# Large Spin-to-Charge Conversion in Ultrathin Gold-Silicon Multilayers

Mohammed Salah El Hadri  Center for Memory and Recording Research, University
of California, San Diego, La Jolla, California, 92093-0401, USA
<EMAIL_ADDRESS>Jonathan Gibbons  Department of Physics, University of
California San Diego, La Jolla, California, 92093-0401, USA  Materials Science
Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
Department of Materials Science and Engineering, University of Illinois at
Urbana-Champaign, Urbana, Illinois 61801, USA  Yuxuan Xiao  Center for Memory
and Recording Research, University of California, San Diego, La Jolla,
California, 92093-0401, USA  Haowen Ren  Center for Memory and Recording
Research, University of California, San Diego, La Jolla, California,
92093-0401, USA  Hanu Arava  Northwestern-Argonne Institute of Science and
Engineering (NAISE), Northwestern University, Evanston, Illinois 60208, USA
Materials Science Division (MSD), Argonne National Laboratory, Argonne,
Illinois 60439, USA  Yuzi Liu  Center of Nanoscale Materials, Argonne National
Laboratory, Argonne, Illinois 60439, USA  Zhaowei Liu  Department of
Electrical and Computer Engineering, University of California, San Diego, 9500
Gilman Drive, La Jolla, California 92093-0407, USA  Materials Science and
Engineering Program, University of California, San Diego, 9500 Gilman Drive,
La Jolla, California 92093-0418, USA  Amanda Petford-Long  Northwestern-
Argonne Institute of Science and Engineering (NAISE), Northwestern University,
Evanston, Illinois 60208, USA  Materials Science Division (MSD), Argonne
National Laboratory, Argonne, Illinois 60439, USA  Axel Hoffmann  Materials
Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
Department of Materials Science and Engineering, University of Illinois at
Urbana-Champaign, Urbana, Illinois 61801, USA  Eric E. Fullerton  Center for
Memory and Recording Research, University of California, San Diego, La Jolla,
California, 92093-0401, USA  Department of Electrical and Computer
Engineering, University of California, San Diego, 9500 Gilman Drive, La Jolla,
California 92093-0407, USA

(August 27, 2024)

###### Abstract

Investigation of the spin Hall effect in gold has triggered increasing
interest over the past decade, since gold combines the properties of a large
bulk spin diffusion length and strong interfacial spin-orbit coupling.
However, discrepancies between the values of the spin Hall angle of gold
reported in the literature have brought into question the microscopic origin
of the spin Hall effect in Au. Here, we investigate the thickness dependence
of the spin-charge conversion efficiency in single Au films and ultrathin
Au/Si multilayers by non-local transport and spin-torque ferromagnetic
resonance measurements. We show that the spin-charge conversion efficiency is
strongly enhanced in ultrathin Au/Si multilayers, reaching exceedingly large
values of 0.99 $\pm$ 0.34 when the thickness of the individual Au layers is
scaled down to 2 nm. These findings reveal the coexistence of a strong
interfacial spin-orbit coupling effect which becomes dominant in ultrathin Au,
and bulk spin Hall effect with a relatively low bulk spin Hall angle of 0.012
$\pm$ 0.005. Our experimental results suggest the key role of the Rashba-
Edelstein effect in the spin-to-charge conversion in ultrathin Au.

##  I Introduction

The interplay between spin-orbit coupling (SOC) and low dimensionality has
attracted significant interest over the last decade due to the prospect of
exploring rich physical mechanisms, as well as the potential impact on
emerging spintronics technologies Hellman2017 ; Soumyanarayanan2016 ;
Manchon2015 ; Sklenar2016 . One of the most prominent mechanisms arising from
the relativistic SOC is the spin Hall effect (SHE) Hoffmann2013 ; Sinova2015 ,
where a transverse spin current is generated from an unpolarized charge
current. Since its initial prediction by D’yakonov and Perel in 1971
Dyakonov1971 , the spin Hall effect has attracted increasing interest from
theoretical Hirsch1999 ; Zhang2000 ; Sinova2004  and experimental
Valenzuela2006 ; Kato2004 ; Wunderlich2005 ; Saitoh2006 ; Kimura2007
viewpoints, and has become an important tool for the injection, detection and
manipulation of spin currents in thin films and heterostructures Hoffmann2013
; Sinova2015 ; Pai2012 ; Liu2012a ; Liu2012b ; Liu2012c ; Manchon2019 . The
microscopic origin of the SHE is a material-dependent combination of intrinsic
and extrinsic mechanisms. Its efficiency is characterized by the spin Hall
angle (SHA) ($\theta$${}_{\text{SHE}}$), which describes the conversion of
charge into spin currents. Recent studies have explored new pathways to
enhance the SHE by investigating novel chemically inhomogeneous Zhu2018 ;
Demasius2016 ; An2018a ; An2018b  and multilayer Zhu2019a ; Zhu2019b  systems,
and reported large spin-torque efficiencies, namely 0.35 for
Au${}_{\text{1-x}}$Pt${}_{\text{x}}$ alloys Zhu2018 , -0.49 for oxidized W
Demasius2016 , 0.9 for oxidized Pt An2018a ; An2018b , 0.37 for Pt/Hf
multilayers Zhu2019a , and 0.35 for Pt/Ti multilayers Zhu2019b . More
importantly, the spin-torque efficiencies reported for these novel systems are
much larger than the SHA values reported for single-element layers, namely
-0.33 for $\beta$-W Pai2012 , $\sim$0.1 for Pt Althammer2013 ; Zhang2013  and
0.11 for Au Seki2008 , thus highlighting the importance of chemical
inhomogeneity and heterostructures in the SHE mechanism. On the other hand,
introducing low dimensionality to heavy metals with a large bulk SHE can also
significantly enhance the spin-charge conversion efficiency via interfacial
SOC-related effects, such as the Rashba SOC Rashba1960 ; Edelstein1990 ;
Bychkov1984 ; Burkov2004 . Hence, these emergent interfacial SOC phenomena
offer promising routes for 2D-spintronics applications Hellman2017 ;
Soumyanarayanan2016 ; Manchon2015 ; Rojas-Sanchez2013 ; Jungfleisch2016 .

Since Au combines the properties of strong SOC at interfaces Seki2008 ;
LaShell1996 ; Nicolay2001 ; Nechaev2009  and a relatively large bulk spin
diffusion length Johnson1993 ; Ji2004 ; Ku2006 , it has been the focus of
intense research interest, evidenced by many experimental and theoretical
investigations. In 2008, Seki et al. reported a giant SHA of 0.11 in 10-nm-
thick Au using an FePt perpendicular spin injector Seki2008 . Later, non-local
transport measurements by Mihajlović et al. showed the absence of the giant
SHE in a 60-nm-thick H-shaped Au structure ($\theta$${}_{\text{SHE}}$ $\leq$
0.023) Mihajlovic2009 , thus triggering a debate on the microscopic origin of
the giant SHE in Au films. Follow up experimental investigations using various
methods, such as non-local spin injection Seki2010 , spin pumping Brangham2016
, and non-local transport Tian2016 ; Chen2019 , have revealed that the SHA of
Au can be significantly reduced for films thicker than 10 nm. More recently,
first-principles calculations demonstrated the presence of a strong
interfacial contribution to the SHE in Au-Fe bilayers, which was attributed to
spin-dependent transmission occurring within a few atomic layers Li2019 . More
importantly, such an interfacial contribution occurs at the Au(111) interface
where a strong Rashba SOC exists LaShell1996 ; Nicolay2001 ; Nechaev2009 ,
which is a hint that the Rashba-splitting of the Au(111) surface states plays
an important role in the spin-to-charge conversion mechanism in Au Li2019 .
These investigations give insights into the origin of the large SHE in Au and
suggest the important role of the interface scattering Seki2010 ; Brangham2016
; Chen2019  and/or the Rashba SOC Li2019 .

To further elucidate the microscopic origin of the SHE in Au films, we present
an experimental investigation of the SHE in ultrathin Au films and ultrathin
Au/Si multilayers, where the thickness of the individual Au layers is scaled
down to 2 nm. We utilized two different transport measurement techniques to
probe the SHE, non-local transport and spin-torque ferromagnetic resonance
(ST-FMR), which probe the spin currents flow in the ultrathin Au layers in the
in-plane and the out-of-plane directions, respectively (see Fig. 1). In these
two measurements, we are probing the spin-to-charge conversion in ultrathin Au
arising from both bulk SHE and interfacial SOC-related effects. Hence, the
spin-to-charge conversion in ultrathin Au will be characterized by a spin-
charge conversion efficiency ($\theta$${}_{\text{sc}}$), rather than by a bulk
SHA. We demonstrate that $\theta$${}_{\text{sc}}$ is strongly enhanced in
ultrathin Au/Si multilayers, reaching values much larger than all SHA values
previously reported for Au films Seki2008 ; Brangham2016 ; Chen2019 .
Moreover, a similar thickness-dependent behavior of $\theta$${}_{\text{sc}}$
was obtained using the ST-FMR technique, however, with much lower
$\theta$${}_{\text{sc}}$ values. These findings indicate the coexistence of
the bulk SHE with a relatively low bulk SHA and a strong interfacial SOC
effect which becomes dominant in ultrathin Au. Our results rule out an
interpretation of the thickness-dependent behavior of the spin-charge
conversion efficiency in Au by the intrinsic SHE or the extrinsic skew
scattering SHE mechanisms and, more importantly, suggest the key role of the
Rashba-Edelstein mechanism in the giant spin-to-charge conversion in ultrathin
Au.

