# Unidirectional spin Hall magnetoresistance and spin-orbit torques in
HM1/Co/HM2 trilayer systems

Anastasiia Moskaltsova  Center for Spinelectronic Materials and Devices,
Department of Physics, Bielefeld University, Universitätsstrasse 25, 33615
Bielefeld, Germany  Denis Dyck  Center for Spinelectronic Materials and
Devices, Department of Physics, Bielefeld University, Universitätsstrasse 25,
33615 Bielefeld, Germany  Jan-Michael Schmalhorst  Center for Spinelectronic
Materials and Devices, Department of Physics, Bielefeld University,
Universitätsstrasse 25, 33615 Bielefeld, Germany  Günter Reiss  Center for
Spinelectronic Materials and Devices, Department of Physics, Bielefeld
University, Universitätsstrasse 25, 33615 Bielefeld, Germany  Timo Kuschel
<EMAIL_ADDRESS>Center for Spinelectronic Materials and
Devices, Department of Physics, Bielefeld University, Universitätsstrasse 25,
33615 Bielefeld, Germany

###### Abstract

We present a detailed analysis of harmonic longitudinal and Hall voltage
measurements for in-plane magnetized Pt/Co/Ta and Ta/Co/Pt trilayers in
reference to Pt/Co and Ta/Co bilayers. Enhancement of spin-orbit torques
(SOTs) and unidirectional spin Hall magnetoresistance (USMR) is achieved by
introducing the second heavy metal (HM) with the opposite sign of the spin
Hall angle. The extracted SOT efficiencies are larger for the trilayers as
compared to the bilayers, confirming the enhanced values reported for the
trilayers with perpendicularly magnetized Co. The maximum effective spin Hall
angle found for the Pt/Co/Ta trilayer reaches $\theta_{SH}$ = 20 %. The USMR
of the trilayer yields up to 27% higher effect as for the respective bilayers
with the largest effective USMR amplitude of -0.32 $\times$ 10-5 for the
Pt/Co/Ta trilayer at a charge current density of 107 A/cm2.

##  I Introduction

Magnetoresistive (MR) effects play an important role in today’s spintronic
research [1, 2]. Anisotropic magnetoresistance, giant magnetoresistance and
tunneling magnetoresistance are widely used for memory applications [3, 4] or
as sensing devices [5].

Recently, a new MR effect has been found in heavy metal (HM)/ferromagnetic
insulator (FMI) hybrid structures called the spin Hall magnetoresistance
(SMR). It has been intensively studied [6, 7, 8, 9] with additional
discussions and reports on HM/ferromagnetic metal (FMM) hybrids [10, 11, 12].
The SMR is based on the spin Hall effect (SHE) [13, 14, 15, 16], which occurs
in the HM and converts a charge current into a perpendicular spin current. Due
to the inverse SHE, part of the spin current is converted back to the charge
current, after it has been reflected from the HM/FMM(FMI) interface. The SHE
emerges as a result of the strong spin-orbit coupling in HM materials such as
Ta, Pt, W etc.

The perpendicular spin current can cross the interface from HM to FMM, but
also from HM to FMI, thus converting from a spin-polarized charge current to a
magnon spin current. Depending on the FM magnetization direction with respect
to the spin polarization direction at the HM interface, the spin current can
produce a torque on the FM’s magnetization. If this SHE-induced spin-orbit
torque (SOT) is strong enough, it can even switch the FM magnetization [17,
18]. The SOT magnetization switching is at present intensively studied due to
its potential use for memory and logic applications [19, 20, 21].

Nowadays, primarily spin-transfer torque (STT) [22] magnetization switching is
used in magnetic tunnel junctions. However, the comparison between the SOT and
STT- based MRAM is not straightforward, as was discussed by Grimaldi et al.
[23]. The SOT-MRAM requires an improvement of the critical current density to
achieve high effectiveness, comparable to STT. However, the combination of
both SOT and STT switching, so-called SHE-assisted STT switching can be
advantageous and a key to low-power, ultra-fast and high density memory
applications [4, 24, 25]. Recent reports discussed that the insertion of light
elements or oxidization can enhance the SOT efficiency [26, 27, 28, 29, 30,
31]. One reason could be that additional orbital Hall effects can occur and
support the SOT switching [32].

