# Spin-valley coupling anisotropy and noise in CMOS quantum dots

Cameron Spence<EMAIL_ADDRESS>Univ. Grenoble Alpes, CNRS,
Grenoble INP, Institut Néel, 38402 Grenoble, France  Bruna Cardoso Paz  Univ.
Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38402 Grenoble, France
Bernhard Klemt  Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38402
Grenoble, France  Emmanuel Chanrion  Univ. Grenoble Alpes, CNRS, Grenoble INP,
Institut Néel, 38402 Grenoble, France  David J. Niegemann  Univ. Grenoble
Alpes, CNRS, Grenoble INP, Institut Néel, 38402 Grenoble, France  Baptiste
Jadot  Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38402
Grenoble, France  Vivien Thiney  Univ. Grenoble Alpes, CNRS, Grenoble INP,
Institut Néel, 38402 Grenoble, France  Benoit Bertrand  CEA, LETI, Minatec
Campus, F-38054 Grenoble, France  Heimanu Niebojewski  CEA, LETI, Minatec
Campus, F-38054 Grenoble, France  Pierre-André Mortemousque  CEA, LETI,
Minatec Campus, F-38054 Grenoble, France  Xavier Jehl  Univ. Grenoble Alpes,
CEA, IRIG, 38000 Grenoble, France  Romain Maurand  Univ. Grenoble Alpes, CEA,
IRIG, 38000 Grenoble, France  Silvano De Franceschi  Univ. Grenoble Alpes,
CEA, IRIG, 38000 Grenoble, France  Maud Vinet  CEA, LETI, Minatec Campus,
F-38054 Grenoble, France  Franck Balestro  Univ. Grenoble Alpes, CNRS,
Grenoble INP, Institut Néel, 38402 Grenoble, France  Christopher Bäuerle
Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38402 Grenoble,
France  Yann-Michel Niquet  Univ. Grenoble Alpes, CEA, IRIG, 38000 Grenoble,
France  Tristan Meunier  Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut
Néel, 38402 Grenoble, France  Matias Urdampilleta
<EMAIL_ADDRESS>Univ. Grenoble Alpes, CNRS, Grenoble INP,
Institut Néel, 38402 Grenoble, France

###### Abstract

One of the main advantages of silicon spin qubits over other solid-state
qubits is their inherent scalability and compatibility with the
$300\text{\,}\mathrm{m}\mathrm{m}$ CMOS fabrication technology that is already
widely used in the semiconductor industry, whilst maintaining high readout and
gate fidelities. We demonstrate detection of a single electron spin using
energy-selective readout in a CMOS-fabricated nanowire device with an
integrated charge detector. We measure a valley splitting of
$0.3\text{\,}\mathrm{m}\mathrm{e}\mathrm{V}$ and
$0.16\text{\,}\mathrm{m}\mathrm{e}\mathrm{V}$ in two similar devices. The
anisotropy of the spin-valley mixing is measured and shown to follow the
dependence expected from the symmetry of the local confinement, indicating low
disorder in the region of the quantum dot. Finally the charge noise in the
spin-valley coupling regime is investigated and found to induce fluctuations
in the qubit energy in the range of
$$0.6\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$/\sqrt{$\text{\,}\mathrm{H}\mathrm{z}$}$.

††preprint: APS

##  I Introduction

Silicon spin qubits are a highly promising candidate for scalable quantum
computation. High-fidelity spin measurement with integrated charge sensing up
to relatively high temperature, fast ESR or EDSR manipulation for one- and
two-qubit gates, and long coherence times in isotopically purified silicon all
point towards the high potential of the silicon platform for solid-state qubit
[1, 2, 4, 3, 5]. Additionally, industrial expertise in CMOS semiconductor
fabrication provides a clear path towards mass production of nanoscale qubit
devices [6, 7]. Spin readout and manipulation have been demonstrated in CMOS
quantum dots with high fidelity [8, 9, 10]. However characterization of the
spin physics in these types of devices remains an open problem, with
indications of local disorder and variability across similar devices [11].

In this letter, we present the measurement of spin relaxation in CMOS quantum
dots fabricated on a foundry-compatible 300 mm wafer. We first show how we can
rapidly probe the spin using an energy selective readout with more than $90\%$
readout fidelity. Secondly, we explore the dynamics of spin relaxation in the
system and the the coupling of spin and valley states, by measuring the spin
lifetime as a function of magnetic field strength and direction. Finally, we
investigate the charge noise in this system by performing spin-valley
relaxometry.

Figure 1:  (a) Schematic of a CMOS-fabricated nanowire type device identical
in structure to the device used here. The polysilicon channel (yellow)
connects two electron reservoirs labelled $S$ and $D$. The electrostatic
environment of the channel is controlled by two front gates, $G_{1}$ and
$G_{2}$, which are isolated from the channel by
$6\text{\,}\mathrm{n}\mathrm{m}$ of SiO2 and $5\text{\,}\mathrm{n}\mathrm{m}$
of TiN. A metallic top gate is positioned $400\text{\,}\mathrm{n}\mathrm{m}$
above the channel in the region indicated by the white dashed lines and is
biased to $+$2\text{\,}\mathrm{V}$$ to increase the coupling between the dots.
Finally, the silicon bulk below the buried oxide is polarized and used as a
back gate(+5V). (b) Stability diagram of the first electron transition. The
electron occupancy of the qubit dot under $G_{1}$ is indicated. The bright
regions of current correspond to coulomb peaks where transport is possible
through the sensor dot under $G_{2}$. The addition of an electron to the qubit
dot causes a shift in the potential of the sensor, indicated by the sharp cut.
(c) Representative time traces of the current through the sensor dot $I_{SD}$
during spin measurement. If a spin-up electron is loaded, it is able to
rapidly tunnel out of the dot, causing a transient shift in the sensor current
as the dot is briefly emptied, indicated in blue. If a spin-down electron is
loaded, it remains in the qubit dot and the sensor current does not change,
indicated in orange. A threshold current $I_{thr}$ is defined to distinguish
between the two states. (d) State fidelity analysis at an optimized
measurement point. A histogram of the maximum current of more than $1000$
measurements is binned (blue). The black dashed line is the total distribution
obtained from simulation of more than 10 000 sample traces using experimental
parameters. Inset: The individual state fidelity is calculated for varying
threshold current level, with $F(\left|\uparrow\right\rangle)$ in blue and
$F(\left|\downarrow\right\rangle)$ in orange. The product of these, the state
visibility $V$, is plotted in green.

The two devices we present here are depicted in Fig.1(a). They consist of a
pair of split front gates, of length $50\text{\,}\mathrm{n}\mathrm{m}$ and
separated by $50\text{\,}\mathrm{n}\mathrm{m}$, which are lying on a silicon
nanowire of width $90\text{\,}\mathrm{n}\mathrm{m}$ and thickness
$15\text{\,}\mathrm{n}\mathrm{m}$. Two electron reservoirs are formed by ion
implantation for the first device and in situ growth of degenerate n-doped
silicon for the second one. They have been measured at low temperature,
between $200$ and $350~{}$\mathrm{mK}$$. At this temperature, a QD is formed
under each front gate, $G_{1}$ and $G_{2}$. We operate the device as follows:
the top quantum dot (QD) is used to trap a single charge and the bottom one as
a charge sensor (CS). Figure 1(b) shows the stability diagram with respect to
$V_{G1}$, $V_{G2}$. Shifts in the coulomb peaks indicate it is possible to
detect the first electron entering the top QD, using the CS. When the QD is
depleted to the few-electron regime, the current passes only through the CS
and electrons are loaded onto QD from CS via the inter-dot tunnel barrier. We
operate the device at the transition signalling the addition of the first
electron in QD.

##  II Single shot readout of a single electron spin

To readout the spin state, we exploit a spin-to-charge conversion based on
energy-selective tunneling [12]. For this purpose, at finite magnetic field,
we first load QD with a single electron and then pulse the chemical potential
where only the highest spin state can tunnel out of the dot. Therefore, when
the electron is in a up spin state, we observe a signal click, characteristic
of the tunneling out of a up spin electron, followed by the tunnelling in of a
down spin electron, depicted in Fig. 1(c) (blue curve). On the opposite, for a
spin down, the signal is constant. It is important to note that similarly to
Ref [12], in both devices, the loading and unloading of QD is achieved through
the CS and not through the reservoir. This single shot detection of the spin
state is further analysed by setting the detection threshold at the point of
maximum visibility. To find this point, we build the histogram presented in
Fig. 1(d) where we bin the maximum of each measurement trace which lasts for
$1~{}$\mathrm{ms}$$ with a sampling rate at $50~{}$\mathrm{kHz}$$. The
visibility is obtained by using the same method as in reference [12], which
consists in simulating single shot traces using the extracted tunneling in and
out times (respectively $250~{}$\mathrm{\SIUnitSymbolMicro s}$$ and
$411~{}$\mathrm{\SIUnitSymbolMicro s}$$) to describe the current distribution.
We obtain an average readout fidelity above 92% (and 86% visibility) limited
by the tunneling in and out rates of the single electron [13].