##  II Sample fabrication

We have chosen to study the SHE in ultrathin Au/Si multilayers as they provide
a unique opportunity to investigate spin-charge conversion efficiency of Au
averaged over many individual Au layers, thereby giving more accuracy in the
spin Hall properties measurements. Moreover, it has been shown experimentally
that Au/Si(111) interfaces can have metallic spin-split surface states with an
energy splitting up to 190 meV, which at the same time is very sensitive to
the local structure Bondarenko2013 . Furthermore, Au/Si multilayers present a
very promising system that exhibits the properties of hyperbolic metamaterials
(HMMs), which have recently emerged as one of the prime candidates for
extraordinary manipulation of light Shen2015 ; Qian2021 . In our non-local
transport experiments, which probe the spin currents flow in the in-plane
direction, as shown in Fig. 1(a), four different samples were investigated:
two single polycrystalline Au films [Au (10 nm) and Au (60 nm)]; and two Au/Si
multilayers [[Si (1.8 nm)/Au (2 nm)]${}_{\text{x5}}$ and Au (5 nm)/[Si (4
nm)/Au (5 nm)]${}_{\text{x5}}$]. Each sample was deposited on a glass/Cr (3
nm) substrate using a DC sputtering technique. The Cr buffer layer is used to
ensure good adhesion of the single Au layers and the Au/Si multilayers to the
substrate (see Supplemental Material, Methods Supplemental ). The thickness of
the insulating Si interlayers is chosen to be sufficiently large
(t${}_{\text{Si}}$ $\geq$ 1.5 nm) to prevent strong coupling between the
individual Au layers Cherradi1989 . To verify the multilayer nature of the
studied sample with the thinnest Si and Au layer thicknesses of 1.8 nm and 2
nm, we performed dark-field cross-sectional scanning transmission electron
microscopy (STEM). Fig. 1(c) shows the cross-sectional STEM view of the [Si
(1.8 nm)/Au (2 nm)]${}_{\text{x5}}$ multilayer structure, indicating a well-
defined layered Au/Si structure and the absence of a strong cumulative
roughness along the growth direction. The multilayer nature of the studied
Au/Si films was also confirmed by X-ray reflectivity measurements, and with
high-resolution transmission microscopy (HR-TEM) imaging on ultrathin Au/Si
multilayers grown on a c-Si substrate (see Supplemental Material, Fig. S1
Supplemental ).

To further investigate the dependence of spin Hall properties on the direction
of the spin currents, we also used the ST-FMR technique which probes the spin
currents that flow in the out-of-plane direction, as illustrated in Fig. 1(b).
In our ST-FMR experiments, we investigated both single Au films and ultrathin
Au/Si multilayers: three single polycrystalline Au (t${}_{\text{Au}}$) films,
where t${}_{\text{Au}}$ = 2, 3, 5 nm; and nine Au (t${}_{\text{Au}}$)/[Si
(t${}_{\text{Si}}$)/Au (t${}_{\text{Au}}$)]${}_{\text{x4}}$ multilayers, where
t${}_{\text{Au}}$ = 2, 3, 4 nm and the thickness of the insulating Si
interlayers t${}_{\text{Si}}$ = 2, 3, 4 nm. Each of these single Au films and
Au/Si multilayers was sputter-deposited on a glass/Si (5 nm) substrate, and
was capped with Ni${}_{\text{81}}$Fe${}_{\text{19}}$ (4 nm)/SiN${}_{\text{x}}$
(3 nm). The relatively low thickness of the
Ni${}_{\text{81}}$Fe${}_{\text{19}}$ layer is chosen to ensure that the radio-
frequency (RF) charge current flows evenly through the
Ni${}_{\text{81}}$Fe${}_{\text{19}}$ and individual Au layers, while the 3-nm-
thick SiN${}_{\text{x}}$ capping layer is used to prevent oxidation of the
Ni${}_{\text{81}}$Fe${}_{\text{19}}$ layer (see Supplemental Material, Methods
Supplemental ).

Figure 1:  a) and b) Schematic representation of the spin Hall effect in
ultrathin Au/Si multilayers showing the in- and out-of-plane spin currents,
respectively. c) Dark-field cross-sectional STEM image of [Si (1.8 nm)/Au (2
nm)]${}_{\text{x5}}$ multilayer stack sputtered on a glass/Cr (3 nm), showing
well-defined layered structure. The lighter regions correspond to the Au
layers, while the dark regions correspond to the Si interlayers and the Cr
buffer layer.

##  III Results

###  III.1 Non-local transport measurements

To probe the non-local transport, we patterned the four studied films into
H-bar devices depicted in Fig. 2(a) using e-beam lithography and Ar ion-beam
etching (see Supplemental Material, Methods Supplemental ). A top-view
scanning electron microscope (SEM) image of the central region of such a H-bar
device is shown in Fig. 2(b). The Hall bar device consists of six vertical
wires of a width w separated by a center-to-center distance L and bridged by a
horizontal wire of the same w. For the two Au/Si multilayers and the single Au
(10 nm) samples, w is chosen to be 90 nm; this dimensionality is confirmed
from SEM images, from which w is measured to be (90 $\pm$ 5) nm. On the other
hand, the width w for the single Au (60 nm) sample is (110 $\pm$ 5) nm to be
consistent with the previous study by Mihajlović et al. on the non-local
transport in Au (60 nm) H-bar structures Mihajlovic2009 . Moreover, the
distance between the vertical wires L is varied from (180 $\pm$ 10) nm to (550
$\pm$ 10) nm for all studied samples. To perform the non-local transport
measurements, an unpolarized AC current is injected along the left vertical
wire (y-axis) while a non-local voltage is measured in the adjacent wire (y
direction). Three different transport mechanisms contribute to the non-local
signal – the spin diffusive, the charge diffusive and the quasi-ballistic
electron transport, as illustrated in Fig. 2(c), 2(d) and 2(e), respectively.

Figure 2:  a) Experimental schematic of the non-local resistance measurement
on Au/Si multilayers. b) Top-view SEM image of the Si (1.8 nm)/Au (2 nm)
multilayer film patterned into a H-bar device with six vertical 90-nm-wide
wires separated by various distances and bridged by a horizontal one. c), d)
and e) Schematic representation of the three mechanisms involved in the non-
local transport in H-bar structures, namely the spin diffusive, the charge
diffusive and the quasi-ballistic transport, respectively.

In the previous experimental studies utilizing non-local transport, the spin
diffusive contribution to the non-local signal was interpreted solely in terms
of the bulk SHE Mihajlovic2009 ; Tian2016 ; Chen2019 . As shown in Fig. 2(c),
the unpolarized charge current injected along the vertical wire induces a spin
current in the horizontal wire due to the direct SHE. The spin current then
diffuses and induces charge accumulation across the adjacent vertical wire via
the inverse spin Hall effect (ISHE). Nevertheless, it was reported by Abanin
et al. Abanin2009  that the spin diffusive contribution can result not only
from the bulk SHE, but also from interfacial SOC-related effects such as the
Edelstein effect and the Rashba SOC. Unlike for bulk SHE, the charge current
in systems with strong 2D Rashba SOC induces a spin accumulation rather than a
spin current, which creates a charge current in the adjacent wire via the
inverse Edelstein effect. In our study, the spin diffusive contribution to the
non-local transport in single Au layers and ultrathin Au/Si multilayers will
be interpreted as originating from both the bulk SHE and interfacial SOC-
related effects. Therefore, the spin-to-charge conversion in the studied H-bar
structures is characterized by a spin-charge conversion efficiency
$\theta$${}_{\text{sc}}$, rather than by a bulk SHA $\theta$${}_{\text{SHE}}$.
According to the model by Abanin et al. Abanin2009 , the spin diffusive
contribution to the non-local resistance for l${}_{\text{e}}$ $\leq$ w, where
l${}_{\text{e}}$ is electron mean free path, is expressed by:

$\
R_{\mathrm{nl}}^{sd}=\frac{1}{2}R_{\mathrm{sq}}\theta_{\mathrm{sc}}^{2}\frac{w}{l_{\mathrm{s}}}\exp\left(-\frac{L}{l_{\mathrm{s}}}\right)$
(1)

where l${}_{\text{s}}$ is the spin diffusion length, $\theta$${}_{\text{sc}}$
is the spin-charge conversion efficiency, and R${}_{\text{sq}}$ is the sheet
resistance of the wire. In the case of [Au (t${}_{\text{Au}}$)/Si
(t${}_{\text{Si}}$)]${}_{\text{N}}$ multilayers where we assume that charge
transport is negligible in Si, the sheet resistance equals
$\frac{\rho_{\mathrm{Au}}}{N\textit{t}_{\mathrm{Au}}}$, where
$\rho$${}_{\text{Au}}$ is the resistivity of the individual Au layers,
t${}_{\text{Au}}$ is the thickness of the individual Au layers, and N is the
number of repeats.