Some of the MR effects depend quadratically on the magnetization m, although
the physical origin differs from one MR effect to the other. However, Avci et
al. explored a new MR effect in Ta/Co/AlOx and Pt/Co/AlOx called
unidirectional spin Hall magnetoresistance (USMR) that is linear in m and
linear in the charge current density j [33]. Up to now, several theoretical
studies have been conducted to determine the USMR origins in various metallic
bilayer systems. The first reports on HM/FMM thin films associate the USMR
with the spin-diffusion theory [34], in which the linear dependence on j is
due to the SHE-induced spin accumulation at the HM/FMM interface. This spin
accumulation can be described as $R^{2\omega}_{USMR}$ $\sim$ $|$j $\times$
m$|$, with $R^{2\omega}_{USMR}$ being the second harmonic longitudinal
resistance term corresponding to USMR. The recent works on similar systems,
e.g. permalloy/Pt bilayers [35], discuss that USMR is likely dominated by the
dipolar magnons, whereas Avci et al. broaden the understanding of the origins
of the effect, attributing it to three different mechanisms: bulk and
interface spin-dependent USMR as well as spin-flip USMR [36]. For the case of
HM/FMI bilayers, Sterk et al. report USMR due to pure magnonic contributions
[37].

The USMR makes it possible to determine the in-plane direction of the
magnetization or applied current and has a potential use as a magnetization
read out mechanism in a multi-state memomry device [38]. After the first
report of USMR in HM/FMM bilayers, there have been several follow-up studies
including large USMR in FM/paramagnetic GaMnAs bilayers [39] and in
topological insulator/FM heterostructures [40], as well as in Heusler
compound/HM bilayers [41]. A comprehensive investigation of the thickness
dependence of USMR in Pt/Co bilayers has been performed by Yin et al. [42].
Additionally, Hasegawa et al. reported enhancement of the USMR in Pt/Co system
with a Cu interlayer [43].

The magnetic proximity effect (MPE) can potentially influence the SOT
efficiencies and magnetoresistance effects, as was shown for various HM/FMM
bilayer systems [44, 45, 46]. Although, some studies claim irrelevance of the
MPE in the bilayer systems with thin Co layer [46] it is essential to know the
strength of the MPE for a clear picture of the magnetic properties [47].

In this work, we present a detailed study of the bi- and trilayer structures
of HM/FM and HM1/FM/HM2, respectively. By switching the order of the HM1 and
HM2, we can manipulate the HM/FM interfaces and thus tune both USMR and SOTs.
As it was predicted by Zhang and Vignale [34], one expects the enhancement of
the USMR in such heterostructures with the FM sandwiched between two HMs with
the opposite sign of the spin Hall angle $\theta_{SH}$. In such a case, an
enhancement of the USMR is expected since both HMs generate spin currents with
the same spin orientation, which can be controlled by the charge current
direction and/or sign of the $\theta_{SH}$. It has been shown already for out-
of-plane magnetized Co in a Pt/Co/Ta trilayer that one can tailor the stack
and HM/FM interfaces to achieve higher effective $\theta_{SH}$ [48]. Here, we
investigate this approach for in-plane magnetized trilayers.

The sample stacks studied in this work are: sub/Pt 6/ Co 2.5/MgO
2/TaO${}_{\text{x}}$ and sub/Ta 6/Co 2.5/MgO 2/TaO${}_{\text{x}}$, further
mentioned as Pt/Co and Ta/Co bilayers, respectively. The trilayers consisted
of sub/Pt 6/ Co 2.5/Ta 6/MgO 2/TaO${}_{\text{x}}$ and sub/Ta 6/Co 2.5/Pt 6/MgO
2/TaO${}_{\text{x}}$, mentioned here as Pt/Co/Ta and Ta/Co/Pt, respectively.
The thicknesses of the layers are indicated in nm. The substrate (sub) used
for all the samples was Si/SiO2 with an SiO2-thickness of 50 $\mu$m. The
proximity induced moments have been already studied and are published in Ref.
[47]. The extracted thicknesses of the Pt spin-polarized layer for the
trilayer samples are 0.9 nm and 0.8 nm for Ta/Co/Pt and Pt/Co/Ta,
respectively. The induced Pt magnetic moments of 0.56 $\mu_{B}$ per Pt atom at
the interface for Ta/Co/Pt and 0.42 $\mu_{B}$ per Pt atom at the interface for
Pt/Co/Ta have been extracted [47].

##  II Experimental details

The samples were prepared by DC magnetron sputtering (except for MgO, for
which RF sputtering was used) on thermally oxidized Si substrates at room
temperature. The top MgO/TaO${}_{\text{x}}$ is a capping layer to protect the
stacks from oxidation. The topmost TaO${}_{\text{x}}$ layer was obtained by
natural oxidation of a 2 nm metallic Ta film. In-plane and out-of-plane
saturation fields, as well as saturation magnetizations, were determined from
vibrating sample magnetometry (VSM) loops measured up to 4 T at room
temperature (see Ref. [47]). The samples are in-plane magnetized with $M_{s}$
= 1500 kA/m for Pt/Co and 1400 kA/m for all the other samples. The in-plane
saturation fields are 0.4 T for both trilayers and the Ta/Co bilayer, while
Pt/Co exhibits $B_{s}=1.0\,\textrm{T}$. The coercive fields are in the range
between 6.8 and 13 mT. The films were further patterned via one-step electron
beam lithography into Hall bar structures with a width $w$ and lengths
$l=5\,w$, as shown in Fig. 1.