Figure 2:  (a) Spin-up population during measurement as a function of the
waiting time after loading. It is fitted with an exponential decay function to
extract $T_{1}$, the spin relaxation time. (b) The average relaxation rate
$T_{1}^{-1}$ for two similar devices is plotted as a function of the magnetic
field orthogonal to the nanowire axis. It is fitted (solid line) with a
combination of the spin-valley contribution $\Gamma_{SV}$ (dashed line) and
the spin-orbit contributions $\Gamma_{SO}$ to the relaxation rate. A single
prominent increase of relaxation rate, occurring at $2.6\text{\,}\mathrm{T}$
and $1.7\text{\,}\mathrm{T}$ respectively, is induced by spin valley mixing
close to $E_{Z}=E_{SV}$ and coupling to the phonon bath. Outside of this
hotspot, the spin relaxation is induced by spin-orbit mixing with higher
orbital states.

##  III Spin-valley coupling

We now move on to the characterization of relaxation time. Relaxation curves
are measured by first loading an electron with random spin orientation, and
then probing the spin up population after a given waiting time in the loading
region. We obtain the curve in Fig. 2(a), which is characteristic of spin
relaxation and presents a T1 of $10\text{\,}\mathrm{m}\mathrm{s}$.

###  III.1 Determination of valley splitting

To further investigate the presence of excited states, we measure the
relaxation rate as a function of the magnetic field on the two devices. Figure
2(b) present the results obtained on device 1 and device 2 (blue and red data
points respectively). The two curves feature a hotspot in relaxation at two
different magnetic fields ($2.6\text{\,}\mathrm{T}$ and
$1.6\text{\,}\mathrm{T}$ respectively). At these points, the two valley states
with opposite spins anticross (the valley splitting $E_{VS}$ is equal to the
Zeeman splitting $E_{Z}$), and give rise to a relaxation channel through spin-
valley mixing [14].

To support this interpretation we fit the data points with a model comprising
spin-orbit and spin-valley contributions [14, 15], which is represented by the
blue and red solid lines.

$T_{1}^{-1}=\Gamma_{Ph,SV}+\Gamma_{JN,SO}+\Gamma_{Ph,SO}$ (1)

where $\Gamma_{Ph,SV}$ corresponds to the relaxation rate due to spin-valley
mixing and coupling to phonons, while $\Gamma_{Ph,SO}$ and $\Gamma_{JN,SO}$
correspond to the relaxation rates due to spin orbit coupling via phonons and
Johnson-Nyquist noise respectively. From these fits we obtain a valley
splitting energy, $E_{VS}$, of $191(16)\text{\,}\mathrm{\SIUnitSymbolMicro
eV}$ and $300(13)\text{\,}\mathrm{\SIUnitSymbolMicro eV}$ respectively and a
gap at the spin valley anticrossing of
$4.0(3)\text{\,}\mathrm{\SIUnitSymbolMicro eV}$ and
$0.20(3)\text{\,}\mathrm{\SIUnitSymbolMicro eV}$ respectively. The effect of
Johnson-Nyquist noise on the spin-valley contribution has been neglected as at
the two hotspots the density of phonon modes is high enough to dominate the
relaxation process. The $\Gamma_{Ph,SV}$ contribution is therefore represented
by the dashed blue and red curve which are in good agreement with the
experimental data around the hotspot. The spin orbit contribution (baseline)
follows in both cases a similar model which accounts for Johnson-Nyquist noise
at low field (where the density of phonons is small) and phonon emission at
higher field [16]. Interestingly, the two devices present the same relaxation
rates outside the hotspots. This indicates that the overall structure of the
quantum dots is similar in both cases. This is an important result toward the
realisation of reliable and low variability quantum dots when operated far
from the hotspot.

###  III.2 Anisotropic spin-valley mixing

Figure 3:  Evolution of the relaxation rate with rotation of the magnetic
field. (a-c) Evolution of the relaxation rate within the $XZ$ ($XY$, $YZ$)
plane (under rotation about the $y$ ($z$, $x$) axis, corresponding
approximately to the $[\bar{1}10]$ ($[001]$, $[110]$) crystallographic axis).
Dashed curves in (a) and (b) correspond to sin2 functions fitted to the data.
(d) Schematic representation of the device and its spatial orientation.

The spin valley mixing is an excellent probe of the local symmetry of the
quantum dot [11, 15, 17, 18]. It is indeed expected that the spin-valley
mixing vanishes in the presence of more than one mirror plane in the structure
[9]. The presence of a hotspot is already the sign of a lower symmetry of the
system. The present quantum dots are formed in the corner of the nanowire,
therefore, in absence of local disorder, we expect a single mirror plane with
its normal vector along $\mathbb{x}$, the nanowire axis.

To probe the presence of local disorder, we investigate the anisotropic
behaviour of the spin-valley mixing. Such measurements can be used to
determine the direction of the spin orbit contribution which can be directly
correlated to the local planes of symmetry experienced by the quantum dot.
Figure 3 (a) (b) and (c) presents the measurement of the relaxation rate as
the field direction is rotated in three different orthogonal planes. To
achieve the maximum sensitivity, the magnitude of the magnetic field is set
close to the hotspot where the relaxation rate is dominated by the spin-valley
mixing ($2.4\text{\,}\mathrm{T}$). When the magnetic field scans the XZ and YZ
plane, we observe a drop in the relaxation rate when it crosses the $x$ axis.
On the opposite the relaxation rate is constant in the YZ plane.

To interpret these data, we need to consider the Hamiltonian
$H_{\textrm{SOC}}$ that couples the spin and $v_{1}$, $v_{2}$ valley orbitals
through the spin-valley mixing matrix element
$\left<v_{1}\uparrow\right|H_{\textrm{SOC}}\left|v_{2}\downarrow\right>$,
[19]. In the presence of a (yz) mirror symmetry plane $H_{\textrm{SOC}}$ takes
the form
$H_{\textrm{SOC}}=(\alpha_{y}p_{y}+\alpha_{z}p_{z})\sigma_{x}+(\beta_{y}\sigma_{y}+\beta_{z}\sigma_{z})p_{x}$,
with $p_{x}$, $p_{y}$ and $p_{z}$ the electron momentum along x, y and z
directions and $\sigma_{x}$, $\sigma_{y}$, $\sigma_{z}$ the Pauli matrices.
The valley orbitals $v_{1}$ and $v_{2}$ being invariant by the (yz) mirror
plane,
$\left<v_{1}\right|p_{x}\left|v_{2}\right>=\left<v_{1}\right|-p_{x}\left|v_{2}\right>=0$,
see SI of reference [11]. Therefore the spin mixing term reads
$\left<v_{1}\uparrow\right|(\alpha_{y}p_{y}+\alpha_{z}p_{z})\sigma_{x}\left|v_{2}\downarrow\right>$.
When the magnetic field is aligned with x, $\left|\uparrow\right>$ and
$\left|\downarrow\right>$ are eigenstates of $\sigma_{x}$, which leads to a
vanishing spin-valley mixing. As the magnetic field is tilted away from x with
an angle $\theta$, the remaining projection leads to
$|\left<v_{1}\uparrow\right|H_{\textrm{SOC}}\left|v_{2}\downarrow\right>|^{2}\propto$
sin${}^{2}\theta$ [9, 15]. Following this model, we obtain a quantitative
agreement between the experimental data and the sin2 function as shown in Fig.
3(a) and (b). From these fits, we obtain the minimum relaxation rate along the
nanowire axis ([110]), see diagram in Fig. 3(d). Along this axis, the
relaxation is dominated only by the spin-orbit interaction. It is important to
note that there a slight offset in the angle in the XY measurement because the
nanowire axis is not perfectly aligned with the coil axes. Moreover, the small
discrepancy between the XY and XZ measurements suggests that Y and Z
directions are not equivalent. This second order anisotropy can be explained
by the overlap of the front gate being non equivalent between the side and the
top facets of the wire.

##  IV Low frequency charge noise on valley-splitting

Figure 4:  (a) Variation in the spin-lattice relaxation rate over time. Each
measurement point represents a $T_{1}$ measurement of duration
$4\text{\,}\mathrm{m}\mathrm{i}\mathrm{n}$. (b) Frequency-domain fluctuations
of the valley splitting energy $E_{VS}$. The fit is proportional to
$1/f^{1.25}$. Extrapolation to $1\text{\,}\mathrm{H}\mathrm{z}$ reveals
fluctuations in $E_{VS}$ of
$23(1)\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{e}\mathrm{V}^{2}\mathrm{/}\mathrm{H}\mathrm{z}$.

