at approximately 17
m. In
Fig. 3 (A and B), we emphasize the spectral shift in the peak position
of the absorptivity and offset the data for clarity. The overall absorp-
tivity for s-polarized light does not change with varying magnetic
field. Furthermore, we do not observe any detectable polarization
conversion from p to s or s to p polarization, confirming the proper
alignment of our GMR structure relative to the optical beam path of
the light (Fig. 3, C and D). The InAs layer is optically thick, and
therefore, no light is transmitted through the sample, allowing us to
only measure the absorptivity and reflectivity. We observed a substan
-
tial redshift of the absorptivity peak due to the GMR, especially in
the positive field case (0 to 1.2 T). The strong magnetic dependence
of the absorptivity spectrum clearly demonstrates the reciprocity
breaking effect. This nonreciprocal effect is observed in a wide
angular and wavelength range.
To deconvolve the contribution coming from the n-type InAs
and the entire GMR structure (n-type InAs with
-Si on top), we
simulated angular absorption spectra as a function of magnetic field
for both cases and compared the simulations to our measurements
(Fig. 4). The simulations were performed using a finite-difference,
frequency-domain electromagnetic simulation tool and incorporated
the measured InAs optical properties and
-Si grating parameters.
The simulated and measured plasma edge splitting for the un-
patterned InAs wafer are in good qualitative agreement, with a broad
resonance visible for the positive-field surface magnetoplasmon and
a shorter wavelength onset (16.5
m) for the negative-field surface
magnetoplasmon (Fig. 4, A and C). The addition of the periodic
-Si does not increase the wavelength shift induced by the plasma
edge splitting into two separate surface magnetoplasmons observed
in the unpatterned InAs case. However, clear maxima are seen from
the coupled GMR structure that can be evaluated for multiple
angles and compared to the data, which is further discussed in the
following section.
Comparing the measured positive field for the GMR structure
(Fig. 4B, red curve) and the simulation (Fig. 4D, red curve), we note
that both maxima occur at a resonance centered at 17.5
m. How-
ever, a second shoulder resonance is present in the simulation at
16.7
m, which is not easily visible in the experiment. The shoulder
resonance is much weaker in the experiment likely because of the
larger material loss in both the
-Si and InAs. Going from zero to
negative applied magnetic field at a
i
= 50°, we did not see a large
Fig. 2. Drude reflectance and dielectric constant of degenerately doped
n-
InAs.
(
A
) Drude reflectance of the InAs wafer. The transparent black dots show the mea-
sured data, and the dashed red curve gives the fit for a Drude-like optical response
with
n
= 1.5 × 10
18
cm
−3
and
= 4.5 THz. (
B
) Real and imaginary parts of the dielectric
function for the isotropic case. The transparent dots mark the permittivity values
directly calculated from the data, and the solid blue and red curves show the
extracted values from fitting the ellipsometry values
and
. The chartreuse strips
mark ENZ wavelength regime where we expect to see large nonreciprocal behavior.
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shift in the resonant peak position for either the simulation or the
measurement but we do observe the resonance narrowing for the nega
-
tive field case. The simulated and experimental traces for more angles
of incidence and an intermediary 0.8-T field are included in figs. S2 to S4.
To further highlight the effect of the GMR structure on nonre-
ciprocal absorption, we look at the intensity effect on the absorption
resonance at more oblique angles. Taking
i
= 70°, we can subtract the
absorption of the bare InAs around the plasma shoulder from the
GMR structure absorption and fit a Lorentzian to the difference (Fig. 5A).
When the magnetic field is then turned on, the resonant intensity
peak can be markedly tuned from absorption that greatly exceeds the
plasma shoulder (positive field) to well below (negative field).
Angle dependence of
nonreciprocal absorption behavior
To more comprehensively understand and characterize the non-
reciprocal response of the hybrid GMR structure, we compare the
experimental and simulated absorptivity maxima for p-polarized
light over a range of incidence angles for
B
= 0, 0.8, and 1.2 T.