Figure 1: (a) Microscope image of a 10 $\mu$m wire-bonded Hall bar and
electrical connections. (b) Schematic representation of the zoomed-in region
with the geometry definitions.

The harmonic longitudinal and transverse voltage measurements are used here to
characterize the spin dependent transport in the samples. The rotational
measurements in xy plane were carried out inside a dual Halbach cylinder array
with a rotating magnetic field in the range from 0.05 to 1 T (MultiMag,
Magnetic Solutions Ltd.). By using two Signal Recovery SR7230 Lock-In
amplifiers with two demodulators, we were able to measure simultaneously both
first ($\omega$) and second (2$\omega$) harmonics of longitudinal and
transverse (Hall) voltages. The measurements were performed at room
temperature at a modulation frequency of f = ${\omega/2\pi}$ = 1176 Hz and
with varied AC current amplitudes up to 2.5 mA. Anomalous Hall resistances
$R_{AHE}$ are obtained from magnetic field loops measured up to 4 T at room
temperature.

##  III Results and discussion

###  III.1 Harmonic Hall voltage analysis: SOTs and thermal effects

First, we present the raw data and fits for the second harmonic transverse
(Hall) resistance $R_{H}^{2\omega}$ measured as a function of the in-plane
rotation angle $\varphi$ with respect to the external magnetic field. Figure 2
shows the data for the bi- and trilayers. The data analysis was based on the
method developed by Avci et al. [33, 49].

Figure 2: Second harmonic Hall resistances for the studied (a), (b) bi- and
(c), (d) trilayers with a Hall bar width of $w=4\,\mu\textrm{m}$. Red and
light blue circles correspond to the measured data at 1 and 0.05 T,
respectively. The fits (black dashed lines) are based on Eq. (1).

Following the analysis method, we first focus on the transverse second
harmonic voltage, to obtain the information on the SOTs as well as to extract
the transverse thermal effects. These effects arise from spin Seebeck and
anomalous Nernst effects (SSE and ANE respectively) and must be taken into
account. The second harmonic Hall voltage can be described as [50, 51]

$V^{2\omega}_{H}=[-\frac{B_{FL+Oe}}{B_{ext}}\,R_{PHE}\,\cos 2\varphi+\\\
(-\frac{1}{2}\frac{B_{DL}}{B_{total}}\,R_{AHE}+\alpha^{\prime}I_{0})]\,\textit{I}_{rms}\,\cos\varphi.$
(1)

$B_{FL+Oe}$ is the field-like (FL) SOT and Oersted field contribution, while
$B_{DL}$ corresponds to the damping-like (DL) SOT field. $R_{PHE}$ and
$R_{AHE}$ are the planar Hall effect (PHE) and the anomalous Hall effect (AHE)
resistances, respectively. The term $B_{total}$ is the total magnetic field.
The term $\alpha^{\prime}$ $I_{0}$ describes any thermal contribution arising
from SSE/ANE and $I_{rms}$ is the root mean square amplitude of the applied AC
charge current. Thus, we can describe the transverse second harmonic
resistance as a sum of the contributions

$R_{H}^{2\omega}=R_{DL}^{2\omega}+R_{\nabla T}^{2\omega}+R_{FL+Oe}^{2\omega}.$
(2)

The term $R_{\nabla T}^{2\omega}$ corresponds to the thermal effects driven by
out-of-plane thermal gradients (SSE, ANE). As one can see from Eq. (1), the
first term has a ($2\,\text{cos}^{3}\,\varphi-\text{cos}\,\varphi$)
dependence, while the remaining two terms follow a cos $\varphi$ angular
dependence.

We first fit the $R_{H}^{2\omega}$ raw data with a $a$ cos $\varphi$ \+ $b$
($2\,\text{cos}^{3}\,\varphi-\text{cos}\,\varphi$) function. We then extract
the cos $\varphi$ contribution, which corresponds to the sum of DL SOT and
thermal effects, as well as the (2 cos${}^{3}\varphi$ \- cos $\varphi$)
contribution to extract FL SOT. After the extraction of the cos $\varphi$
component, we can further separate the DL and thermal contributions by
plotting the corresponding fit parameter against the inverse total magnetic
field 1/$B_{total}$, with $B_{total}$= $B_{ext}$ \+ $B_{demag}$ \- $B_{anis}$.
The term ($B_{demag}$ \- $B_{anis}$) can be identified as the out-of-plane
saturation field. The example of such a separation is shown in Fig. 3(a) for
the bi- and trilayers. The DL SOT is expected to have no influence in the
large field regime. Therefore, the only contribution left at large magnetic
fields is related to the thermal effects. The $B_{DL}$ is extracted from the
slope of the linear fits depicted in Fig. 3(a). Thus, we define $R_{\nabla
T}^{2\omega}$ as a y-axis intercept of the 1/$B_{total}$ plotting. For further
calculations of the USMR, we then convert the obtained $R_{\nabla
T}^{2\omega}$ via the geometrical factor $l/w$ = 5 and subtract it from the
raw longitudinal $R^{2\omega}$.