The valley splitting is sensitive to the electric field as it arises from the
strong confinement against the top interface [20]. Here, we use the relaxation
at the hotspot to probe the local fluctuations in electric field induced by
low frequency charge noise. For this purpose, we sit at a measurement point
next to the hotspot and record the evolution of $T_{1}$ with time. To
transform this time evolution in a power spectral density for $E_{VS}$, we
assume that the dependence of the valley splitting on the electric field is
linear for small noise amplitude [21]. From the hotspot fitting we extract the
gradient at the measurement point, which combined with a Fourrier transform of
the time domain signal, Fig. 4(a), yields the power spectral density (PSD) in
Fig. 4(b).

The PSD follows a $1/f$ dependence which, extrapolated at
$1\text{\,}\mathrm{H}\mathrm{z}$, gives
$23\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{e}\mathrm{V}^{2}\mathrm{/}\mathrm{H}\mathrm{z}$.
In term of qubit energy fluctuations, the obtained value is relatively large
if we consider the operation of the qubit in a spin-valley mode. In this mode,
the spin-valley mixing is exploited to drive coherent oscillations through
electric dipole spin resonance next to the hotspot [19]. Fluctuations of the
valley splitting translate into fluctuations of the Larmor frequency $h\delta
f=1/2\delta E_{VS}$ at the hotspot[9]. It corresponds to a fluctuation in the
spin precession of about
$$0.6\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$/\sqrt{Hz}$, which is faster than
the decoherence rate due to the hyperfine fluctuations in natural silicon, and
is on the order of the decoherence rate of charge and valley qubits [22, 23].
This could prove detrimental for EDSR exploiting the spin-valley mode,
limiting the coherence time when the spin-valley coupling is turned on [24,
25]. It may therefore be necessary to operate further away from the hotspot to
avoid fast decoherence, at the cost of slower Rabi frequency or to lower the
confinement potential to reduce the valley splitting sensitivity to electric
field [19].

##  V Conclusion

In conclusion, we have demonstrated fast and reproducible spin
characterization in CMOS nanowire devices. Similar spin-orbit induced
relaxation rate was found across two identically patterned and fabricated
devices, which is an important result toward the improvement of the CMOS
fabrication process at the quantum dot level. Moreover, the spin-valley
coupling was found to be highly anisotropic, with a strong symmetry plane
oriented perpendicular to the channel axis, indicating the absence of strong
local disorder at the quantum dot site. These results are of prime importance
toward the fabrication of large scale structures containing many quantum dots
with low variability. Finally, low-frequency fluctuations in the valley
splitting were measured to cause fluctuations in the Larmor frequency at
$$0.6\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$/\sqrt{Hz}$ which would be
detrimental to the operation of the qubit as a spin-valley or valley qubit to
enhance Rabi frequencies. This motivates further work on dependence and
sensitivity of the valley splitting with respect to the electric field and the
investigation of potential sweetspot.

##  VI Acknowledgments

We acknowledge fruitful discussions with J. Li and L. Hutin and support from
P. Perrier, H. Rodenas, E. Eyraud, D. Lepoittevin, I. Pheng, T. Crozes, L. Del
Rey, D. Dufeu, J. Jarreau, J. Minet and C. Guttin. D.J.N. , B.K. and C.S.
acknowledge the GreQuE doctoral programs (G.A. No 754303). The device
fabrication is funded through the QuCube project (G. A. 810504) This work is
supported by the Agence Nationale de la Recherche through the CRYMCO and MAQSi
projects (ANR-21-XXX).

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# Multi-Antenna Configuration with Reduced Passive Self-Interference for Full-
Duplex Intelligent Transportation System

Jogesh Chandra Dash, Debdeep Sarkar, J. C. Dash and D. Sarkar are with the
Department of Electrical Communication Engineering, Indian Institute of
Science, Bangalore, Karnataka, 560021, India e-mail<EMAIL_ADDRESS>and
<EMAIL_ADDRESS>
###### Abstract

In this paper, we propose a closely spaced multi-antenna system with passive
self-interference cancellation (p-SIC) of $\approx 90$ dB between the
transmitter and receiver antenna for full-duplex application. The p-SIC is
achieved by field confinement near individual antennae using shorted metallic
vias and the application of U-shaped perturbation in the ground plane. The
p-SIC technique is initially implemented in a 1-Tx and 1-Rx antenna system and
explained using transmission line-based theory. Further, it is extended to
1-Tx and 2-Rx configurations. Here the proposed full-duplex antenna system is
designed at $5.9$ GHz ($5.855-5.925$ GHz, IEEE 802.11p / WAVE technology)
intelligent transportation system (ITS) application band using a microstrip
patch configuration. The individual antenna exhibits an impedance bandwidth of
$93$ MHz ($5.850-5.944$ GHz), $5.63$ dBi gain at $5.9$ GHz operating frequency
and X-pol level less than $20$ dB in the broad side direction. The proposed FD
configuration exhibits $|S_{ij}|$ of less than $-50$ dB over the complete
operating band and $\approx-90$ dB is achieved at the operating frequency
between the Tx and Rx. Similarly, $|S_{ij}|$ of less the $-30$ dB is achieved
between 2-Rx antennas for a three-element FD configuration. The design
procedure of the proposed FD configuration is explained and verified using
fabrication and measurement. An experimental demonstration of the self-
interference channel and its suppression using the proposed p-SIC technique is
also provided. Further, to study the diversity performance of the proposed
multi-antenna configuration, the MIMO performance metrics such as ECC and CCL
are evaluated using simulation and measurement.

###### Index Terms:

Full-Duplex, Microstrip Antenna, Self-Interference Cancellation, Intelligent
Transportation System (ITS), V2X, MIMO, Mutual Coupling Reduction.

##  I Introduction

Intelligent transportation system (ITS) is the future of vehicular wireless
communication as the advanced driving experience and active safety are now
priorities of every autonomous industry for upcoming vehicles. To reduce the
impact on environment and to improve the traffic safety intelligent
transportation systems (ITS) for vehicular communication such as vehicle-to-
vehicle (V2V), vehicle-to-infrastructure (V2I) or in-short vehicle-to-
everything (V2X) communication is the study of great interest for industry as
well as academia [1]. A simplified architecture of ITS showing V2X
connectivity is shown Fig. 1. In addition, ITS caters various smart
applications such as safety warnings, emergency alert, vehicle platooning,
vehicle internet, etc [2].

Figure 1: Simplified architecture of intelligent transportation system (ITS)
showing V2X connectivity.

A report on legacy ITS and advanced ITS is provided in [3]. Accordingly, ITS
is termed as cooperative-ITS (C-ITS) in Europe and some Asia-Pacific regions
which work at the 5.855-5.925 GHz band. Similarly, in the USA and some other
countries in North America dedicated short-range communication (DSRC) serves
under ITS at the operating band of 5.850-5.925 GHz. Apart from C-ITS and DSRC,
some other vehicular communication technologies such as V2X-WAVE (wireless
access in the vehicular environment) and V2X- ITS connect come under ITS based
on 5.9 GHz IEEE 802.11p standard [3].

The ITS application scenario, in contrast to conventional mobile
communication, requires an antenna system enabling ultra-high reliability and
low latency communication [4]. There are certain single antenna configurations
for ITS application available in literature [5] \- [7]. In [5], a low profile
integrated microstrip antenna for dual-band application is proposed. A stacked
slot antenna structure with additional slots on the top metallic part,
floating metal layer, and reflector metal with additional dielectric layers is
proposed in [6], which is quite bulky and may face integration issues in a
vehicle. Similarly, a single left-hand circularly polarised (LHCP) antenna
having $40\times 40$ mm2 size is proposed in [7]. However, future autonomous
vehicles are expected to have a multi-antenna configuration, with 5G
connectivity, installed at different parts of the vehicle to provide $360^{0}$
field-of-view [8], where a single antenna configuration is no longer a
suitable solution for ITS application to cater the demand of ultra-high
reliability and low latency.

Multi-antenna configuration based on full-duplex (FD) technology would be the
best possible solution for ITS application considering the future
requirements. Full-duplex topology concurrently uses time/frequency slots both
for transmission and reception. This can be integrated with the 5G system over
the conventional half-duplex (HD) system, which operates either frequency-
division duplex (FDD) or time-division duplex (TDD), to improve the system
efficiency [9]. A schematic of the HD and FD communication system is provided
in Fig. 2 for better visualization. As far as ITS application is concerned,
the simultaneous transmission and reception capability of FD system
theoretically double the spectral efficiency of HD system [10], which
eventually reduces latency [11]. In addition, the FD technology improves
throughput [11] and provides high-speed ultra-reliable V2X link in vehicular
communication [12]. Moreover, FD technology is one of the candidate
technologies for future 6G services which facilitates enhanced capabilities
than 5G counterpart (see Table 1)) [13] and can efficiently serve the ITS
purpose. However, the key challenge in an FD system is the issue of self-
interference due to the infliction of high-power local transmit a signal upon
its own receiver, which leads to device saturation and failure in receiving
actual signal of interest [14], [15]. To combat SI and make the FD system
applicable in practice the high isolation of more than $100$ dB [16] (however
it may vary based on the type of wireless system [17]) between the transmitter
and receiver unit is highly desirable. In general, such high isolation is
achieved jointly by passive(p) and active(a) SI-cancellation (SIC) techniques,
where p-SIC deals with the antenna/propagation domain SIC and a-SIC deals with
rf/analog and digital domain SIC [9], [18]. However, analog-SIC is not
sufficient to provide enough isolation to restrict the saturation of active
components such as LNA (low noise amplifier) and ADC (analog-to-digital
converter) [19]. On the contrary, the antenna is the very first component in
the rf front end which experiences all external stimuli and activates the rest
of the rf component in the chain. Therefore, to reduce the system cost and
burden on a-SIC stage, p-SIC technique (antenna isolation) is very much
essential in an FD communication system.