In addition to the spin diffusive contribution, charge diffusion also
contributes to the non-local signal when l${}_{\text{e}}$ $\leq$ w. This
corresponds to the spreading of the charge current density into the horizontal
wire, leading to a non-zero voltage in the adjacent wire, as illustrated in
Fig. 2(d). The charge diffusion contribution is defined as:

$\ R_{\mathrm{nl}}^{cd}=R_{\mathrm{sq}}\exp\left(-\pi\frac{L}{w}\right)$ (2)

On the other hand, the electrons can also travel ballistically over the
horizontal wire and then scatter ballistically into the lower region of the
adjacent wire, thus generating a negative voltage as shown in Fig. 2(e). As
described in Mihajlovic2009 , the quasi-ballistic contribution to the non-
local signal can be expressed by:

$\
R_{\mathrm{nl}}^{b}=-bR_{\mathrm{sq}}\exp\left(-\frac{w}{l_{\mathrm{e}}}\right)\exp\left(-\pi\frac{L}{w}\right)$
(3)

Figure 3:  a) Resistance of each bridge wire between adjacent vertical wires
of Au (5 nm)/Si (4 nm) multilayers as a function of L at T = 5 K. The blue
solid line is a linear fit to the data. Upper inset: Experimental schematic of
the local resistance measurement on Au/Si multilayers. b) Resistivity
$\rho$${}_{\text{Au}}$ and the corresponding electron mean free path
l${}_{\text{e}}$ as a function of the inverse Au thickness 1/t${}_{\text{Au}}$
at 5 K, measured for the Au (t${}_{\text{Au}}$ = 10, 60 nm) films, as well as
Au (t${}_{\text{Au}}$ = 2, 5 nm)/Si multilayers. The lines are guide to the
eyes.

where l${}_{\text{e}}$ is the electron mean-free path and b is a fitting
parameter. Hence, measuring a negative non-local resistance in the studied
H-bar structures would be a signature of the quasi-ballistic transport
mechanism Mihajlovic2009 . To determine the sheet resistance R${}_{\text{sq}}$
of our four samples, we measured the local resistance R${}_{\text{xx}}$ as a
function of temperature T for each segment of the horizontal wire between the
adjacent vertical wires, as shown in the inset of Fig. 3(a). One can see from
Fig. 3(a) that the local resistance R${}_{\text{xx}}$ increases linearly with
the distance L at T = 5 K. Moreover, the linear fit of R${}_{\text{xx}}$
crosses the L-axis in a finite distance L${}_{\text{0}}$, indicating that the
effective distance between each of the adjacent vertical wires corresponds to
L${}_{\text{eff}}$ = L \- L${}_{\text{0}}$. This finding is in agreement with
previous studies Mihajlovic2009 , and is attributed to the spreading of the
charge current density into the vertical wires due to their finite width
Mihajlovic2009 . For wires with w = 90 nm, we measured an L${}_{\text{0}}$ of
(135 $\pm$ 5) nm. In the following, we will use L = L${}_{\text{eff}}$ in
Equation 1, 2 and 3.

To accurately estimate the resistivity of the Au layers
$\rho$${}_{\text{Au}}$, we first measured the resistivity of the 3-nm-thick Cr
buffer layer $\rho$${}_{\text{Cr}}$ by performing temperature dependent
resistance measurements on a glass/Cr (3 nm)/AlO${}_{\text{x}}$ (3 nm) sample.
The AlO${}_{\text{x}}$ capping layer is used to prevent oxidation of the Cr
layer. We found that the resistivity of the 3-nm-thick Cr layer decreases with
increasing temperature from 250.1 $\mu\Omega$.cm at 5 K to 232.9
$\mu\Omega$.cm at 300 K. Therefore, the high resistivity of the 3-nm-thick Cr
layer relative to that of Au indicates that most of the charge current flows
through the Au layers, thus ruling out any strong contribution of the Cr layer
to the non-local transport in the four investigated samples. Having considered
the resistivity of the Cr buffer layer, we measured the temperature dependence
of the resistivity of the individual Au layers ($\rho$${}_{\text{Au}}$) for
the four studied samples. Fig. 3(b) shows that the resistivity
$\rho$${}_{\text{Au}}$ is inversely proportional to the thickness of the
individual Au layers t${}_{\text{Au}}$. Indeed, $\rho$${}_{\text{Au}}$
strongly increases from a bulk value of 2.2 $\mu\Omega$.cm (resp. 3.79
$\mu\Omega$.cm) at 5 K (resp. 300 K) for the single Au (t${}_{\text{Au}}$ = 60
nm) sample, to a much higher value of 29.4 $\mu\Omega$.cm (resp. 35.27
$\mu\Omega$.cm) at 5 K (resp. 300 K) for Au (t${}_{\text{Au}}$ = 2 nm)/Si (1.8
nm) multilayers. Such an increase in resistivity for ultrathin Au is in
agreement with previous studies Brangham2016 , and is mainly attributed to the
dominance of surface scattering for ultrathin films. We further calculated the
electron mean free path l${}_{\text{e}}$ values for the four studied samples
using the Drude formula with an electron density for Au of $n=5.9\times
10^{28}$ m-3 Mihajlovic2009 . We found that l${}_{\text{e}}$ strongly
decreases from 38.2 nm (resp. 22.12 nm) at 5 K (resp. 300 K) for the single Au
(60 nm) layer sample (in agreement with Ref. Mihajlovic2009 ) to 2.95 nm
(resp. 2.48 nm) at 5 K (resp. 300 K) for Au (t${}_{\text{Au}}$ = 2 nm)/Si (1.8
nm) multilayers. These findings are attributed to the strong increase of
$\rho$${}_{\text{Au}}$ in the ultrathin Au layers, and suggest that the quasi-
ballistic contribution to the non-local resistance will be strongly suppressed
in ultrathin Au-based multilayers.

Figure 4:  a) Temperature dependence of R${}_{\text{nl}}$/R${}_{\text{sq}}$
measured for Au (t${}_{\text{Au}}$ = 10, 60 nm) films and for adjacent wires
separated by a distance L = 340 nm. b) Temperature dependence of
R${}_{\text{nl}}$/R${}_{\text{sq}}$ measured for Au (t${}_{\text{Au}}$ = 5
nm)/Si (4 nm) and Au (t${}_{\text{Au}}$ = 2 nm)/Si (1.8 nm) multilayers and
for wires separated by a distance L = 340 nm and 450 nm, respectively. c)
Logarithmic plot of the spin-charge conversion efficiency
$\theta$${}_{\text{sc}}$ as a function of t${}_{\text{Au}}$ measured at T = 5
K for the single Au (t${}_{\text{Au}}$= 10, 60 nm) films, as well as Au
(t${}_{\text{Au}}$ = 5 nm)/Si (4 nm) and Au (t${}_{\text{Au}}$ = 2 nm)/Si (1.8
nm) multilayers. The blue solid line is a fit to the non-local transport data.
For comparison, we also plot the $\theta$${}_{\text{SHE}}$ values of Au from
literature. Red square: study of perpendicularly spin-polarized FePt/Au (10
nm) structure from Seki et al. Seki2008 . Magenta diamond: non-local transport
in Au (60 nm) H-bar structure from Mihajlović et al. Mihajlovic2009 . Green
triangle: non-local transport in Au (10 nm) H-bar structure from Chen et al.
Chen2019 .

We further measured the temperature dependence of the non-local resistance
R${}_{\text{nl}}$ and extracted $\theta$${}_{\text{sc}}$ for the four studied
samples. Since all three different contributions to R${}_{\text{nl}}$ are
proportional to the sheet resistance R${}_{\text{sq}}$, we used the reduced
non-local resistance R${}_{\text{nl}}$/R${}_{\text{sq}}$ to investigate their
temperature dependence. Fig. 4(a) displays the T dependence of
R${}_{\text{nl}}$/R${}_{\text{sq}}$ measured for the single Au (60 nm) layer
with L = 340 nm. One can see from Fig. 4(a) that
R${}_{\text{nl}}$/R${}_{\text{sq}}$ decreases when T is lowered and becomes
negative around 33 K. This finding indicates that the non-local transport
becomes dominated by the quasi-ballistic contribution at low temperatures in
agreement with previous studies Mihajlovic2009 ; Chen2019 . In order to
extract $\theta$${}_{\text{sc}}$ of the 60-nm-thick Au layer, we followed the
method of Mihajlović et al. Mihajlovic2009  by plotting
R${}_{\text{nl}}$/R${}_{\text{sq}}$ as a function of l${}_{\text{e}}$. As
expected, we found that R${}_{\text{nl}}$/R${}_{\text{sq}}$ fits with the
quasi-ballistic and charge diffusive contributions to the non-local signal
($R_{\mathrm{nl}}^{cd}$ \+ $R_{\mathrm{nl}}^{b}$)/R${}_{\text{sq}}$, where the
fitting parameter b = 22.14 is used (see Supplemental Material, Fig. S2).
Thus, we deduced the T dependence of $R_{\mathrm{nl}}^{sd}$/R${}_{\text{sq}}$
by subtracting ($R_{\mathrm{nl}}^{cd}$ \+
$R_{\mathrm{nl}}^{b}$)/R${}_{\text{sq}}$ from
R${}_{\text{nl}}$/R${}_{\text{sq}}$. By assuming the spin diffusion length of
Au l${}_{\text{s}}$ = 168 nm (resp. 65 nm) reported in Ref. Ku2006  (resp.
Ref. Ji2004 ), we extracted an upper limit for $\theta$${}_{\text{sc}}$ of the
Au (60 nm) sample of 0.012 (resp. 0.022) at 5 K, thus confirming the absence
of a giant SHE in the studied Au (60 nm) sample. These
$\theta$${}_{\text{sc}}$ values are consistent with the work by Mihajlović et
al. Mihajlovic2009  and, more importantly, confirm the absence of any
contribution from the 3-nm-thick Cr buffer layer to the non-local transport.