To calculate the DL and FL SOT fields ($B_{DL}$ and $B_{FL+Oe}$, respectively)
we again utilize Eq. (1). Here, the $B_{FL+Oe}$ term corresponds to a sum of
FL SOT and Oersted field contributions. The Oersted field originates from the
charge current flowing in the Pt and/or Ta layer(s) and can be estimated as
$\mu_{0}I_{rms}$/2$w$, with $\mu_{0}$ as the vacuum permeability, $I_{rms}$ as
the root-mean-square current amplitude and $w$ as the width of the current
line. $B_{Oe}$ was estimated to be -0.39 mT and was subtracted from
$B_{FL+Oe}$ for the FL SOT efficiency calculations. The SOT fields for bi- and
trilayers are shown in Fig. 3(b). As expected, there is no magnetic field
dependence, except for the unsaturated regime in the magnetic field range
$\textless$ 0.4 T. We calculate the SOT efficiencies ($\xi_{DL}$ and
$\xi_{FL}$) as [52]

$\xi_{DL(FL)}=\frac{2e}{\hbar}B_{DL(FL)}\frac{M_{s}t_{FM}}{j_{HM}},$ (3)

with e being the electron charge, $\hbar$ the reduced Planck constant, $M_{s}$
and $t_{FM}$ the saturation magnetization and thickness of the FM,
respectively. $j_{HM}$ is the charge current density amplitude in a HM layer.

Figure 3: (a) $R_{H}^{2\omega}$ cos $\varphi$ contribution plotted against the
inverse total magnetic field for the bi- and trilayers. Linear fits performed
for the in-plane saturated regime $\textgreater$ 0.4 T. (b) FL and DL SOTs as
a function of the external magnetic field. The orange shaded area encloses the
data in unsaturated regime.

Using the DL SOT values, we calculate the spin Hall angle $\theta_{SH}$,
following a model in which the DL torque is entirely ascribed to the
absorption of the spin current produced by the bulk spin Hall effect in the HM
[18, 53]. In the case of bilayers, $\xi_{DL}$ = $\theta_{SH}$. We thus
obtained $\theta_{SH}^{Pt}$ = 10%, $\theta_{SH}^{Ta}$ = -3.5% which is in
agreement with the literature [49, 54]. For the trilayers, however, we are
only able to extract the effective spin Hall angle $\theta^{eff}_{SH}$, to
which both Pt and Ta contribute. The obtained values yield 20% for Pt/Co/Ta
and -13% for Ta/Co/Pt (see Table 1). The lower value for the latter trilayer
may be attributed to the Ta oxidation at the substrate interface or due to a
lower interface quality. The $\theta^{eff}_{SH}$ values obtained for the
trilayers in this work are slightly lower than those previously reported (34%)
for the same trilayer structures with perpendicularly magnetized Co [48].

Table 1: A summary of the results for the Pt and Ta systems. sample | $R_{AHE}$ | $R_{PHE}$ | $B_{DL}$ | $B_{FL+Oe}$ | $\xi_{DL}$ | $\xi_{FL}$ | $R_{USMR}^{2\omega}$ |  $\frac{R_{USMR}}{R_{HM}}$ $\times$ 10-5
---|---|---|---|---|---|---|---|---
| ($\Omega$) | ($\Omega$) | (mT) | (mT) |  |  | m$\Omega$ | per 107 A/cm2
Pt/Co | 0.35 | 0.11 | 0.721 | -0.194 |  $\sim$0.1 | 0.0006 | -0.79 | -0.26
Ta/Co | 1.1 | 0.12 | -0.133 | -0.136 |  $\sim$-0.035 | 0.013 | 0.95 | 0.11
Pt/Co/Ta | 0.23 | 0.07 | 0.84 | -0.056 |  $\sim$0.2 | -0.011 | -0.66 | -0.32
Ta/Co/Pt | 0.24 | 0.05 | -0.71 | 0.335 |  $\sim$-0.13 | 0.07 | 0.23 | 0.14

###  III.2 Harmonic longitudinal voltage analysis: USMR comparison in bi- and
trilayers

Figure 4: Longitudinal second harmonic resistance for the studied (a), (b) bi-
and (c), (d) trilayers with a Hall bar width of $w$ = 4$\mu$m. Red and light
blue circles correspond to the measured data at 1 T and 0.05 T, respectively.
The fits (black dashed lines) were performed with the $a$ sin $\varphi$ \+ $b$
(2 cos ${}^{3}\varphi$ \- cos $\varphi$) function.