Figure 2: Schematic representation of HD and FD communication system.

There are various techniques have been reported to improve the inter-element
isolation between the antenna elements, but either only in transmitting or
receiving mode i.e in the HD scenario. For example, [20] provides an isolation
improvement of $26.2$ dB using a parallel coupled line resonator between two
microstrip antennas, isolation improvement of $22.3$ dB is achieved in [21]
between two microstrip antennas using polarisation conversion isolator.
Similarly, several other techniques such as defected ground structure [22],
split-ring resonator [23], frequency selective surface [24] etc. result in
improved isolation around $15$ dB are reported. It shows that due to either
only transmission or reception capability of HD system there is no issue of SI
here, where it can operate smoothly having limited antenna isolation. However,
this is not the scenario in the FD communication system. There are various
categories of SIC in FD antenna configuration available in the literature.
Polarization multiplexing with hybrid-coupler-based SIC techniques is
exploited in [25] \- [28] and [29] to achieve very high inter-port isolation
in expense of large size and stacked structure respectively. Similarly, a
dual-polarized multi-layered antenna configuration with an additional feeding
network and another dual polarized horn antenna configuration with high inter-
port isolation for FD communication are proposed in [30] and [31] respective.
However, due to their multi-layered and bulky structure, these are not
suitable for integration in compact modules. A dual-polarized rectangular
cavity-backed antenna with high inter-port isolation is described in [32]. The
antenna has a 3D volumetric structure with very complex design and integration
challenges. Co-linearly polarized compact size microstrip antenna with fence-
strip resonator (FSR) for good isolation between transmitter and receiver
port, a stacked structure FD antenna with the combination of a microstrip and
surface integrated waveguide cavity backed slot antenna with cavity-patch
coupling (CPC) path is added for cancelling the slot-patch coupling (SPC) by
using four probe and surface integrated wave guide based FD antenna with SIC
using metallic vias are proposed in [33], [34] and [35] respectively. However,
the techniques proposed in [33] \- [35] provides SIC between $30-40$ dB, which
is quite limited for FD communication. In our earlier work, a very closely
spaced planer FD antenna configuration having $90$ dB inter-port isolation, at
the operating frequency, between the antenna elements is proposed in [15].

TABLE I: Performance Comparison between 5G and 6G [13] Performance parameter | 5G | 6G
---|---|---
Energy Efficiency | $1x$ | $2x$
Spectral Efficiency | $1x$ | $2x$
Air Latency (ms) | $1$ | $0.1$
Connection Density (devices/km^2) | $10^{6}$ | $10^{7}$
Reliability | $10^{-6}$ | $10^{-7}$
Peak Data Rate (Gbps) | $20$ | $1000$
User Experience Data Rate (Gbps) | $0.1$ | $1$

Therefore, considering the application scenario and requirement for FD
communication system in ITS, in this paper, we propose a very closely spaced
planer easy to integrate FD antenna systems with a very high p-SIC. This work
builds upon work earlier work [36] by: (i) a detailed explanation for
2-element FD-antenna (1-Tx and 1-Rx) design steps and working mechanism of
proposed p-SIC technique, (ii) extension of 2-element FD-antenna to 3-element
antenna system having 1-Tx and 2-Rx (or 2-Tx and 1-Rx) configuration followed
by fabrication, measurement and study of multi-antenna (MIMO) performance, and
(iii) experimental demonstration of the real-time self-interference channel
and its suppression using proposed p-SIC technique. To the best of the
authors’ knowledge, a compact FD antenna configuration having more than $85$
dB of p-SIC and antenna performance parameters such as a gain of $5.6$ dB, a
cross-polar level less than $-20$ dB with good MIMO diversity for ITS
application is not available in the open literature.

##  II  Design and p-SIC Mechanism of two element (1-Tx and 1-Rx) Full Duplex
Antenna System

The 3D perspective view of the proposed two port (1-Tx and 1-Rx) FD antenna is
shown in Fig. 3. The antenna is designed on the RTD 5880 dielectric substrate
having dielectric constant $\epsilon_{r}=2.2$, dielectric loss tangent
$tan\delta=0.0009$ and $1.6$ mm thickness ($h$). The overall substrate
dimension is $L_{g}\times W_{g}(38$ mm $\times 80$ mm). In this section, the
design stages of the proposed FD structure with the p-SIC (antenna isolation)
mechanism are discussed. For every design stage the corresponding E- and H-
field distribution along the isolation parameter ($S_{ij}$, where $i\neq j$)
are utilised to illustrate the operating mechanism.

Figure 3: 3D schematic representation of proposed 2-element FD antenna.

###  II-A Design Stage-1

Initially, two element inset-fed microstrip patch antennas are placed in a
closed proximity ($g$) with $180^{0}$ orientation representing Tx and Rx
antenna for FD communication as shown in Fig. 4. The inset-fed structure is
powered through a co-axial probe. The dimensions (see Fig. 4) of physical
notch width ($g_{1}$), width of microstrip feed line ($w_{f}$) and the inset
depth ($l_{1}$) are considered to maintain the individual antenna input
impedance at the operating frequency which can be approximately computed using
the following equations [37], [38]

$R_{in}=R_{in}(l_{1}=0).cos^{4}\left(\frac{\pi l_{1}}{w}\right)$ (1)
$R_{in}(l_{1}=0)=\frac{1}{2G}=\frac{1}{2}.\left(\frac{w}{120\lambda_{0}}\left[1-\frac{(k_{0}h)^{2}}{24}\right]\right)^{-1}$
(2)

where $R_{in}$ and $R_{in}(l_{1}=0)$ are the input impedance of the patch at
$l_{1}$ and zero inset depth respectively. $G$ is the radiating edge
conductance of the patch and $h$ denotes the substrate thickness. $k_{0}$ and
$\lambda_{0}$ represent the free space wave-number and wavelength
respectively.

The individual antenna element operates in $TM_{01}$ fundamental mode at $5.9$
GHz operating frequency having $3.38\%$ $-10$ dB impedance bandwidth
($\%$IBW)(See Fig. 5). Fig. 5 (a) and (b) depict the E- and H-field
distribution showing the strong inter-element coupling between the antenna
elements, which can also be observed from the S-parameter curve in Fig. 5(c)
having very high value of $|S_{21}|=|S_{12}|=-11.8$ dB. This strong coupling
is due to the close inter-element spacing and identical polarization of the Tx
and Rx antennas.

Figure 4: Schematic of two inset-fed patch antenna designed at 5.9 GHz
operating frequency. Dimension (in mm):
$l_{p}=16.2,w_{p}=21.6,l_{f}=8,w_{f}=2.75,l_{1}=5,g_{1}=0.625,g=6.$ Figure 5:
(a) E-field, (b) H-field distribution at 5.9 GHz (Port-1 is excited while
terminating port-2 to matched load), and (c) Frequency variation of
S-parameters of design Stage-1 as shown in Fig. 4.

###  II-B Design Stage-II

Fig. 6 shows the schematic of antenna design at stage-II. In this design
stage, initially two shorting vias are placed at two corners of Tx
(@$-l_{p}/2$, see Fig. 4) and RX (@$l_{p}/2$, see Fig. 4) antenna elements.
Further, a series of shorting vias are placed along at $g_{3}$ distance away
from the non-radiating edges of the antennas along the $y$ direction, see Fig.
6. Here, the shorting via diameter ($d$) and distance between two consecutive
vias ($p$) are $1$ mm and $1.5$ mm respectively. The objective of this design
stage is reduce the high field coupling zone in the antenna elements and to
limit the power flow between the Tx and Rx antenna by restricting the surface
wave. It is evident from Fig. 5 (a) that the E-field coupling intensity has
reduced compared to stage-I, which is also reflected in S-parameter response
(see Fig. 7(c). The $|S_{21}|$ parameter is reduced to $-19$ dB in this stage.
The stage-II design exhibits no adverse effect to antenna polarization and
operating frequency though it reduces the antenna $\%$IBW to $1.6$.