In contrast to the single Au (60 nm) layer,
R${}_{\text{nl}}$/R${}_{\text{sq}}$ measured for the single Au (10 nm) layer
with L = 340 nm is always positive and increases when T is lowered, as shown
in Fig. 4(a). This finding is attributed to the increase of the resistivity
$\rho$${}_{\text{Au}}$ in the Au (10 nm) layer, as shown in Fig. 3(b), leading
to much lower l${}_{\text{e}}$ values ranging from 7.47 nm at 300 K to 9.92 nm
at 5 K. Therefore, the contribution of ($R_{\mathrm{nl}}^{cd}$ \+
$R_{\mathrm{nl}}^{b}$)/R${}_{\text{sq}}$ to
R${}_{\text{nl}}$/R${}_{\text{sq}}$ measured for the Au (10 nm) layer is not
as dominant as for the Au (60 nm) layer, which explains the difference
observed in the T dependence of R${}_{\text{nl}}$/R${}_{\text{sq}}$ between
these two samples. By assuming the b value of $\sim$ 22.14 , we found that
($R_{\mathrm{nl}}^{cd}$ \+ $R_{\mathrm{nl}}^{b}$)/R${}_{\text{sq}}$
corresponds to $7.18\times 10^{-4}$ at 5 K for the Au (10 nm) layer. By
subtracting ($R_{\mathrm{nl}}^{cd}$ \+
$R_{\mathrm{nl}}^{b}$)/R${}_{\text{sq}}$ from
R${}_{\text{nl}}$/R${}_{\text{sq}}$, we deduced a spin diffusion contribution
$R_{\mathrm{nl}}^{sd}$/R${}_{\text{sq}}$ of $4.27\times 10^{-4}$. To extract
$\theta$${}_{\text{sc}}$ of Au (10 nm), we assumed l${}_{\text{s}}$ = (75
$\pm$ 5) nm at 5 K, as demonstrated in a recent study on the non-local
transport in Au (10 nm) Chen2019 . From this, we extracted
$\theta$${}_{\text{sc}}$ of 0.1 $\pm$ 0.05 for the Au (10 nm) layer, which is
in good agreement with other previous studies Seki2008 ; Tian2016 ; Chen2019
as shown in Fig. 4(c). We now elucidate the non-local transport in the
ultrathin Au/Si multilayers via the same approach previously used for the
single Au layers. For Au (t${}_{\text{Au}}$ $\leq$ 5 nm) layers, the electron
mean free path l${}_{\text{e}}$ is drastically reduced (l${}_{\text{e}}$
$\leq$ 6 nm) as previously discussed in Fig. 3(b). Hence, the quasi-ballistic
contribution $R_{\mathrm{nl}}^{b}$/R${}_{\text{sq}}$ will be strongly
suppressed for the ultrathin Au/Si multilayers. Fig. 4(b) shows that
R${}_{\text{nl}}$/R${}_{\text{sq}}$ measured for the Au (t${}_{\text{Au}}$
$\leq$ 5 nm)/Si multilayers is always positive and increases when T is
lowered, thus indicating that the non-local transport in these two multilayers
is mostly dominated by the spin diffusion.

To extract $\theta$${}_{\text{sc}}$ in these multilayers, we should first take
into consideration the change of the spin diffusion length with the increase
of $\rho$${}_{\text{Au}}$ in the ultrathin Au. Indeed, it was previously
reported in literature on materials with large l${}_{\text{s}}$ and spin
relaxation via the Elliott-Yafet mechanism such as Au Ku2006  and Cu
Villamor2013 , that l${}_{\text{s}}$ at low T decreases with the resistivity
following the opposite trend of the thickness Ku2006 ; Villamor2013 . On the
other hand, we measured a strong increase of $\rho$${}_{\text{Au}}$ at 5 K
from the bulk value of 2.2 to 29.4 $\mu\Omega$.cm for 2-nm-thick Au.
l${}_{\text{s}}$ is thus expected to be shorter for the ultrathin Au/Si
multilayers. Therefore, it is reasonable to assume, for our estimation of a
lower limit of $\theta$${}_{\text{sc}}$, that l${}_{\text{s}}$ corresponds to
at most (43 $\pm$ 5) nm and (35 $\pm$ 5) nm at 5 K for each of the individual
Au (5 nm) and Au (2 nm) layers, respectively. At T = 5 K, we extracted the
following values: $\theta$${}_{\text{sc}}$ (t${}_{\text{Au}}$ = 5 nm) = 0.41
$\pm$ 0.09 and $\theta$${}_{\text{sc}}$ (t${}_{\text{Au}}$ = 2 nm) = 0.99
$\pm$ 0.34, which are significantly larger than those extracted for the single
Au (t${}_{\text{Au}}$ = 10, 60 nm) films. Furthermore, we extracted a room-
temperature (RT) $\theta$${}_{\text{sc}}$ value of 0.87 $\pm$ 0.34 for Au (2
nm)/Si (1.8 nm) multilayers by assuming l${}_{\text{s}}$ = (35 $\pm$ 5) nm,
which is exceedingly larger than bulk $\theta$${}_{\text{SHE}}$ values
reported for other heavy metals, such as -0.33 for $\beta$-W (from Pai2012 ),
-0.12 for $\beta$-Ta (from Liu2012a ), and 0.1 for Pt (from Althammer2013 ;
Zhang2013 ). This implies that the extracted spin-charge conversion efficiency
$\theta$${}_{\text{sc}}$ from the spin diffusive term of the non-local
resistance cannot be interpreted solely in terms of the bulk SHE. By plotting
the $\theta$${}_{\text{sc}}$ values measured for the four samples in a single
graph on a logarithmic scale, one can see from Fig. 4(c) that
$\theta$${}_{\text{sc}}$ at T = 5 K is strongly enhanced for ultrathin Au
thickness. This finding implies that the thickness and, therefore, the
resistivity have a decisive effect on the spin-to-charge conversion in Au.
More importantly, this strongly suggests the coexistence of a bulk SHE
($\theta_{\mathrm{SHE}}^{bulk}\approx\theta_{\mathrm{sc}}(t_{\mathrm{Au}}=60$
nm) = 0.012 $\pm$ 0.005) with a strong interfacial SOC effect which becomes
dominant in ultrathin Au.

###  III.2 ST-FMR measurements

To give more insight into the microscopic origin of the SHE in the ultrathin
Au layers, it is important to elucidate the anisotropy of the SHE with respect
to the spin current flow direction. In this context, we further investigate
the thickness-dependence of the SHE in Au by using the ST-FMR technique which
probes the spin currents flow in the out-of-plane direction, as illustrated in
Fig. 5(a). We studied both single Au
(t${}_{\text{Au}}$)/Ni${}_{\text{81}}$Fe${}_{\text{19}}$ (4 nm) bilayers,
where t${}_{\text{Au}}$ = 2, 3, 5 nm; and ultrathin Au (t${}_{\text{Au}}$)/[Si
(t${}_{\text{Si}}$)/Au
(t${}_{\text{Au}}$)]${}_{\text{x4}}$/Ni${}_{\text{81}}$Fe${}_{\text{19}}$ (4
nm) multilayers, where t${}_{\text{Au}}$ = 2, 3, 4 nm and t${}_{\text{Si}}$ =
2, 3, 4 nm. The magnetization M of the 4-nm-thick
Ni${}_{\text{81}}$Fe${}_{\text{19}}$ layer is oriented in-plane.