After the detailed analysis of the second harmonic Hall voltages, we take a
closer look at the second harmonic longitudinal voltages. The corresponding
data and fits are shown in Fig. 4. We observe a similar behavior as for the
transverse case, in which for the samples containing Pt, extrema arise at
lower magnetic fields at about $\varphi$ = 45∘, 135∘, 225∘, 315∘.

In order to investigate the influence in a different material with negative
$\theta_{SH}$, but lower resistivity as compared to Ta, two samples with W
instead of Ta were prepared. The W samples stacks are: Si/SiO2/W 7/ Co 2.5/MgO
2/TaO${}_{\text{x}}$ and Si/SiO2/W 8/Co 2.5/Pt 6/MgO 2/TaO${}_{\text{x}}$.
These samples have been measured and analyzed in the same manner as the
aforementioned Pt and Ta systems.

The $R^{2\omega}$ magnetic field dependence of the Pt and Ta samples is
plotted in Fig. 5(a). The samples containing W do not show a comparable
$R^{2\omega}$ magnetic field dependence, as shown with magenta and violet
stars in Fig. 5(b). Following Ref. [36], we fit the data with a $c$ \+ const
$\cdot$ B-p function (dashed line), with $c$ being an offset. It is clear,
that in the saturated regime, above 0.4 T, there is no dependence on the
magnetic field. However, for lower magnetic field strengths (unsaturated
state) the effect magnitude varies, although this behavior predominantly
appears in Pt samples (blue and turquoise circles, as well as orange squares)
with FL SOTs, hence, there is no magnetic field dependence for the Ta/Co
bilayer (red squares). This finding confirms that the USMR effect is magnetic
field-independent and the only reason for the higher signal amplitudes at
lower fields is the FL SOT contribution.

Figure 5: (a) Second harmonic longitudinal resistance dependence on magnetic
field for bi- and trilayers with Pt, Ta and W. Dashed lines are fit with the
$c$ \+ const $\cdot$ B-p function. The orange shaded area encloses the data in
unsaturated regime. (b) Zoomed-in region with focus on W samples. Figure 6:
(a) USMR dependence on total charge current for bi- and trilayers with Pt and
Ta. (b) Normalized USMR dependence on HM charge current density normalized to
the HM resistance. Dashed lines are linear fits with fixed zero offset.

Finally, the USMR is calculated via $R_{USMR}^{2\omega}$ =
$R^{2\omega}-\frac{l}{w}R_{\nabla T}^{2\omega}$, with $\frac{l}{w}$ = 5. A
detailed analysis of the $R_{USMR}^{2\omega}$ current dependence is shown in
Fig. 6(a). For further comparison, the values at 1 $\times$ 107 A/cm2 (slope
of the linear fit) are discussed. It can be seen that for the Ta-based systems
with positive USMR, the bilayer exhibits the highest value of 0.95 m$\Omega$,
while the respective trilayer yields $R_{USMR}^{2\omega}$ = 0.23 m$\Omega$. In
the case of the Pt based samples with negative USMR, the difference between
the extracted USMR values is not large ($R_{USMR}^{2\omega}$ = -0.79 m$\Omega$
vs. $R_{USMR}^{2\omega}$ =-0.66 m$\Omega$), however, here, no enhancement for
the trilayer is found. First of all, when we explore in more detail the Ta/Co
bilayer, Ta in our film stacks has a resistivity 180 $\mu\Omega$ cm, which is
$\sim$ 4-5 times higher than Co (40 $\mu\Omega$ cm) and, therefore, it is
anticipated that most of the charge current flows through the Co layer. The
resistivity of Co was taken from the literature for the same thin film
thickness [49, 55], while the resistivities of Ta and Pt were calculated using
the parallel resistor model with known Co resistivity. Thus, when Pt is added
on top, the charge current distribution changes.

Thus, to correctly compare the USMR effect between the different samples, we
take the ratio between the USMR effect $R_{USMR}^{2\omega}$ and the HM
resistance $R_{HM}$. In case of the trilayers, with both Pt and Ta present, we
calculate the current density flowing through both heavy metals using the
parallel resistors model. Figure 6(b) presents the current density dependence
of the normalized USMR. We observe an enhancement of the effect in trilayers,
of up to 27%. The maximum effect of -0.32 $\times$ 10-5 per 107 A/cm2 is
observed in the Pt/Co/Ta trilayer.