###  II-C Design Stage-III

In this stage, to reduced the H-field coupling present in stage-II (see Fig.
7(b)) and to further reduce the E-field coupling, a series of shorting vias
are placed at E-field minima positions (see Fig. 7(a)) of both Tx and Rx
antenna along $x$-direction as shown in Fig. 8. The shorting pin dimension and
the relation gap between the pins are kept identical as in stage-II. The
loading of shorting vias along width of the patch at the zero potential
location reduces the antenna size and made antenna operate at $TM_{0,1/2}$
mode. It is clearly visible in the Fig. 9 (a) and (b) that the changes made in
this design stage reduces the field coupling compared to stage-II (see Fig.
7). Similarly, the $|S_{21}|$ response reduces to $-31$ dB without affecting
antenna impedance matching and bandwidth. The isolation achieved in this stage
is suitable for HD applications, however this is not desirable for a FD
systems.

Figure 6: Schematic of two inset-fed patch antenna designed at 5.9 GHz
operating frequency. Dimension (in mm): $l_{p1}=20.52$, $w_{p}=21.6$,
$l^{\prime}_{1}=7.1$, $g^{\prime}_{1}=1.625$, $w^{\prime}_{f}=1.75$,
$l^{\prime}_{f1}=10.1$, $g_{2}=0.75$, $g_{3}=1.5$, $g=6$. Figure 7: (a)
E-field, (b) H-field distribution at 5.9 GHz (Port-1 is excited while
terminating port-2 to matched load), and (c) Frequency variation of
S-parameters of design Stage-1.5 as shown in Fig. 6. Figure 8: Schematic of
two inset-fed patch antenna designed at 5.9 GHz operating frequency. Dimension
(in mm): $l_{p2}=13.2$, $w_{p}=21.6$, $l^{\prime}_{2}=7.6$,
$g^{\prime}_{1}=1.625$, $w^{\prime}_{f}=1.75$, $l^{\prime}_{f2}=10.6$,
$g_{2}=0.75$, $g_{3}=1.5$, $g=6$, $d=1$, $p=1.5$. Figure 9: (a) E-field, (b)
H-field distribution at 5.9 GHz (Port-1 is excited while terminating port-2 to
matched load), and (c) Frequency variation of S-parameters of design Stage-1
as shown in Fig. 4.

###  II-D Design Stage-IV

In this stage, two U-shaped perturbations are incorporated in the ground plane
near the feed locations of both Tx and Rx to achieve the desired p-SIC
(antenna isolation) between the Tx and Rx antennas. The schematic of the final
FD antenna configuration is depicted in Fig. 10. The proposed antenna
arrangement with the ground plane perturbation provides band-stop
characteristics, which can easily be explained using the transmission line
analogy.

Figure 10: Schematic of two inset-fed patch antenna designed at 5.9 GHz
operating frequency. Dimension (in mm): $l_{d1}=3$, $l_{d2}=11.5$, $w_{d}=1$,
$d_{s}=0.5$, $y_{s}=21.15$. Figure 11: Variation of $S21$ with frequency for
the microstriop transmission line (m-line) analogy of the proposed two port FD
antenna as showing in Fig. 10 without and with DGS.(Dimensions in mm:
$l_{t}=12.4,w_{t}=1.05$), $l_{d1}=4,l_{d2}=13.22,w_{d}=1$).

  * •

p-SIC (Antenna Isolation) Mechanism using Transmission Analogy: A microstrip
transmission line is designed at $5.9$ GHz operating frequency, as shown in
Fig. 11 (inset), on a RTD 5880 substrate to best describe the proposed antenna
configuration. $l_{t}$, $w_{t}$, p1 and p2 are the length, width and the two
ports of the transmission line respectively. $|S_{21}|=-0.05$ dB response of
Fig. 11 for the transmission line without slots shows a passband response
centered at $5.9$ GHz operating frequency. Further, two U-shaped perturbations
are incorporated in the ground plane (i.e. defected ground structure (DGS)) of
the transmission line near p1 and p2, as shown in Fig. 11 (inset). Similarly,
the $|S_{21}|=-41.28$ dB response of the two DGSs loaded transmission line
showing the stop-band response ($|S_{21}|=|S_{21}|$) at 5.9 GHz operating
frequency is shown in Fig. 11. The design guidelines and equivalent circuit
model of the DGS can be found from [39], where the length ($2l_{d1}+l_{d2}$)
and width ($w_{d}$) of the DGS defines the resonant frequency which can be
represented using an $LC$ equivalent circuit.

The analysis can be re-direct to the stage-IV response as shown in Fig. 12.
Fig. 12 (a) and (b) show the E- and H-field distributions of the final FD
antenna configuration shown in Fig. 10, which depict approximately no field
coupling between the Tx and Rx antenna element. This can also be observed in
the S-parameter curve in Fig. 12 (c), where the isolation ($|S_{21}|$) is
$87.08$ dB at the $5.9$ GHz operating frequency and more the $50$ dB over the
operating band ($5.85-5.944$ GHz), which is very high compared to earlier
stage-I and suitable for FD application. Dimensions of DGS, $g_{2}$ and
$y_{s}$ are obtained using parametric study, as described in [36] to get the
best possible p-SIC between the Tx and Rx antennas.

  * •

Effect of Ground Plane on Proposed FD Antenna Performance: The parametric
studies on the antenna ground plane dimensions ($L_{g}$ and $W_{g}$) are
conducted as shown in Fig. 13 (a) and (b). It can be observed in Fig. 13 (a)
and (b) that isolation between the antenna elements varies with the variation
of the antenna ground plane. The variation in the ground plane varies the
electrical path length of the current distribution between the slots and
eventually changes the effective inductive reactance introduced by the slots
at the operating frequency [40], thereby changing the isolation between
antenna elements. However, the antenna $|S_{11}|$ parameter is unaffected (see
Fig. 13(a) and (b)) as the ground plane variation does not affect the current
distribution in the radiating patch. The stated design parameters for the
proposed antenna are chosen for the ground plane size of $L_{g}\times
W_{g}=38$ mm$\times 80$ mm to adequately confined the microstrip antenna
fringing field and to get the best possible antenna performance.

Figure 12: (a) E-field, (b) H-field distribution at 5.9 GHz (Port-1 is excited
while terminating port-2 to matched load), and (c) Frequency variation of
S-parameters of design Stage-2 as shown in Fig. 8.

(a)

(b)

Figure 13: Parametric studies on ground plane dimensions (a) $L_{g}$, and (b)
$W_{g}$ (Unit: mm).

##  III Design of Multi-Element ($1-$Tx and $2-$Rx) Full Duplex Antenna System

The $1-$Tx and $1-$Rx FD antenna system is extended to $1-$Tx and $2-$Rx FD
system to verify the design scalability of the proposed p-SIC technique.
Moreover, the multi-antenna receiver system provides the additional degree of
freedom to improve the system diversity, i.e. the capability of multiple-input
multiple-output (MIMO) configuration, in a multi-path crowded application
environment as in ITS. The schematic of the proposed $3-$element ($1-$Tx and
$2-$Rx) FD antenna system is shown in Fig. 14. The S-parameter response of
this FD configuration is provided in Fig. 15, illustrates more than $70$ dB
p-SIC between $Tx_{1}$-$Rx_{1}$ and $Tx_{1}$-$Rx_{2}$ at the 5.9 GHz operating
frequency, which satisfies the FD requirements. Moreover, the isolation
between two Rx element is more than 30 dB over the operating band full fills
the MIMO requirement. S-parameter response in Fig. 15 signifies that the
proposed p-SIC technique is also applicable to the $3-$element FD system with
a minor design modification on $l_{d}$, $y_{s}$ and $g_{2}$. The modified
design parameters are provided in Fig. 14.

Figure 14: Schematic of 3-element (1-Tx and 2-Rx) in-set fed FD antenna system
at 5.9 GHz. Dimension (in mm):
$l_{d}=2l_{d1}+l_{d2}=17.15,y_{s}=0.65,g_{2}=2.$ Figure 15: Frequency
variation of S-parameters of 3-element (1-Tx and 2-Rx) FD antenna system as
shown in Fig. 14.

##  IV Prototype Fabrication and Measurement Results

The fabricated prototype of the proposed two and three element FD antenna
system are shown in Fig. 16 and 17 respectively. The S-parameters of these two
and three element prototypes are measured using Agilent N5230A PNA and
compared with the simulation results as shown in Fig. 18 and 19 respectively
with their measurement set-up. Similarly , the 2D radiation pattern of Tx
antenna element showing the simulated and measured curves of two and element
configuration are provided in Fig. 20 and 21 respectively. The X-pol level of
the two and three element configuration is below $20$ dB. The measured results
are in good agreement with the simulated ones, which validates the proposed
p-SIC technique. A complete performance parameters of the proposed FD antenna
configuration provided in table II.