To
map our dispersion across positive and negative angles, we confirm
that Onsager-Casimir relations hold (fig. S2). When
B
= 0 T, reciproc-
ity is preserved, and we do not expect to see any reciprocity-breaking
behavior. Consequently, the angular dispersion relation of the GMR
at the plasma edge of the InAs remains symmetric. Figure 6A shows
the symmetric case measured in our experiment and the correspond
-
ing absorptivity maxima from simulations (Fig. 6D). We also ob-
serve a narrowing of the resonant linewidth for more oblique angles
of incidence in both the simulated and experimental data when no
magnetic field is applied, as shown by the vertical bars marking the
full width at 5% maximum of each absorptivity spectrum. When
the in-plane magnetic field is applied, reciprocity is broken, and the
measured dispersion of the absorptivity maxima becomes asymmetric
(Fig. 6, B and C). The degree of reciprocity breaking grows at
narrower angles, which is expected from the absorptivity maxima
found from the simulations (Fig. 6, E and F).
We also observe a clear detuning of the absorptivity maxima with
an increase in the magnetic field. For both the experimental (Fig. 6B)
Fig. 3. Polarization-dependent reflection measurements for varying applied magnetic field.
(
A
) p to p polarization, (
B
) s to s polarization, (
C
) s to p polarization, and
(
D
) p to s polarization. The dotted points are experimental data, and the solid lines are fits to the data points. We only show data for the incident angle
i
= 50° in this
figure; data for other incident angles are included in the Supplementary Materials. We see a clear tuning of the peak position with magnetic field for p to p polarization
but no spectral shape change for s to s polarization. We do not observe polarization conversion, further demonstrating that the change in the p to p polarization is not
due to misalignment of the device in the setup. The data in (A) and (B) are artificially offset to highlight the spectral peak shift (p polarization) and no shift (s polarization).
The data for other angles for p polarization (figs. S2 to S4) also show an intensity change that overall aligns with simulations. a.u., arbitrary units.
Fig. 4. Magnetic field effect on p-polarized absorptivity spectra for bare InAs and
the GMR structure at
i
= 50°.
(
A
) The measured shift in absorptivity of bare InAs as a
function of magnetic field emanates from the splitting of the plasma edge in InAs into
a positive (red) and negative (blue) magnetoplasmon. (
B
) Data for the GMR structure
showing the effect of adding the
-Si structure on top of the InAs wafer, which pro-
duces resonant absorptivity peaks for both positive and negative applied magnetic
fields. (
C
and
D
) The simulated results for bare InAs and the GMR structure, respectively.
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and simulated (Fig. 6E) absorptivity maxima at the intermediate
0.8-T magnetic field, the lineshape width for positive angles of inci-
dence grows considerably. This makes the detuning of the absorp-
tivity maxima at narrow incidence angles difficult to resolve.
Increasing the magnetic field to 1.2 T separates the maxima at narrow
angles such that the 5% bars do not overlap.
Unfortunately, our measurement system only allows for incidence
angles down to 35°, limiting the ability to compare experiments and
Fig. 5. Intensity effect of GMR on nonreciprocal absorption at
i
= 70°.
(
A
) Experimental data at 70° incidence for the GMR structure and
n
-InAs with no patterned
-Si
on top. The blue trace is the offset difference between the GMR and the
n
-InAs to highlight the resonant effect of the GMR. (
B
and
C
) Simulated and experimental data for
positive and negative field showing the strong resonance intensity tuning at this angle.
Fig. 6. Magnetic field strength and angular dependence of reciprocity breaking.