When we take a closer look at the bilayers, we see that the weighted USMR
effect is stronger for Pt than Ta. Such a behavior can be explained by
intermixing at the Ta/Co interface or oxidation of Ta at the substrate. By
adding another HM interface to the bilayer, spin current is then driven from
both sides into Co, and thus an increase of the USMR effect is achieved.

In case of the W-based samples, both bi- and trilayer show equal values within
the uncertainty limit, as compared to the corresponding Ta samples. As was
discussed by Pai et al. [56], the $\theta_{SH}^{W}$ and resistivity strongly
depend on the phase, with the highest $\theta_{SH}^{W}$ value being -33% and
resistivity in the range of 100-300 $\mu\Omega$cm reported by the authors for
the $\beta$ phase of tungsten. In this work, we determined the W resistivity
to be $\approx$ 90 $\mu\Omega$cm, indicating a mixture of both $\alpha$ and
$\beta$ phases, thus a lower $\theta_{SH}^{W}$ is expected.

##  IV Conclusions

In summary, we have discussed harmonic voltage measurements of Pt/Co and Ta/Co
bilayers, as well as their HM1/Co/HM2 trilayers. By analyzing the $2\omega$
Hall resistance, we were able to extract the important information about SOTs,
as well as spin Hall angle for bilayers. Averaged extracted values of
$\theta_{SH}^{Pt}$ $\approx$ 10% and $\theta_{SH}^{Ta}$= -3.5% are in
agreement with previously reported ones. For the trilayers, effective
$\theta_{SH}^{eff}$ are found to be $\theta_{SH}^{eff}$ = 20% and -13% for the
Pt/Co/Ta and Ta/Co/Pt, respectively. Finally, the USMR effect in the studied
samples have similar values for bilayers, when compared to the literature. The
obtained values for bilayers $R_{USMR}^{2\omega}/R_{HM}$ are -0.26 $\times$
10-5 and 0.11 $\times$ 10-5 for Pt/Co and Ta/Co, respectively. For trilayers,
we observe a modest enhancement, with $R_{USMR}^{2\omega}/R_{HM}$ found to be
-0.32 $\times$ 10-5 for Pt/Co/Ta and 0.14 $\times$ 10-5 for Ta/Co/Pt samples
per 107 A/cm2, respectively. Additionally, two samples with W instead of Ta
were measured, to compare the USMR effect size, as W is expected to have lower
resistivity and higher negative spin Hall angle. The obtained USMR values for
these samples, however, are equal to Ta-based systems within the uncertainty
limit, thus no increase in USMR is observed. This is contrary to the
expectations, but can be linked to the W-phase and film oxidation. These
factors when combined can lead to the higher resistivity values, comparable to
those of Ta.

###### Acknowledgements.

The authors thank Daniel Carsten for help with initial experiments. We further
thank Markus Meinert, Johannes Mendil and Pietro Gambardella for valuable
discussions and comments. Finally, we thank Tristan Matalla-Wagner and Jan
Biedinger for help with VSM and AGM measurements.

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# Real-Time FPGA Demonstrator of ANN-Based Equalization for Optical
Communications
††thanks: This work was carried out in the frameworks of the CELTIC-NEXT
project AI-NET-ANTILLAS (C2019/3-3, grant 16KIS1316 and 16KIS1317), funded by
the German Federal Ministry of Education and Research (BMBF), and the RENEW
project, funded by the European Research Council (ERC) under the European
Union’s Horizon 2020 research and innovation programme (grant agreement No.
101001899).

Jonas Ney,1,* Patrick Matalla,2 Vincent Lauinger,3 Laurent Schmalen,3
Sebastian Randel,2 and Norbert Wehn1
1Microelectronic Systems Design (EMS), RPTU Kaiserslautern-Landau, 67653
Kaiserslautern, Germany
2Institute of Photonics and Quantum Electronics (IPQ), Karlsruhe Institute of
Technology (KIT), 76131 Karlsruhe, Germany
3Communications Engineering Lab (CEL), Karlsruhe Institute of Technology
(KIT), 76131 Karlsruhe, Germany
<EMAIL_ADDRESS>
###### Abstract

In this work, we present a high-throughput field programmable gate array
(FPGA) demonstrator of an artificial neural network (ANN)-based equalizer. The
equalization is performed and illustrated in real-time for a 30 GBd, two-level
pulse amplitude modulation (PAM2) optical communication system.

###### Index Terms:

FPGA, ANN, Optical Communications

##  I Introduction

Short-reach optical communication systems must be cost and power efficient
while satisfying the increasing demand of data rates. For these reasons, they
typically rely on intensity-modulation and direct-detection (IM/DD) of the
optical signal. In such systems, the achievable data rate is limited due to
severe nonlinear signal impairments caused for example by low-cost components
such as electro-absorption modulators and semiconductor optical amplifiers, or
by nonlinear channel effects caused, e.g., by chromatic dispersion (CD) with
square-law detection.