Figure 16: Fabricated prototype of the proposed 2-element FD antenna system of Fig. 3: (a) Top view, (b) Bottom view and (c) Far-field radiation pattern measurement setup in Anechoic chamber. Figure 17: Fabricated prototype of the proposed 3-element FD antenna system of Fig. 14: (a) Top view, (b) Bottom view and (c) Far-field radiation pattern measurement setup in Anechoic chamber. Figure 18: Frequency variation of simulate and measured S-parameters of 2-element (1-Tx and 2-Rx) FD antenna system as shown in Fig. 3. Figure 19: Frequency variation of simulate and measured S-parameters of 3-element (1-Tx and 2-Rx) FD antenna system as shown in Fig. 3. Figure 20: 2D radiation pattern of the Tx antenna of 2-element prototype of Fig. 16 (a) xoz-plane, (b) yoz-plane. Figure 21: 2D radiation pattern of the Tx antenna of 3-element prototype of Fig. 17 (a) xoz-plane, (b) yoz-plane. TABLE II: Proposed 2-element FD Antenna Performance Parameter Parameter | value
---|---
No of antenna element |  $2$($1$-Tx and $1$-Rx)
Operating Frequency |  $5.9$ GHz
Impedance Bandwidth |  $5850-5944$ MHz
Maximum Gain |  $5.63$ dBi
Total efficiency | $90.5\%$
Cross polar level |  $<20$ dB
Maximum \textit{p}-SIC |  $\approx 90$ dB
Application | FD ITS
Figure 22: Schematic representation of real-time measurement setup to observe
self-interference channel.

###  IV-A Experimental Demonstration of Self-Interference Channel Between Tx
and Rx and Its Suppression using Proposed p-SIC Technique

We carried out two-set of experiments using stage-I (See Fig. 4) and stage-IV
(see Fig. 10) FD antenna to visualize the real-time self-interference between
Tx and Rx. The schematic representation of experimental set-up is shown in
Fig. 22, as described in [41]. Here, we use Adalm-Pluto software defined radio
(SDR) through the MATLAB’s-Simulink as a source (transmitter) and Tektronix
RSA306B real-time spectrum analyser as receiver connected to Tx and Rx of FD-
antenna respectively as shown in Fig. 22. Fig. 23 (a) and (b) show the real-
time experimental set-up using proposed stage-I and stage-IV FD-antenna along
with the DPX (Digital Phosphor Technology)-spectrum indicating the self-
interference between the Tx and Rx of FD antenna when operating
simultaneously. It is clearly observed that the FD-antenna having least Tx-Rx
coupling (see Fig. 23(a)) shows nearly no interference above system noise
floor (here $-90$ dB) compared to FD-antenna having high Tx-Rx coupling (see
Fig. 23(a)), which exhibits very high (nearly $40$ dB above system noise
floor) signal interference. This signifies the practical utility of the
proposed p-SIC technique.

(a)

(b)

Figure 23: Received DPX (Digital Phosphor Technology)-spectrum at $5.9$ GHz
opearting frequency and measurement setup (inset) showing the signal
interference between the Tx and Rx of (a) Stage-I, and (b) Stage-IV FD-antenna
module. (SDR: Software Defined Radio, SA: Spectrum Analyser)

###  IV-B MIMO Performance Parameters

MIMO performance study of the proposed two and three element FD antenna
configuration is carried out by evaluating envelop correlation coefficient
(ECC) and channel capacity loss (CCL) in the operating band (see Fig. 24 (a)
and (b)) as discussed in [15]. The value of ECC is much less than 0.5 in the
uniform propagation environment, which indicates excellent diversity
performance, which is further reflected in the low value of channel capacity
loss ($<0.5$ bits/s/Hz) in the operating band.

(a)

(b)

Figure 24: Parametric study of design parameters: (a) $l_{d}$, (b) $y_{s}$ and
(c) $g_{2}$ to observe the effect of parameter variation on FD antenna
S-parameter. (Unit: mm)

##  V Conclusion

In this paper, the design of a two-element, as well as a three-element inset-
fed antenna configuration for FD implementation, are presented along with a
novel p-SIC technique between the antenna elements. The complete proposed FD
antenna configuration, together with p-SIC technique, is planar in form, easy
to implement, and avoids the conventional use of bulky hybrid coupler-based FD
antenna technique to achieve high p-SIC. The mechanism of the proposed p-SIC
technique along with antenna design steps is described using field
distribution between the antenna elements and DGS loaded microstrip line
analogy. The p-SIC technique provides the maximum isolation of $\approx 90$ dB
and $\approx 80$ dB for two and element FD antenna configuration respectively.
It is verified using a real-time experimental demonstration using SDR and SA
that the proposed p-SIC effectively suppresses the unwanted signal
interference in Rx from its own Tx. Further, MIMO performance parameters such
as ECC and CCL are evaluated to study the diversity performance of the
proposed FD antenna systems. The antenna configurations are best suitable for
FD ITS application.

##  VI Acknowledgement

Authors would like to thank Prof. K. J. Vinoy, Chair, Dept. of ECE, IISc
Bangalore for providing the measurement facilities (PNA and Anechoic chamber).
Authors would also like to thank Mr. Debaprasad Barad (M. Tech, Res) and Mr.
Yugesh Chandrakapure (M. Tech), ECE, IISc Bangalore for their help in
fabrication and measurement respectively. This work is jointly supported by
IoE-IISc postdoctoral fellowship and SID-IISc.

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# Current-induced magnon trapping in spin torque oscillation

Takahiko Makiuchi<EMAIL_ADDRESS>Quantum-Phase Electronics
Center, the University of Tokyo, Tokyo 113-8656, Japan.  Naoki Kanazawa  IBM
Quantum, IBM Research – Tokyo, Tokyo 103-8510, Japan.  Eiji Saitoh  Quantum-
Phase Electronics Center, the University of Tokyo, Tokyo 113-8656, Japan.
Department of Applied Physics, the University of Tokyo, Tokyo 113-8656, Japan.
Institute for AI and Beyond, the University of Tokyo, Tokyo 113-8656, Japan.
RIKEN Center for Emergent Matter Science (CEMS), Wako 0351–0198, Japan.
Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577,
Japan.  Advanced Science Research Center, Japan Atomic Energy Agency, Tokai
319-1195, Japan.

###### Abstract

Spin torque nano-oscillators realized by magnetization dynamics trapped in a
current-induced potential are reported. We fabricated Ni81Fe19/Pt
nanostructures and measured current-induced microwave emission from the
structures. The result shows an increase in the magnitude and spectral
narrowing of the microwave emission. We demonstrate that the current-induced
magnetic field suppresses magnon radiation loss and significantly reduces the
linewidth and the threshold current required for the spin torque oscillation.

Spin Hall nano-oscillator, spin torque nano-oscillator, microwave generation,
low temperature, nonlinear effect, magnetization dynamics, spintronics

††preprint: v2

Spin torque oscillators have gained significant interest in their ability to
convert direct current into microwave [1, 2, 3, 4]. This conversion occurs
when the spin-transfer torque, which is proportional to the intensity of the
direct current, surpasses a damping and initiates magnetic oscillation. One of
the primary contributors to the damping is the diffusion of magnons beyond the
excitation region [5]. While one approach to address this issue is to
fabricate small magnetic structures, this method often introduces defects
during processing, which can serve as additional sources of damping.

In this study, we demonstrate that the direct current not only induces the
magnetic oscillation but also stabilizes it through the Oersted field
(induction magnetic field). To clarify the effect of the Oersted field, we
utilize spin torque nano-oscillators (STNOs) comprising a ferromagnetic
permalloy (Ni81Fe19 or NiFe) and heavy-metal platinum (Pt) bilayer [6, 7, 8,
9, 10, 11]. We change the profile of current-induced Oersted field by
employing two types of STNOs with reversed layer orders: NiFe/Pt (Ni81Fe19 on
Pt) and Pt/NiFe. We show that only the NiFe/Pt STNO exhibits a trapping
Oersted field for spin waves (magnons). Spectroscopic experiments reveal that
the NiFe/Pt configuration yields a larger microwave intensity, narrower
linewidth, and smaller threshold current, attributed to the current-induced
trapping effect on spin waves. The NiFe/Pt configuration exhibits a localized
magnetic oscillation, whereas the Pt/NiFe configuration, with an anti-trapping
Oersted field, shows extended and unstable oscillation profiles.

Figure 1: (a) Cross-sectional illustration of a Ni81Fe19/Pt STNO. (b,c)
Calculated Oersted field in the Ni81Fe19 layer for the NiFe/Pt and Pt/NiFe
STNOs, respectively. The input direct current is $I=-20$ mA.