Figure 5:  ST-FMR measurement on single
Au/Ni${}_{\text{81}}$Fe${}_{\text{19}}$ bilayers and ultrathin
[Si/Au]${}_{\text{N}}$/Ni${}_{\text{81}}$Fe${}_{\text{19}}$ multilayer stacks.
a) Schematic representation of the ST-FMR measurement in the ultrathin Au
(t${}_{\text{Au}}$)/[Si (t${}_{\text{Si}}$)/Au
(t${}_{\text{Au}}$)]${}_{\text{x4}}$/Ni${}_{\text{81}}$Fe${}_{\text{19}}$ (4
nm) multilayer stack. I${}_{\text{RF}}$ and H${}_{\text{RF}}$ represent the
applied radio-frequency (RF) current and the corresponding Oersted field,
respectively. The out-of-plane spin current generated via the SHE in the top
ultrathin Au layer induces a spin-transfer torque $\tau$${}_{\text{ST}}$ in
the Ni${}_{\text{81}}$Fe${}_{\text{19}}$ layer. $\tau$${}_{\text{H}}$
illustrates the torque induced by the Oersted field. H and M correspond to the
external applied field and the magnetization of the
Ni${}_{\text{81}}$Fe${}_{\text{19}}$ layer, respectively. $45^{\circ}$ is the
angle between applied field H and the magnetization M. b) and c)
Representative ST-FMR resonance signals measured on Au
(t${}_{\text{Au}}$)/Ni${}_{\text{81}}$Fe${}_{\text{19}}$ (4 nm) under a
driving frequency f = 8 GHz and at room temperature, where t${}_{\text{Au}}$ =
2, 3 and 5 nm. The symbols in b) represent the measured DC voltage
V${}_{\text{mix}}$ data. The solid lines in b) and c) represent the
antisymmetric and symmetric Lorentzian fitting curves, respectively, whose sum
fits the measured V${}_{\text{mix}}$ data. d) $\theta$${}_{\text{sc}}$
measured for single Au (t${}_{\text{Au}}$)/Pt (4 nm) bilayers as a function of
t${}_{\text{Au}}$, where t${}_{\text{Au}}$ = 2, 3, 5 nm. e)
$\theta$${}_{\text{sc}}$ measured for ultrathin Au (t${}_{\text{Au}}$)/[Si
(t${}_{\text{Si}}$)/Au
(t${}_{\text{Au}}$)]${}_{\text{x4}}$/Ni${}_{\text{81}}$Fe${}_{\text{19}}$ (4
nm) multilayers as a function of t${}_{\text{Au}}$, where t${}_{\text{Au}}$ =
2, 3, 4 nm and t${}_{\text{Si}}$ = 2, 3, 4 nm.

To probe the ST-FMR, we first patterned these studied films into
24-$\mu$m-wide and 88-$\mu$m-long microstrips using photolithography, and then
fabricated symmetric waveguide contacts using DC sputtering and lift-off (see
Supplemental Material, Methods Supplemental ). We applied an oscillating
radio-frequency (RF) charge current I${}_{\text{RF}}$ at fixed frequencies
(7-9 GHz) along the microstrips, and swept an external magnetic field H in the
in-plane direction at a $45^{\circ}$ angle with respect to the RF current
direction, as illustrated in Fig. 5(a). An oscillating transverse spin current
is then generated in each of the individual Au layers via the SHE. Hence, an
oscillating spin-transfer torque induced by the out-of-plane spin current from
the top Au layer is exerted on the Ni${}_{\text{81}}$Fe${}_{\text{19}}$ layer,
leading to magnetization precession and an oscillation of the anisotropic
magnetoresistance of Ni${}_{\text{81}}$Fe${}_{\text{19}}$. This anisotropic
magnetoresistance transforms the magnetization precession in
Ni${}_{\text{81}}$Fe${}_{\text{19}}$ into an RF resistance oscillation, which,
by mixing with the RF current, generates a measurable dc voltage signal
V${}_{\text{mix}}$ across the sample. By varying the strength of the applied
magnetic field H, the precession frequency of
Ni${}_{\text{81}}$Fe${}_{\text{19}}$ is controlled, creating a resonance in
V${}_{\text{mix}}$. To extract the spin-charge conversion efficiency of Au, we
then use a lineshape analysis of the measured V${}_{\text{mix}}$. Indeed, the
resonance peak of the measured V${}_{\text{mix}}$ can be fitted by the sum of
a symmetric Lorentzian F${}_{\text{Sym}}$ (H) and an antisymmetric Lorentzian
F${}_{\text{Asym}}$ (H) as [S F${}_{\text{Sym}}$ (H) + A F${}_{\text{Asym}}$
(H)] Liu2011 . The symmetric component S is a consequence of the spin Hall
anti-damping torque induced by the out-of-plane spin current from the top Au
layer. The antisymmetric component A arises from the field-like torques,
expected to be dominated by the Oersted field H${}_{\text{RF}}$ from the RF
current in each of the individual Au layers. The ST-FMR resonance signal
V${}_{\text{mix}}$ measured on single Au
(t${}_{\text{Au}}$)/Ni${}_{\text{81}}$Fe${}_{\text{19}}$ (4 nm) bilayers is
exemplarily shown in Fig. 5(b). The corresponding antisymmetric and symmetric
peaks are shown in Fig. 5(b) and Fig. 5(c), respectively.

We further quantitatively determined the $\theta$${}_{\text{sc}}$ values in
the studied samples by using the ratio of the symmetric component S to the
antisymmetric component A. As described in Ref. Liu2011 ,
$\theta$${}_{\text{sc}}$ of Au can be expressed by:

$\
\theta_{\mathrm{sc}}=\frac{S}{A}\frac{e\mu_{\mathrm{0}}M_{\mathrm{s}}t_{\mathrm{NiFe}}Nt_{\mathrm{Au}}}{\hbar}\left(1+\frac{4\pi
M_{\mathrm{eff}}}{H}\right)^{\frac{1}{2}}$ (4)

where $\mu$${}_{\text{0}}$ is the permeability in vacuum, M${}_{\text{s}}$ is
the saturation magnetization of Ni${}_{\text{81}}$Fe${}_{\text{19}}$,
M${}_{\text{eff}}$ is the effective magnetization of
Ni${}_{\text{81}}$Fe${}_{\text{19}}$ which characterizes the out-of-plane
demagnetization field, t${}_{\text{NiFe}}$ is the thickness of the
Ni${}_{\text{81}}$Fe${}_{\text{19}}$ layer, t${}_{\text{Au}}$ is the thickness
of the individual Au layers, N is the number of the individual Au layers, and
H is the external magnetic field. For each of the studied samples,
M${}_{\text{s}}$ is measured with vibrating sample magnetometry (VSM), while
$4\pi M_{\mathrm{eff}}$ is extracted by fitting the frequency dependence of
the resonance field to the Kittel equation Liu2011 . We found that the values
M${}_{\text{s}}$ and M${}_{\text{eff}}$ are very similar, around $6.7\times
10^{5}$ A/m, which is mainly due to the strong in-plane anisotropy of the
Ni${}_{\text{81}}$Fe${}_{\text{19}}$ layer.

Fig. 5(d) displays the Au thickness dependency of the room-temperature
$\theta$${}_{\text{sc}}$ values measured for single Au
(t${}_{\text{Au}}$)/Ni${}_{\text{81}}$Fe${}_{\text{19}}$ (4 nm) bilayers,
where t${}_{\text{Au}}$ = 2, 3, 5 nm. One can see from Fig. 5(d) that
$\theta$${}_{\text{sc}}$ strongly increases from $8.5\times 10^{-3}$ to 0.025
when t${}_{\text{Au}}$ is scaled down from 5 to 2 nm, a trend that is
consistent with the non-local transport results. Nevertheless, these room-
temperature $\theta$${}_{\text{sc}}$ values obtained from the ST-FMR are much
smaller than those extracted from the non-local transport at T = 5 K. First,
this finding can be attributed to the decrease of $\theta$${}_{\text{sc}}$
with T, as reported in a previous study on Au Isasa2015 . Second, the
$\theta$${}_{\text{sc}}$ values obtained from the ST-FMR do not account for
the reduction of the spin transparency at the
Au/Ni${}_{\text{81}}$Fe${}_{\text{19}}$ interface originating from the spin
backflow (SBF) and the spin memory loss (SML) Pai2015 , which is thought to
often reduce of the out-of-plane spin torques by at least a factor of two.
Hence, it is reasonable to attribute the discrepancy between the
$\theta$${}_{\text{sc}}$ values obtained with both ST-FMR and non-local
transport techniques to the reduction of the spin transparency at the
Au/Ni${}_{\text{81}}$Fe${}_{\text{19}}$ interface. On the other hand, these
findings might also suggest that the SHE in ultrathin Au is anisotropic,
favoring more efficient spin-to-charge conversion in the in-plane direction
rather than the out-of-plane direction. We further extracted the room-
temperature $\theta$${}_{\text{sc}}$ values in ultrathin Au
(t${}_{\text{Au}}$)/[Si (t${}_{\text{Si}}$)/Au
(t${}_{\text{Au}}$)]${}_{\text{x4}}$/Ni${}_{\text{81}}$Fe${}_{\text{19}}$ (4
nm) multilayers, as shown in Fig. 5(e). Similarly to the single
Au/Ni${}_{\text{81}}$Fe${}_{\text{19}}$ bilayers, $\theta$${}_{\text{sc}}$
increases from 0.012 to 0.039 by scaling down t${}_{\text{Au}}$ from 4 to 2 nm
in ultrathin [Si/Au]${}_{\text{N}}$/Ni${}_{\text{81}}$Fe${}_{\text{19}}$
multilayers. Note that these $\theta$${}_{\text{sc}}$ values are slightly
larger than those obtained for single Au/Ni${}_{\text{81}}$Fe${}_{\text{19}}$
bilayers. This finding may be explained by the enhanced surface scattering in
[Si/Au]${}_{\text{N}}$/Ni${}_{\text{81}}$Fe${}_{\text{19}}$ multilayers due to
the sample roughness, which enhances the extrinsic contribution to the SHE
and, therefore, the $\theta$${}_{\text{sc}}$ value.