Digital linear equalization can compensate for such nonlinear distortions only
to a certain extent. Thus, nonlinear equalization methods draw the attention
of the community. In particular, machine learning using ANNs, which proved to
be highly capable of compensating for nonlinear impairments, is a contender
for future equalizers [1]. However, compared to conventional algorithms, which
have been optimized for decades, ANNs often introduce high computational
complexity, limiting the achievable throughput of the hardware implementation.
Previous works showed that even with advanced FPGA platforms, it is
challenging to meet the strict performance requirements of optical
communication systems [2, 3].

In this work, we present an FPGA demonstrator that tackles the challenges of
real-time ANN-based equalization by featuring an optimized ANN topology and a
highly parallelized hardware architecture. The optical PAM2 signal is
transmitted at $30\text{\,}\mathrm{G}\mathrm{B}\mathrm{d}$ over a
$20.56\text{\,}\mathrm{k}\mathrm{m}$ long standard single-mode fiber (SSMF).
The digital signal processing of the receiver, including clock recovery, ANN-
based equalization, downsampling, decisioning, and bit error rate (BER)
calculation, is fully implemented on an FPGA. Furthermore, the demonstrator
provides a visualization of the equalization performance on a monitor in real-
time.

##  II Scientific and Technical Description

In the following, we provide a short overview of our work, starting from the
algorithm and its implementation down to the actual demonstrator. For the
interested reader, we refer to the provided references for a more detailed
explanation.

###  II-A ANN Topology

In contrast to classical linear equalizers based on finite impulse response
(FIR) filters, the demonstrator features an ANN-based equalizer. Specifically,
we choose a convolutional neural network (CNN) as neural network type since it
resembles the structure of conventional digital filters. In particular, the
model consists of $3$ convolutional layers with a kernel size of $9$ where the
first two layers are followed by batch-normalization and ReLU activation
function. The feature maps of the first two layers consist of $5$ channels
while the last feature map has $8$ channels. Correspondingly, the first layer
has a stride of $8$, which allows for the processing of $8$ symbols with one
run of the network.

The model has been selected based on an extensive design space exploration,
described in detail in [4]. As a result, the ANN achieves around one order of
magnitude lower BER than a linear digital filter with the same computational
complexity.

###  II-B FPGA ANN Implementation

For FPGA implementation of the ANN, Vivado HLS in combination with Vivado
2022.2 is used. The hardware architecture is based on arbitrary precision
fixed-point format for weights and activations while the 6-bit inputs and
outputs are transferred using the AXI-Stream interface.

The main target of our demonstrator is to satisfy the high-throughput
constraints of the $30\text{\,}\mathrm{G}\mathrm{B}\mathrm{d}$ optical
communication channel. Thus, the aim of our hardware architecture is to
utilize the available resources efficiently by boosting parallelism on all
implementation levels. The first level of parallelism is based on our
streaming hardware architecture, where each of the layers is implemented as an
individual hardware instance. This way, the data is processed in a pipelined
fashion, with each layer corresponding to a separate pipeline stage. Hence,
each layer can start its operation as soon as the first inputs are received.
Further, our convolutional layer exploits multiple types of parallelism: on
the level of input channels, on the level of output channels, and on the
kernel level. Another level of parallelism that is exploited by our
implementation is the number of CNN instances. We place and connect multiple
instances of the CNN in one design to further boost the throughput. Therefore,
the input is split into multiple streams, so each instance operates on a
subset of the input sequence and produces a subset of the output sequence. For
further information about the hardware architecture and the quantization, we
refer to [4].

###  II-C Demonstrator

The experimental setup including the digital signal processing of the receiver
is depicted in Fig. 1. We use the Keysight USPA prototyping platform, which
contains a Xilinx VU9P FPGA on transmitter and receiver side, and a
$60\text{\,}\mathrm{G}\mathrm{S}\mathrm{a}\mathrm{/}\mathrm{s}$ digital-to-
analog converter (DAC) and analog-to-digital converter (ADC) with
$6\text{\,}\mathrm{b}\mathrm{i}\mathrm{t}$ resolution. At the transmitter
side, a $30\text{\,}\mathrm{G}\mathrm{B}\mathrm{d}$, non-return-to-zero (NRZ),
PAM2 signal is generated and drives the EAM to modulate the optical carrier at
$1540\text{\,}\mathrm{n}\mathrm{m}$, which is provided by an distributed-
feedback (DFB) laser. The optical signal is then transmitted over a
$20.56\text{\,}\mathrm{k}\mathrm{m}$ SSMF to accumulate CD. At the receiver
side, the signal is detected by a photodiode and amplified by a transimpedance
amplifier. Afterwards, the received signal is sampled by an ADC and processed
by the receiver FPGA. As part of the digital signal processing of the
receiver, the twofold oversampled received signal is first synchronized to the
transmit clock utilizing a feedforward clock recovery architecture as
described in [5]. Afterwards, the signal is equalized using our high-
throughput ANN-based equalizer. Finally, we implement the decisioning and BER
tester to evaluate the signal quality and BER. This way, the communication
performance is visualized in real-time and the equalizer’s compensation
capabilities are showcased.