First, we calculate the spatial profile of the Oersted field for three-
dimensional STNO models by using the finite element method (COMSOL
Multiphysics). The device consists of an extended bilayer disk of Ni81Fe19(5
nm)/Pt(5 nm) on which triangular Au(80 nm)/Ti(10 nm) electrodes are formed, as
shown in Fig. 1(a). The values in the parentheses are the thicknesses. The
diameter of the bilayer disk is 4 µm. Each Au/Ti electrode has a round tip of
50 nm in radius, and the pair of electrodes is placed with a 100 nm gap. A
direct current of $I=-20$ mA (current from $+y$) is supplied to the
electrodes. The electrical conductance values of
$\sigma_{\mathrm{Au}}>\sigma_{\mathrm{Pt}}>\sigma_{\mathrm{Ti}}>\sigma_{\mathrm{Ni_{81}Fe_{19}}}$
(45.6, 8.9, 2.6, 1.74 MS/m, respectively) are used. A large portion of the
direct current passes through the Au/Ti electrodes and goes into the Pt layer
near the nano-gap region. The simulation yields the Oersted field and charge
current density.

Figures 1(b) and 1(c) illustrate the Oersted fields in the NiFe layer of the
NiFe/Pt and Pt/NiFe STNO, respectively. In the NiFe/Pt device, a local dip
appears in the nano-gap region where the current penetrates into the
underlying Pt layer [Fig. 1(a)]. The dip of the Oersted field serves as a
trapping potential for spin waves [12, 13, 14]. In contrast, the Pt/NiFe STNO
exhibits a saddle-like field profile in the proximity of the nano-gap.

The current density profiles ($j_{x},\ j_{y}$) in the Pt layer are similar in
both NiFe/Pt and Pt/NiFe devices. The current density reaches a minimum of
approximately $j_{y}\approx-6\times 10^{12}\ \mathrm{A/m^{2}}$ at the center
of the nano-gap in both cases. Consequently, the same value of current $I$
yields a similar amount of spin-transfer torque, irrespective of the layer
order. Therefore, any observed differences in experiments and simulations are
likely to stem from variations in the Oersted field.

To investigate the impact of the Oersted field on magnetic oscillation, we
fabricate two types of STNO and conducted spectroscopic measurements. We
prepare sputtered Ni81Fe19(5 nm)/Pt(5 nm) and Pt(5 nm)/Ni81Fe19(5 nm) films on
separate sapphire substrates. Each film is shaped into a 4-µm-diameter disk
with electron beam lithography and Ar ion milling techniques. We make a pair
of nano-gapped Au(80 nm)/Ti(10 nm) electrodes on each disk by using an
electron beam lithography and sputtering. Figure 2(a) is a scanning electron
microscope image of the NiFe/Pt STNO. Both NiFe/Pt and Pt/NiFe STNOs have the
same Au/Ti electrode gap of 110 nm. The electrodes are wire-bonded to a
waveguide that introduces the direct current and receives the microwave
generated by the STNO.

The STNO is placed inside a cryostat with a superconducting magnet. The angle
between the current $I$ and the external field $B_{\mathrm{ext}}$ directions
is set to 120 degrees as shown in Fig. 2(a), which is the optimum condition
for the microwave generation in terms of the spin polarization direction and
anisotropic magnetoresistance [7, 11]. The cryogenic environment helps to
decrease the magnetic damping. The ambient temperature is kept at 1.8 K while
the STNO is heated above 10 K during the current injection, inferred from the
device resistance. We inject the direct current and retrieved the microwave
signal from the STNO with a bias tee. The microwave is amplified and measured
with a spectrum analyzer, as shown in 2(b). The gain and loss in the microwave
components are subtracted from the presented data.

Figure 2: (a) Scanning electron microscope image of the NiFe/Pt STNO. The gap
is 110 nm. The arrows indicate positive directions of $I$ and
$B_{\mathrm{ext}}$. (b) Measurement circuit. (c) Microwave signal from the
NiFe/Pt STNO. (d) Highest $Q$ power spectral density (PSD) from the NiFe/Pt
STNO. The red curve is a Lorenzian fitting. $B_{\mathrm{ext}}=30$ mT; $I=-$
39.2 mA; $Q=6900$. (e) Microwave signal from the Pt/NiFe STNO. (f) Highest $Q$
PSD from the Pt/NiFe STNO. $B_{\mathrm{ext}}=30$ mT; $I=$ 50.8 mA; $Q=990$.

Figures 2(c) and 2(e) depict the microwave power spectrum as a function of the
direct current for the NiFe/Pt and Pt/NiFe STNOs, respectively. The direction
of the external field $\mathbf{B}_{\mathrm{ext}}$ is fixed, and the sign of
the direct current $I$ is reversed for the two STNOs to observe microwave
signals. The signs of $I$ align consistently with the anti-damping spin-
transfer torque direction for the different layer orders. The threshold
currents for the onset of the microwave signal are remarkably different. The
signal appears above $|I_{\mathrm{th}}|=$ 33 mA in Fig. 2(c), whereas it
requires a notably larger current of $I_{\mathrm{th}}=$ 46 mA in Fig. 2(e).
Two modes coexist at 33 mA $<|I|<$ 38 mA in Fig. 2(c). The higher frequency
mode survives above 38 mA and is entrained to the lower frequency. The
different frequency modes are attributed to modes with different spatial
profiles of the oscillating magnetic moments. The lower and higher frequency
modes can be assigned as bullet and quasi-linear modes, respectively [15, 9,
11, 16]. The bullet mode is a localized mode that, in principle, does not
propagate spin waves [15]. The quasi-linear mode is not as strongly detuned as
the bullet mode from the linear magnon dispersion, allowing it to radiate spin
waves. In contrast, the two modes in Fig. 2(e) are broader and do not coexist
at the same $I$. The coexistence of the two modes [2(c)] indicates that the
mode coupling is strong enough to support energy exchange between them,
whereas their separation [2(e)] indicates that only the mode with a smaller
threshold current is realized due to weak coupling resulting from spatial
separation.

All the modes in Figs. 2(c) and 2(e) have lower frequency than the linear mode
frequency expressed by the Kittel formula
$\omega=\gamma\sqrt{B_{\mathrm{ext}}(B_{\mathrm{ext}}+\mu_{0}M_{\mathrm{s}})}=2\pi\times
4.3$ GHz. These redshifts are consistent with the nonlinear frequency shift
[15, 7] and/or the reduction of the local resonant frequency by the Oersted
field. Here, $\gamma$ is the gyromagnetic ratio, $\mu_{0}$ is the
permeability, and $M_{\mathrm{s}}$ is the saturation magnetization. We
obtained $\mu_{0}M_{\mathrm{s}}=760$ mT from a spin-torque ferromagnetic
resonance measurement on a similar STNO device [17, 18, 19].

The power spectral density (PSD) with the highest quality (Q) factor for each
device is plotted in Figs. 2(d) and 2(f). There is an order of magnitude
difference between the maximal PSDs (26 pW/MHz for the NiFe/Pt device and 1.3
pW/MHz for the Pt/NiFe device) and their corresponding Q factors ($Q=6900$ for
the NiFe/Pt device and 990 for the Pt/NiFe device). These essential
improvements in the NiFe/Pt device can be attributed to the effect of the
Oersted field trapping, by which the localized mode cannot diffuse outside the
excited region.

We conduct micromagnetic simulations using MuMax3 [20] with geometry closely
resembling the experimental setup. The Ni81Fe19 layer is a 5-nm-thick disk of
4 µm in diameter. The entire system is divided into 1024 $\times$ 1024
$\times$ 1 rectangular cells, forming a 4000 nm $\times$ 4000 nm $\times$ 5 nm
cuboid space. The applied in-plane external field $\mathbf{B}_{\mathrm{ext}}$
is tilted at an angle of 120 degrees relative to the current direction and
$|\mathbf{B}_{\mathrm{ext}}|=30$ mT, as in the experiment. The effect of the
Pt layer is taken into consideration to provide spatially-varying spin current
and Oersted field $\mathbf{B}_{\mathrm{Oe}}$ into the Ni81Fe19 layer. The
Slonczewski anti-damping spin-transfer torque acting on the Ni81Fe19
magnetization is described by [20]

$\bm{\tau}\approx\frac{\theta_{\mathrm{SH}}j_{\mathrm{c}}\gamma\hbar
P}{2M_{\mathrm{s}}ed}\mathbf{m}\times(\mathbf{m}_{\mathrm{P}}\times\mathbf{m}),$
(1)

where $\theta_{\mathrm{SH}}=0.07$ is the spin Hall angle of Pt, ($j_{x},\
j_{y}$) is the current density profile in the Pt layer with
$j_{\mathrm{c}}=\sqrt{j_{x}^{2}+j_{y}^{2}}$, $\hbar$ is the Dirac constant,
$P=1$ is the spin polarization, $M_{\mathrm{s}}=597$ kA/m is the saturation
magnetization, $e$ is the elementary charge, $d=5$ nm is the Ni81Fe19
thickness, $\mathbf{m}$ is the reduced magnetization, and
$\mathbf{m}_{\mathrm{P}}=\pm(-j_{y}/j_{\mathrm{c}},j_{x}/j_{\mathrm{c}},0)$ is
the spin polarization direction. The sign in $\mathbf{m}_{\mathrm{P}}$ depends
on the layer order ($-$ for NiFe/Pt and $+$ for Pt/NiFe). Spatial profiles of
$j_{\mathrm{c}}$, $\mathbf{m}_{\mathrm{P}}$ and $\mathbf{B}_{\mathrm{Oe}}$,
calculated with COMSOL, are incorporated in the MuMax3 simulation.
$j_{\mathrm{c}}$ and $\mathbf{B}_{\mathrm{Oe}}$ for a given $I$ are obtained
by using a proportionality relation: $j_{\mathrm{c}}$, $B_{\mathrm{Oe},x}$,
$B_{\mathrm{Oe},y}$, $B_{\mathrm{Oe},z}\propto I$. Other parameters utilized
are the exchange constant $A_{\mathrm{ex}}=13$ pJ/m and Gilbert damping
coefficient $\alpha=0.02$. We set $\alpha$ to 1 at the Ni81Fe19 disk edge to
account for damping affected by the edge roughness. The system temperature is
0 K for simplicity. We confirm that introducing a finite temperature thermal
fluctuation [20] did not qualitatively change the results.