(
A
to
C
) Compiled experimental and simulated (
D
to
F
) absorptivity maxima for
p-polarized light as a function of magnetic field and angle of incidence. When no magnetic field is applied (A and D) the structure behaves reciprocally. At 0.8 T (B and E)
and 1.2 T (C and F), the
n
-InAs no longer satisfies Lorentz reciprocity, and the reciprocal absorptivity relationship is broken. The error bars represent data points in the
spectra to within 5% of the maximum value to give the reader an idea of the line shape. Plots of the individual spectra for other angles are included in the Supplementa-
ry Materials (figs. S2 to S4). (
G
to
I
) Heatmap of the simulated absorptivity over the entire angle of incidence range for varying magnetic fields. Horizontal lines mark the
positive (and negative) incidence ranges shown in (A) to (F).
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simulations for near-normal incidence. However, simulations indi-
cate that the difference for positive and negative incidence (positive
and negative field) decreases and approaches zero as the scattering
geometry approaches normal incidence since the first-order magneto-
optic effects go to zero.
The measured maxima for negative incidence angles do not shift
below the zero magnetic field maxima for oblique angles. This con-
trasts with the maxima extracted from simulations, which redshift
for oblique (−65° and − 70°) angles of incidence.
DISCUSSION
In this study, we use a degenerately doped magneto-optical semi-
conductor paired with a GMR coupled to free-space incident radiation
to demonstrate nonreciprocal absorption in the IR regime when a
moderate magnetic field (
B
up to 1.2 T) bias is applied. The degree
of reciprocity breaking is largest at narrower incidence angles
i
(45° to 55°), making the design potentially useful for cascading mul-
tiple emitters/absorbers to achieve directional flow of energy (
39
).
The methods used to model, design, and fabricate the structure pre-
sented in this manuscript can be used for future implementations of
nonreciprocal absorbers. As a future direction for engineering higher
efficiency thermal radiators, direct measurement of the emissivity
could be used to demonstrate applications of systems that violate the
Kirchhoff thermal radiation law. Higher quality factors of the struc-
ture could be obtained using a thinner magneto-optic layer with a
back reflector or a lower doping concentration of InAs; however,
this would result in a longer working wavelength. A higher mobility
magneto-optic material, such as InSb, could also be used to achieve
a narrower linewidth (
40
). The easily identifiable absorptivity peaks
at the plasma edge are a consequence of using a periodic
-Si struc-
ture supporting a GMR, while the nonreciprocal behavior comes
from the plasma-edge splitting of the magneto-optic n-type InAs.
The temperature dependence of the optical properties of the
n
-InAs
is included in the Supplementary Materials as a reference for de-
signing at elevated temperatures to measure emissivity (fig. S5).
Beyond demonstrating nonreciprocal absorption in the IR, hybrid
magneto-
optic and photonic crystal structures such as those re-
ported here are of potential interest for thermal radiation control
and free-space information processing owing to the polarization-
dependent response and low required magnetic fields for resonance
tunability.
MATERIALS AND METHODS
Device fabrication
Our fabrication of the GMR structure started by deposition of
-Si
on the InAs wafer using plasma-enhanced chemical vapor deposi-
tion. The deposition was carried out at a temperature of 200°C and
a pressure of 800 mtorr with a flow rate of 250 standard cm
3
/min
(5% SiH
4
/Ar) for 90 s. We then spin-coated 500 nm of ZEP 520A
resist (1 min at 2000 rpm) and baked the sample for 5 min at 180°C
on a hot plate.
Electron beam lithography was then used to write the desired
pattern into the resist using a beam current of 100 nA with a 300-
m
aperture and a dose of 240
C/cm
2
. After writing the pattern into
the resist, the sample was dipped in ZED N-50 for 2 min and 30 s for
development. Following exposure, the sample was baked at 140°C
for 3 min.
The
-Si pattern was subsequently etched using inductively
coupled plasma–enhanced reactive ion etching. The etching recipe
began with an O
2
followed by an SF
6
cleaning cycle for 10 min, each
followed by 2 min and 30 s of etching with SF
6
as the etchant gas.