##  IV Discussion

The sharp increase of the $\theta$${}_{\text{sc}}$ in ultrathin Au,
demonstrated by both non-local transport and ST-FMR techniques, calls into
question the interpretation of the spin-to-charge conversion as originating
solely from the bulk SHE, and suggests the coexistence of both bulk and
interfacial mechanisms. To further elucidate the microscopic origin of the
spin-to-charge conversion in Au, we discuss the thickness dependence of
$\theta$${}_{\text{sc}}$ by fully accounting for both intrinsic and extrinsic
SHEs. Owing to the intrinsic SOC in the band structure, the intrinsic SHA in
Au can be expressed by $\theta$${}_{\text{SHE}}$intrinsic =
$\sigma$${}_{\text{SHE}}$intrinsic/$\sigma$${}_{\text{Au}}$, where
$\sigma$${}_{\text{SHE}}$intrinsic is the intrinsic SHE conductivity and
$\sigma$${}_{\text{Au}}$ is the longitudinal conductivity of Au. Such an
intrinsic contribution can be the dominant mechanism in a moderately dirty
metal, as reported in an experimental study on Pt by Sagasta et al.
Sagasta2016 . Since scaling down the Au thickness to a few nm is accompanied
by a strong increase of the resistivity $\rho$${}_{\text{Au}}$, one may
intuitively attribute the strong enhancement of $\theta$${}_{\text{sc}}$ in
ultrathin Au to the intrinsic SHE mechanism. Nevertheless, the intrinsic SHE
conductivity of Au is relatively small due to the small d-electron density of
states at the Fermi level, in contrast to that of Pt Tanaka2008 . Indeed,
theoretical studies on Au have predicted relatively small
$\sigma$${}_{\text{SHE}}$intrinsic values, namely 400 $\Omega^{-1}$.cm-1
Guo2009  and 731 $\Omega^{-1}$.cm-1 Yao2005 . To verify the role of the
intrinsic SHE in Au, we plot in Fig. 6 the measured $\theta$${}_{\text{sc}}$
values and the theoretically predicted $\sigma$${}_{\text{SHE}}$intrinsic as a
function of $\sigma$${}_{\text{Au}}$ on a logarithmic scale. Despite the
discrepancy between the $\theta$${}_{\text{sc}}$ values measured with non-
local transport and ST-FMR techniques, one can see from Fig. 6 that
logarithmic slopes of $\theta$${}_{\text{sc}}$ for both techniques are very
similar. Moreover, Fig. 6 shows that $\theta$${}_{\text{SHE}}$intrinsic
increases in ultrathin Au with low $\sigma$${}_{\text{Au}}$ values, with a
logarithmic slope smaller than the one of the measured
$\theta$${}_{\text{sc}}$. More importantly, the predicted
$\theta$${}_{\text{SHE}}$intrinsic values in ultrathin Au are still negligible
compared to the $\theta$${}_{\text{sc}}$ values measured with the non-local
transport as well as the SHA values reported in previous studies Seki2008 ;
Mihajlovic2009 ; Chen2019 . Therefore, the intrinsic SHE contribution is
negligible and cannot explain the strong increase of $\theta$${}_{\text{sc}}$
in ultrathin Au.

Figure 6:  Logarithmic plot of the spin-charge conversion efficiency sc as a
function of the longitudinal conductivity $\sigma$${}_{\text{Au}}$ of Au for
the samples investigated in this work with non-local transport and ST-FMR
measurements. The blue and red solid lines are a fit to the non-local
transport and ST-FMR data, respectively. The green and magenta solid lines
correspond to the intrinsic contribution to the SHA in Au
$\theta$${}_{\text{SHE}}$intrinsic =
$\sigma$${}_{\text{SHE}}$intrinsic/$\sigma$${}_{\text{Au}}$ using
$\sigma$${}_{\text{SHE}}$intrinsic = 400 $\Omega^{-1}$.cm-1 from Guo et al.
Guo2009  and $\sigma$${}_{\text{SHE}}$intrinsic = 731 $\Omega^{-1}$.cm-1 from
Yao et al. Yao2005

The strong increase of $\theta$${}_{\text{sc}}$ is also unlikely to be
explained by the extrinsic skew scattering SHE, since this extrinsic
contribution is dominant only for clean metals Hoffmann2013  and should
decrease in the relatively highly resistive ultrathin Au. Nevertheless,
previous experimental and theoretical studies on the SHE in Au using
perpendicularly spin-polarized FePt/Au structures revealed the key role of the
extrinsic skew scattering contribution Seki2008 ; Seki2010 ; Gu2010 ; Guo2009
. Indeed, it was reported that the large SHA of $\sim$0.11 measured in FePt/Au
(10 nm) structure originates from the extrinsic surface-assisted skew
scattering due to Pt impurities Seki2008 ; Seki2010 ; Gu2010  and/or Fe Kondo
impurities Guo2009 . However, we measured a similar $\theta$${}_{\text{sc}}$
value in Au (10 nm) H-bar structures with the non-local transport, in
agreement with Ref. Chen2019 , where both magnetic and strong SOC impurities
are absent. This finding rules out the interpretation that the strong increase
of $\theta$${}_{\text{sc}}$ in ultrathin Au layers arises from the previously
reported surface-assisted skew scattering mechanism Seki2008 ; Seki2010 ;
Gu2010 ; Guo2009 . Furthermore, it was shown in a recent theoretical study
that the surface scattering combined with a strong interfacial SOC can lead to
a SHE that subscribes only to the extrinsic side-jump SHE, which is usually
dominant for moderately dirty metals Zhou2015 . Hence, this extrinsic
contribution could explain the thickness-dependence of
$\theta$${}_{\text{sc}}$ in Au; however, it is unlikely to explain the large
$\theta$${}_{\text{sc}}$ values measured in ultrathin Au with the non-local
transport.

Previous angle-resolved photoemission spectroscopy (ARPES) studies revealed a
large Rashba-type splitting on Au(111) surface LaShell1996 ; Nicolay2001 ;
Nechaev2009 , indicating the presence of a strong interfacial Rashba SOC. More
importantly, it has been shown in a previous experimental study by Bondarenko
et al. that the Au/Si(111) interface can have metallic spin-split surface
states with a large spin-splitting energy of 190 meV Bondarenko2013 . Since
the sputter-deposited Au/Si multilayer has a strong (111) out-of-plane texture
as shown in Ref. Kan2014 , a strong Rashba spin-orbit splitting should be
present at the Au/Si interfaces in the studied Au/Si multilayers. Note that
since the sputter-growth of Au on Si differs from the one of Si on Au, the
Au/Si and Si/Au interfaces are never quite equivalent. Hence, the Rashba-
Edelstein contributions from opposing interfaces in the investigated Au/Si
multilayers would not cancel out. On the other hand, the spin-splitting energy
at the Au/Si(111) interface is as large as the one reported for the Bi/Ag(111)
interface, i.e., 200 meV Ast2007 . Moreover, Rojas-Sánchez et al.
experimentally demonstrated a large spin-to-charge conversion at the Bi/Ag
Rashba interface Rojas-Sanchez2013 , which yields a SHA of 1.5 when
interpreted only by the bulk SHE. Taking these findings into account, the
increase of $\theta$${}_{\text{sc}}$ in ultrathin Au to exceptionally large
values ($\sim$0.99 for t${}_{\text{Au}}$ = 2 nm) can be plausibly explained by
the Edelstein effect, arising from the strong interfacial Rashba SOC, and not
from the bulk SHE.

##  V Conclusion

In conclusion, we have experimentally investigated the thickness dependence of
the spin-charge conversion efficiency $\theta$${}_{\text{sc}}$ in single Au
films and ultrathin Au/Si multilayers with two different techniques, namely
non-local transport and ST-FMR. We first found that the
$\theta$${}_{\text{sc}}$ values measured for the single Au (t${}_{\text{Au}}$
= 10, 60 nm) layers are consistent with the literature. Moreover, we
demonstrated that $\theta$${}_{\text{sc}}$ of Au measured with the non-local
transport in ultrathin Au (t${}_{\text{Au}}$ = 2, 5 nm)/Si multilayers is
strongly enhanced and reaches exceedingly large values. A similar thickness-
dependent behavior of $\theta$${}_{\text{sc}}$ was obtained using the ST-FMR
technique, however, with much lower $\theta$${}_{\text{sc}}$ values. Our
experimental results evidence the coexistence of a strong interfacial SOC
effect which becomes dominant in ultrathin Au, and bulk SHE with a relatively
low bulk SHA. More importantly, these findings suggest the key role of the
Rashba-Edelstein effect in the spin-to-charge conversion in ultrathin Au, and
help pave the way for the use of ultrathin Au in emerging spintronic devices.

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Acknowledgments

The authors would like to thank A. Fert, G. Mihajlović, M. Stiles, V. P. Amin
and F. Casanova for fruitful discussions, and R. Descoteaux from CMRR for
technical assistance. The sample preparation was supported by the National
Science Foundation under Grant No. NSF-DMR-1610538. The sample
characterization, measurements, and data analysis were supported as part of
Quantum Materials for Energy Efficient Neuromorphic Computing, an Energy
Frontier Research Center funded by the U.S. DOE, Office of Science.

Additional information

The authors declare no competing financial interests.