Figure 3: Micromagnetic simulation for the (a–d) NiFe/Pt and (e–h) Pt/NiFe
devices. (a,e) Temporal dependence of the spatially-averaged out-of-plane
magnetization $\langle m_{z}\rangle$. (b,f) Fourier spectrum of $\langle
m_{z}\rangle$ over a 2.5 µm $\times$ 2.5 µm square area with a time window of
30 ns. (c,g) Snapshot of $m_{z}(x,y)$. Dashed curves represent the edge of
electrodes. (d,h) FFT intensity of $m_{z}(x,y)$ with a frequency window of
3.6–4.0 (NiFe/Pt) and 3.8–4.2 GHz (Pt/NiFe).

Figure 3 shows the results of the micromagnetic simulations. The applied
direct current intensity is set a few milliamperes above the threshold
current: $I=-18$ mA for the NiFe/Pt and 44 mA for the Pt/NiFe case,
respectively. The greater threshold current for Pt/NiFe indicates an
additional dissipation channel.

Figures 3(a) and 3(e) show the time evolution of a spatial average of the
normalized out-of-plane magnetization component $m_{z}(x,y,t)$. Both cases
show a similar period of about 0.25 ns ($\sim 4$ GHz). However, the NiFe/Pt
device manifests stationary oscillation, whereas the Pt/NiFe device exhibits a
non-monotonic envelope.

The fast Fourier transform (FFT) spectrum in Fig. 3(b) exhibits a distinct
peak at 3.8 GHz for the NiFe/Pt configuration. Conversely, the FFT spectrum in
Fig. 3(f) corresponding to the Pt/NiFe device displays a broad peak around 4.0
GHz, indicating poor coherence. Both the simulations [Fig. 3(b) & 3(f)] and
experiments [Fig. 2(c) & 2(e), at relatively large currents] yield the low
(high) frequency mode for the NiFe/Pt (Pt/NiFe). We do not observe a second
peak with $|\mathbf{B}_{\mathrm{ext}}|=$ 30 mT in the simulations. This
indicates that the supplied spin-transfer torque excites only the main mode
and the energy does not transfer from the main to the second mode.

The snapshot of $m_{z}(x,y,t)$ in Fig. 3(c) represents the auto-oscillation
near the nano-gap in the NiFe/Pt device. The mode is confined and has a large
amplitude within the nano-gap. This mode is seen in the FFT intensity image in
Fig. 3(d).

In contrast, the mode in the Pt/NiFe case has amplitudes and wavefronts around
the nano-gap in Fig. 3(g). The waves move outward with a velocity of the order
of 1 µm/ns. This radiative feature is attributed to the reason for the large
threshold current. The spatial profile of the FFT intensity, shown in Fig.
3(h), has a small amplitude at the nano-gap center and a relatively large
amplitude on one side of each electrode, suggesting that a mode generated at
the current concentrated center is delocalized.

The difference in the threshold current is attributed to the effect of the
self-induced trapping field; the simulations of the Pt/NiFe and NiFe/Pt STNOs
differ in their Oersted fields, but the current densities are similar for a
given current magnitude $I$. The confined spin-torque oscillation in the
NiFe/Pt is a manifestation of the trapping effect, whereas the extended
oscillation in the Pt/NiFe case is due to the anti-trapping by the saddle-like
Oersted field profile.

The spatial variation of the Oersted field changes the local resonant
frequency

$\omega(k)=\sqrt{(\omega_{B}+Dk^{2})(\omega_{B}+Dk^{2}+\omega_{M})},$ (2)

where $\omega_{B}=\gamma|\mathbf{B}_{\mathrm{ext}}+\mathbf{B}_{\mathrm{Oe}}|$,
$\omega_{M}=\gamma\mu_{0}M_{\mathrm{s}}$, $D=2\gamma
A_{\mathrm{ex}}/M_{\mathrm{s}}$ is the exchange stiffness, and $k$ is the
wavenumber. In the NiFe/Pt device, the resonant frequency exhibits a local
minimum at the nano-gap region due to the specific Oersted field profile
depicted in Fig. 1(b). This trapping field confines the magnetization dynamics
within the nano-gap, preventing their escape [12, 13, 14]. In contrast, the
Pt/NiFe device demonstrates a saddle point in the Oersted field, as seen in
Fig. 1(c), enabling the magnetization dynamics to attain finite group
velocities and escape from the nano-gap region.

Figure 4: The external field dependence of the threshold current for the
microwave generation. $I_{\mathrm{th}}$ is defined as the minimum current
required to achieve a microwave signal approximately 3 dB above the noise
floor.

Figure 4 shows the threshold current $I_{\mathrm{th}}$ for the onset of spin-
torque oscillation as a function of $B_{\mathrm{ext}}$, derived from the
experimental data. In the Pt/NiFe STNO configuration, $I_{\mathrm{th}}$
consistently surpasses that of the NiFe/Pt, particularly noticeable at lower
external fields $B_{\mathrm{ext}}$. The significant difference in
$I_{\mathrm{th}}$ at small $B_{\mathrm{ext}}$ is attributed to the substantial
contribution of the Oersted field to the effective magnetic field
($\mathbf{B}_{\mathrm{ext}}+\mathbf{B}_{\mathrm{Oe}}$). As $B_{\mathrm{ext}}$
increases, $I_{\mathrm{th}}$ for Pt/NiFe reaches a saturation point, ceasing
to decrease. The finite gap between the threshold currents across the entire
range of external fields signifies that selecting the appropriate order of
magnetic and heavy metal layers contributes to stabilizing spin-torque
oscillation in numerous scenarios.

The spatial profile from the simulation [Figs. 3(d) & 3(h)] and the low/high
frequency relations from both the experiment and simulation [Figs. 2(c), 2(e)
and 3(b) & 3(f)] indicate that the low-frequency localized bullet mode is
facilitated by the trapping Oersted field. In contrast, the anti-trapping
Oersted field allows for the excitation of a high-frequency propagating mode
around the region of current concentration.

Among various methods to stabilize spin torque oscillations, the Oersted field
trap offers distinct advantages. Unlike the dipolar field trap [21, 22, 23] or
geometrical confinements such as nano-constriction [12, 24, 25, 26] and nano-
wire [27, 13], the current-induced magnon trapping by the Oersted field does
not require additional boundaries or magnetic layers, which could increase the
number of standing wave modes, stray fields and defects. Our study reveals
that the Oersted field is not just an accessory [5, 7, 12, 9, 24, 25, 26, 11]
but a crucial factor for the stability of spin torque oscillation. By adopting
this approach, we may be able to attain coherent oscillations without the need
for complex setups, making it an efficient and appealing choice for practical
applications for low-temperature microwave generators.

In summary, our investigation delved into the impact of the current-induced
Oersted field on the spin-torque oscillation. In the experimental
configuration wherein the ferromagnet Ni81Fe19 layer is above the heavy metal
Pt layer, the microwave signal appears with a small threshold direct current,
a large quality factor, and a large microwave power. The characteristics
observed in the time and frequency domain simulations validate the small
threshold current and the localization of the spin-torque oscillation when
influenced positively by the Oersted field.

###### Acknowledgements.

We thank K. Hoshi, T. Hioki, S. Daimon, M. Tokunari, K. Masuda, T. Itoko, and
D. Nakano for fruitful discussions. This work was partially supported by
IBM–UTokyo lab, JSPS KAKENHI (Nos. JP19H05600 and JP22H05114), JST CREST (Nos.
JPMJCR20C1 and JPMJCR20T2) and JST ASPIRE (No. JPMJAP2316).

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