The same cleaning cycle was then repeated in reverse. The sample
was left in remover PG overnight and then checked with a confocal
microscope to ensure that the resist had been removed.
Scanning electron microscope (SEM) images were then taken at
normal and 45° tilted incidence to confirm the GMR structure di-
mensions. For the SEM images shown in this paper, the microscope
was operated at an accelerating voltage of 5 kV.
Measurements
To probe the sample, we used a two-theta stage with a silicon
carbide Globar source and focusing optics, exciting the sample at an
incident angle
i
relative to the
x-z
plane and collect the specular
reflected light at −
i
. For the zero and low (up to but not including
0.8 T) magnetic field measurements, the original sample holder of
the system (J.A.
Woollam I.R.
VASE Mark II) was used. For the
higher magnetic field measurements, we used a separate adapter to
accommodate the Halbach array. The lower magnetic field measure
-
ments are obtained using a specially designed aluminum holder to
separate the two neodymium magnets while holding the sample in
between the two magnets’ poles. The field strength was tuned by
inserting aluminum spacers to increase the gap between the mag-
nets. We used a Halbach array magnet configuration with tunable
pole pieces to apply 0.8 <
B
< 1.2 T (
29
). An image of the magnet
assembly can be found in fig. S7. We measured the magnetic field
strength and uniformity across the sample surface with a transverse
Hall sensor made from InAs (Lakeshore HGT 1010).
The sample was in the Voigt geometry, with an in-plane magnetic
field,
B
, breaking time-reversal symmetry. By changing the sign of
the magnetic field, we produced the same effect as keeping the sign
of magnetic field constant while switching the positions of the source
and detector (
41
–
43
). The use of linear polarizers at both the source
output and detector input allows for a deconvolution of the physical
effects (e.g., ensure that there is no cross-polarization due to sample
misalignment).
Device simulations
We used the COMSOL electromagnetic waves, frequency domain
package to simulate the optical response of the GMR structure. For
the material properties and geometries of the structure, we used the
measured values of the
-Si periodicity and depth from SEM images
and
n
-InAs optical properties from the model fits of ellipsometry
data and four-point probe measurements. For each trace at a fixed
angle of incidence, we swept the wavelength from 16 to 19
m in
12-nm intervals. The absorptivity was found by subtracting the
reflectivity from 1, as there was no transmission for the struc-
ture. This was verified by taking transmission measurements of the
n
-InAs wafer.
SUPPLEMENTARY MATERIALS
Supplementary material for this article is available at https://science.org/doi/10.1126/
sciadv.abm4308
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Acknowledgments:
Y.K. used the Kavli Nanoscience Institute (KNI) at Caltech for fabrication
facilities. K.J.S. would like to acknowledge H.
Akbari, D.
H. Drew, and A.
Laucht for discussions
around the design of the experiment and application of the magnetic field.
Funding:
This
work was supported by DARPA NLM, grant no. HR00111820046 (to K.J.S., B.Z., Y.K., S.F., and
H.A.A.). K.J.S. would like to thank the support by the NSF GRFP for a Graduate Research
Fellowship.
Author contributions:
The manuscript was written through contributions of all
authors. All authors have given approval to the final version of the manuscript. Measurements
were done by K.J.S.
Fabrication was done by Y.K.
The theoretical and modeling work was led by
B.Z. and supported by K.J.S.
Competing interests:
The authors declare that they have no
competing interests.
Data and materials availability:
All data needed to evaluate the
conclusions in the paper are present in the paper and/or the Supplementary Materials.
Submitted 16 September 2021
Accepted 21 March 2022
Published 6 May 2022
10.1126/sciadv.abm4308
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Nonreciprocal infrared absorption via resonant magneto-optical coupling to InAs
Komron J. ShayeganBo ZhaoYonghwi KimShanhui FanHarry A. Atwater
Sci. Adv.
, 8 (
18),
eabm4308.
• DOI: 10.1126/sciadv.abm4308
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