FPGA$30\text{\,}\mathrm{G}\mathrm{B}\mathrm{d}$,PAM2DACEAM$1540\text{\,}\mathrm{n}\mathrm{m}$DFB$20.56\text{\,}\mathrm{k}\mathrm{m}$
SSMFADCFPGAClock RecoveryNeural NetworkDecisioningBER Tester Figure 1:
Transmission setup including digital signal processing at receiver side.

Figure 2 shows the real-time demonstrator including a monitor which
illustrates the functionality of the ANN-based equalizer. Before the
equalizer, the two levels of the PAM2-symbols are partly overlapping around
the decision threshold due to inter-symbol interference (ISI), which is caused
by CD, and nonlinear distortions. After the equalizer, the symbols are well
separated leading to a BER close to zero.

20.56 km SSMF
---
Optical Receiver
---
Distorted Received
---
Signal
Equalized ANN
---
Output
ADC, DAC, FPGA
---
DFB,
---
EAM
Figure 2: Setup of the real-time optical communication demonstrator.

Given the impracticality of transporting the costly and heavy equipment of the
demonstrator, we plan to show a live stream of our demonstrator placed in our
laboratory at the conference venue. On-site we will require two monitors, one
for the live stream and another one for the signal and BER monitoring.

##  III Research Contributions & Conclusion

The main purpose of our demonstrator is to illustrate how ANN-based equalizers
can be applied to high-throughput optical communication systems. Thus, the
demonstrator forms the basis for the visualization of multiple contributions
of previous and future works in the field of ANN-based equalization. It can be
utilized to visualize the contributions of [4], where a similar high-
throughput equalizer was implemented on the Xilinx VU13P FPGA. Another use-
case is the visualization of the novel unsupervised equalization approaches of
[6] and [7]. Therefore, in future work, the demonstrator could further be
extended to illustrate the training process of the ANN.

To summarize, the demonstrator is a first step towards a practical optical
communication system featuring ANN-based equalizers. It shows that, if
efficiently implemented, ANN-based algorithms can satisfy the requirements of
high-throughput communication systems while successfully compensating for
nonlinear distortions.

## References

  * [1] F. N. Khan _et al._ , “An optical communication’s perspective on machine learning and its applications,” _J. Lightw. Technol._ , vol. 37, no. 2, pp. 493–516, 2019.
  * [2] P. J. Freire _et al._ , “Towards FPGA implementation of neural network-based nonlinearity mitigation equalizers in coherent optical transmission systems,” in _Proc. ECOC_ , 2022.
  * [3] N. Kaneda _et al._ , “Fixed-point analysis and FPGA implementation of deep neural network based equalizers for high-speed PON,” _J. Lightw. Technol._ , vol. 40, no. 7, pp. 1972–1980, 2022.
  * [4] J. Ney _et al._ , “From algorithm to implementation: Enabling high-throughput CNN-based equalization on FPGA for optical communications,” in _Proc. Internat. Conf. on Embedded Comp. Syst.: Architect., Model. and Simul. (SAMOS XXIII)_ , 2023.
  * [5] P. Matalla _et al._ , “Hardware comparison of feed-forward clock recovery algorithms for optical communications,” in _Proc. OFC_ , 2021.
  * [6] J. Ney _et al._ , “Unsupervised ANN-based equalizer and its trainable FPGA implementation,” in _Proc. EuCNC_ , 2023.
  * [7] V. Lauinger _et al._ , “Fully-blind neural network based equalization for severe nonlinear distortions in 112 gbit/s passive optical networks,” _arXiv Prepint_ , 2024. [Online]. Available: https://arxiv.org/abs/2401.09579

  *[FPGA]: field programmable gate array
  *[ANN]: artificial neural network
  *[PAM2]: two-level pulse amplitude modulation
  *[IM/DD]: intensity-modulation and direct-detection
  *[CD]: chromatic dispersion
  *[ANNs]: artificial neural network
  *[SSMF]: standard single-mode fiber
  *[BER]: bit error rate
  *[FIR]: finite impulse response
  *[CNN]: convolutional neural network
  *[DAC]: digital-to-analog converter
  *[ADC]: analog-to-digital converter
  *[NRZ]: non-return-to-zero
  *[EAM]: electro-absorption modulator
  *[DFB]: distributed-feedback
  *[ISI]: inter-symbol interference