Supplemental Material

Methods

A. Thin film deposition

Ultrathin Au/Si multilayers were grown by alternately DC magnetron sputtering
Si and Au. Sputtering rates for Au at 50 W and Si at 100 W were 1.15 Å/s and
0.54 Å/s, respectively, as determined by low-angle X-ray reflectivity
measurements of calibration sample film thicknesses. In our non-local
transport experiments, four different samples were studied: two single
polycrystalline Au films (Au (10 nm) and Au (60 nm)); and two Au/Si
multilayers ([Si (1.8 nm)/Au (2 nm)]${}_{\text{x5}}$ and Au (5 nm)/[Si (4
nm)/Au (5 nm)]${}_{\text{x5}}$). Each sample was deposited onto a glass/Cr (3
nm) substrate, where the 3-nm-thick buffer layer is used to ensure good
adhesion of the single Au layers and the Au/Si multilayers to the substrate.
In our ST-FMR experiments, both single Au films and ultrathin Au/Si
multilayers were studied: three single polycrystalline Au (t${}_{\text{Au}}$)
films, where t${}_{\text{Au}}$ = 2, 3, 5 nm; and nine Au/Si multilayers with
the following stacking structure: Au (t${}_{\text{Au}}$)/[Si
(t${}_{\text{Si}}$)/Au (t${}_{\text{Au}}$)]${}_{\text{x4}}$, where
t${}_{\text{Au}}$ = 2, 3, 4 nm and t${}_{\text{Si}}$ = 2, 3, 4 nm. Each of
these samples was deposited on a glass/Si (5 nm) substrate and capped with
Ni${}_{\text{81}}$Fe${}_{\text{19}}$ (4 nm)/SiN${}_{\text{x}}$ (3 nm). The
SiN${}_{\text{x}}$ layer helps prevent Ni${}_{\text{81}}$Fe${}_{\text{19}}$
oxidation. The Ni${}_{\text{81}}$Fe${}_{\text{19}}$ layers were grown by DC
sputtering, while the SiN${}_{\text{x}}$ layers grown by RF sputtering.
Sputtering rates for Ni${}_{\text{81}}$Fe${}_{\text{19}}$ at 100 W and
SiN${}_{\text{x}}$ at 150 W were 0.49 Å/s and 0.092 Å/s, respectively. The
base pressure of the chamber was 5$\times$10-8 Torr, and all depositions were
performed at room temperature in an Ar gas atmosphere with a pressure fixed at
2.7 mTorr.

B. Device fabrication and characterization

In our non-local transport experiments, the four studied films were patterned
into H-bar devices using a PMMA (100 nm)/HSQ (90 nm) bilayer resist e-beam
lithography process. The films were then etched to the glass top surface using
Ar ion beam etching. Photolithography, DC sputtering and lift-off techniques
were then used to fabricate the top contact pads consisting of Ti (10 nm)/Au
(150 nm). Transport experiments on H-bar structures were conducted in a
Physical Property Measurement System (PPMS) (Quantum Design, Inc.), where the
temperature was varied from 5 to 300 K. A resistance bridge (Model 370 AC
Resistance Bridge, LakeShore Cryotronics, Inc.) was used to measure both non-
local and local resistances.

In our ST-FMR experiments, room-temperature magnetic hysteresis loops were
first measured on continuous films by vibrating sample magnetometry (Quantum
Design, Inc.). Slope-correction of the hysteresis loops was conducted to
account for diamagnetic responses from the substrates by subtracting constant
negative slopes at high fields from each dataset. The studied films were then
patterned into 24-$\mu$m-wide and 88-$\mu$m-long microstrips using
photolithography and Ar ion beam etching. Symmetric waveguide contacts
consisting of Ti (10 nm)/Au (150 nm) were fabricated using photolithography,
DC sputtering and lift-off techniques. An oscillating RF charge current was
then applied at fixed frequencies (7-9 GHz) along the microstrips, and an
external magnetic field up to 2000 Oe was applied in the in-plane direction at
a $45^{\circ}$ angle with respect to the RF current direction. The DC voltage
signal generated across the microstrips was then measured as a function of the
applied magnetic field, and a lineshape analysis was used to extract the spin-
charge conversion efficiency of Au.

High resolution transmission electron microscopy (HR-TEM) image of ultrathin
Au/Si multilayers.

Supplemental Figure 1:  The HR-TEM images were obtained on a FEI Talos F200X
TEM/STEM, operating at 200 kV. An $\sim$ 30-nm-thick cross-section of an
ultrathin Au/Si multilayer film grown on a c-Si substrate with a 5-nm-thick
amorphous Si buffer layer was fabricated via lift-out using a Zeiss NVision40
focused ion-beam (FIB) milling system. A protective carbon layer was used to
prevent damage to the sample while being exposed to the Ga ion beam during FIB
milling. The lighter regions correspond to Si layers, and the dark regions to
Au layers. The HR-TEM images reveal that the top three layers are partially
crystalline. The crystalline Au grains have a [111]-type direction along the
growth direction. The lack of a sharp change in intensity between Au and Si
layers is indicative of elemental intermixing at the interfaces.

Fitting of the non-local resistance measured for 60-nm-thick Au film

We followed the method of Mihajlović et al. Mihajlovic2009  by plotting
R${}_{\text{nl}}$/R${}_{\text{sq}}$ as a function of l${}_{\text{e}}$ and
fitting the experimental curve with the following equation:

$\
\frac{R_{\mathrm{nl}}}{R_{\mathrm{sq}}}=a\left(1-b\exp\left(-\frac{w}{l_{\mathrm{e}}}\right)\right)$
(5)

where $a=\exp\left(-\pi\frac{L-L_{\mathrm{0}}}{w}\right)$ with L = 340 nm,
L${}_{\text{0}}$ = 83 nm and w = 110 nm, and the value of fitting parameter b
is 22.14 (see Fig. S2). This fit indicates that the measured
R${}_{\text{nl}}$/R${}_{\text{sq}}$ corresponds to the quasi-ballistic as well
as the charge diffusive contributions to the non-local signal
($R_{\mathrm{nl}}^{cd}$ \+ $R_{\mathrm{nl}}^{b}$)/R${}_{\text{sq}}$,
confirming the absence of a giant SHE in the studied Au (60 nm) sample.

Supplemental Figure 2:  R${}_{\text{nl}}$/R${}_{\text{sq}}$ as a function of
the electron mean free path measured for the studied Au (60 nm) film with
adjacent wires separated by a distance L = 340 nm. Corresponding fit to Eq. 1
is shown as red line.

## References

  * (1) G. Mihajlović, J. E. Pearson, M. A. Garcia, S. D. Bader, A. Hoffmann, Phys. Rev. Lett. 103, 166601 (2009).


# Mitigating Temporal-Drift: A Simple Approach to Keep NER Models Crisp

Shuguang Chen $\dagger$, Leonardo Neves $\ddagger$ Thamar Solorio $\dagger$
University of Houston $\dagger$
Snap Research $\ddagger$
<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

Performance of neural models for named entity recognition degrades over time,
becoming stale. This degradation is due to temporal drift, the change in our
target variables’ statistical properties over time. This issue is especially
problematic for social media data, where topics change rapidly. In order to
mitigate the problem, data annotation and retraining of models is common.
Despite its usefulness, this process is expensive and time-consuming, which
motivates new research on efficient model updating. In this paper, we propose
an intuitive approach to measure the potential trendiness of tweets and use
this metric to select the most informative instances to use for training. We
conduct experiments on three state-of-the-art models on the Temporal Twitter
Dataset. Our approach shows larger increases in prediction accuracy with less
training data than the alternatives, making it an attractive, practical
solution. 111We release the code at https://github.com/RiTUAL-UH/trending_NER.

##  1 Introduction

Prediction performances of live machine learning systems degrade over time due
to changes in the statistical properties of the data used for training them.
This degradation, also known as temporal drift, happens in different ML tasks,
including named entity recognition (NER). Due to the nature of the task,
authors also call this language drift (Fromreide et al., 2014; Derczynski et
al., 2015). Temporal drift effects are amplified in social media. Due to the
ecosystem’s very nature, topics reflect events and interests of a diverse user
base and are continuously and rapidly evolving. To study the impact of
language drift, we focus our analysis on the case of NER on Twitter data.
Emerging and Trending topics are an essential part of Twitter. They change
quite rapidly, reflecting diverse topics and world events of interest.
Entities are a significant component of these changes, generating a diverse
set of NE tokens. These ever-evolving topics pose a challenge as new entities
frequently arise. The new entities are especially problematic as they might
not exist in our previous vocabulary or can potentially transform the meaning
of a previously observed term. Figure 1 shows tweets that include the emerging
topic ’US’. After the release of the film, the topic ’US’ became trending and
aroused wide discussion. To mitigate the impact of temporal drift, we
investigate how to effectively and efficiently adapt an already trained NER
model to sustain prediction performance over time. We propose an intuitive
approach to measure the trendiness of tweets and use this metric to select the
most informative instances for retraining. We show that labeling instances
based on this approach can yield better downstream performance than randomly
sampling tweets for annotation.

Figure 1: Examples of tweets that include the emerging topic ‘US’, a horror
movie released in 2019

Note that topics such as semantic shift (Hamilton et al., 2016; Rosenfeld and
Erk, 2018) and active learning (Sinha et al., 2019; Kirsch et al., 2019) are
related to the work we present here. In semantic shift, the core problem is
how to trace temporal changes in lexical semantics, including linguistic
drifts and cultural shifts. Unlike this task, our goal is to leverage the
emergence of trends to guide an already trained model.

In active learning, researchers have focused on incremental annotation of
instances by selecting the most informative ones. The goal is to achieve
better results than random sampling. Multiple approaches exist to measure the
informativeness of data points, but all of them are domain agnostic (Sinha et
al., 2019; Kirsch et al., 2019). Our proposed solution is more straightforward
than using uncertainty in ensembles or adversarial networks. However, it
effectively increases model performance, and, similar to active learning
approaches, it is more efficient than random sampling.

To summarize, we make the following contributions:

  1. 1.

We propose an approach to measure the potential trendiness of tweets for
selecting the most informative training samples.

  2. 2.

We conduct extensive experiments and demonstrate the effectiveness of our
approach for retraining a NER model.

##  2 Emerging Trend Detection

We want to exploit social media’s inherent characteristics (Benhardus and
Kalita, 2013; Mathioudakis and Koudas, 2010), with a focus on Twitter, to
update model parameters efficiently. We assume that named entities associated
with posts that are likely to become trends will be more informative and
result in larger performance gains. Our emerging trend detection strategy is
based on contrasting frequency of words in older data (training data) against
frequency in newly collected data (recent data). More specifically, we
formulate this task as detection of trending n-grams. We compute the trend
scores for each n-gram, $n$, as follows:

$\left.\begin{aligned}
score(n)=\frac{f_{n,R}-f_{n,P}}{f_{n,P}+k}\end{aligned}\right.$

where $f_{n,R}$ and $f_{n,P}$ are the frequencies of n-gram $n$ in the recent
and past datasets, respectively. In practical applications, $f_{n,R}$ can
refer to the frequency in newly collected data, while $f_{n,P}$ can refer to
the frequency in older data. $k$ is a normalization term used to mitigate the
frequency of the highly-frequent n-grams in the recent datasets. When
computing trend scores, we filter out stop words as they are usually the most
common words but contain the least information. After we compute trend scores
for all n-grams in newly collected data, we assign trend scores to the
instances by summing over the scores of each n-gram in that instance (tweet).
We then use the score to rank instances for labeling and updating the NER
model. Our approach is flexible as it can be used in combination with any NER
model architecture.

(a) BiLSTM + CRF

(b) BERT + CRF

(c) BERTweet + CRF

Figure 2: Data can only be accessed year by year -  Each step represents a
year from 2014 to 2018. At each step, we add instances from its respective
year to the training set. For Temporal, we randomly select instances from that
given year. For Trend, we rank instances based on their trending score. We
experiment with 50 (Appendix B), 100 and 200 (Appendix B) instances per step
to show the impact of training size.

(a) BiLSTM + CRF

(b) BERT + CRF

(c) BERTweet + CRF

Figure 3: Data from all years is available - At each step, we add new
instances to our training set. For Random, we randomly select instances from
the available data. For Trend, we rank all available instances from most
trending to less trending based on their trending scores. We then use this
ranking to select the instances. At each step, we choose the instances with
the highest trending scores that have not yet been added to the training set.
We experiment with 50 (Appendix B), 100 and 200 (Appendix B) instances per
step to show the impact of training size.

##  3 Experiments

We empirically study the impact of retraining NER models on trending data in
two different scenarios. In Scenario 1, we retrain the model in an incremental
manner with $N$ instances from a newer batch of data in the following year at
every iteration. In Scenario 2, we retrain the model incrementally as well,
but the pool of data we used to select instances includes all years available
in the training partitions. In both cases, instances are selected based on
their trend scores.

We use the Temporal Twitter Dataset from Rijhwani and Preotiuc-Pietro (2020)
for all experiments. This dataset is temporally distributed and balanced with
a variety of topics. It has 12K tweets collected from 2014 to 2019, with 2K
samples from each year. In our experiments, the training set comprises of
splits from 2014 to 2018. The validation set and test set have a random sample
of 500 (25%) and 1,500 (75%) tweets from 2019, respectively.

###  3.1 Neural Architectures

As mentioned earlier, our approach is model agnostic. We validate this claim
by experimenting with different NER neural architectures used in the prior
art. The main difference between these models is the representation fed into a
Conditional Random Field (CRF) (Lafferty et al., 2001) for prediction. The
implementation and hyperparameters are described in Appendix A.

#### BiLSTM + CRF

Following Ma and Hovy (2016), we use the GloVe (Pennington et al., 2014) word
embeddings for word representations and Convolution Neural Networks (CNNs) for
character representations. Then a bidirectional LSTM (Graves and Schmidhuber,
2005) takes both word representations and character representations as input
and encodes sentences.

#### BERT + CRF

BERT is a transformer-based model proposed by Devlin et al. (2019). It is pre-
trained using masked language modeling and next sentence prediction objectives
on the corpora from the general domain. BERT takes subwords as input and
generates contextualized word representations for each sentence.

#### BERTweet + CRF

Similar to BERT, BERTweet (Nguyen et al., 2020) is a large-scale language
model with the same configuration as BERT. It is pre-trained on the corpora
from the social media domain and achieves state-of-the-art results on many
downstream Twitter NER tasks.

###  3.2 Results

We empirically examine the performance of models under the influence of data
evolution and temporal drift. We start with doing experiments on trending bi-
grams and use the same amount of training samples at each step to eliminate
the influence of training data size. Below we discuss the results of the two
evaluation scenarios.

#### Scenario 1

In this scenario, we assume that the data can only be accessed chronologically
by year. For each new batch of data selected based on the trendiness score
(trend), we take the model as trained on the previous batch and retrain on the
newest data. In other words, we consider the model from the previous iteration
as a pre-trained model and fine-tune that model on the newest data. For
comparison purposes, we run a temporal version, where the model is fine-tuned
with newer data every time, but the instances are selected randomly for the
corresponding year. Due to the randomness in this approach, we run each model
five times, and then we report the average of the five runs as the final F1
score.

The results are shown in Figure 2. We observe that both temporal and trend F1
scores increase as we move temporally closer to the target data. However, in
all cases, the trend-based models always reach a higher score.

#### Scenario 2

In this scenario, we assume the data can be accessed from all years at once.
We merge the training data from all years and form a single pool of data.
However, we still fine-tune models at each iteration using the same number of
new instances each time. For the trend models, we select instances based on
their trend scores, regardless of the year, whereas for the random model, we
select instances at random from the merged pool of data. Similar to what we
did in scenario 1, we run each model 5 times and report the averaged results.

The results are shown in Figure 3. Similar to scenario 1, the F1 scores of the
models trained on instances selected based on their trend scores are always
higher than random sampling F1 scores. In addition, scenario 2, on average,
works better than scenario 1, which is consistent with Rijhwani and Preotiuc-
Pietro (2020). However, this setting requires the data available from all
years from the very beginning. Compared to scenario 2, scenario 1 is far more
realistic because it can be more easily applied in practice.

###  3.3 Analysis

#### Impact of training data size

We ran additional experiments where we add different amounts of training data
at each iteration (50 and 200). With less training data available, the
benefits of selecting instances based on trend scores are amplified. Even if
more data is available, using trend scores to select which instances to add
always results in better performance than randomly choosing instances. Due to
space limitations, the plots are in Appendix B figures 4, 5, 6 and 7.

#### Impact of pre-trained knowledge

From figures 2 and 3, we observe that, in general, pre-trained models (BERT
and BERTweet) tend to perform closer to that of the trend-based models. Apart
from the well-documented advantages of contextualized representations, we
believe that higher performance here is due to these models’ pre-trained
knowledge. We suspect that if we had the ability to control the data, and in
particular, the year of the data used in pre-training, the results would be
different, and we would observe a larger gap between pre-trained transformer
models and the trend-based approach.

#### Entity-wise Model Performance

We investigate whether our approach affects named entity types differently. To
this end, we create random data and trending data. The random data is randomly
selected, while the trending data is selected based on the trend scores. Each
data has 1,000 samples. Table 1 shows the model performance on the random
data, versus the trending data. We notice that all three models overall
benefit from trend detection with an improvement from 2.70% 5.71% on F1
metric, indicating that the models can adequately learn the context of named
entities.

Model | Random data | Trending data
---|---|---
P | R | F1 | P | R | F1
BiLSTM + CRF | 59.38 | 48.02 | 53.10 | 63.42 | 54.83 | 58.81
BERT + CRF | 62.26 | 73.23 | 67.30 | 70.07 | 69.93 | 70.00
BERTweet + CRF | 60.64 | 64.84 | 62.67 | 65.45 | 70.46 | 67.86

Table 1: Performance comparison on random data and trending data, including
persc.

To better understand the high model performance on trending data, Table 2
shows the distribution of random and trending data. By selecting training
samples based on our approach, the number of entities in the trending data is
77% more than the number of entities in the random data, including 92% more
PER, 38% more LOC, and 91% more ORG. In the token level, there are more 108%
entity tokens in the trending data than in the random data. The higher ratio
of named entities in the trending data increases the diversity of each entity
type, and therefore, decreases the test error.

Entity Type | Random data | Trending data
---|---|---
Entity-level | Token-level | Entity-level | Token-level
PER | 225 | 340 | 432 | 755
LOC | 178 | 226 | 245 | 362
ORG | 281 | 379 | 537 | 848
Total | 684 | 945 | 1,214 | 1,965

Table 2: The distribution of random data and trending data, including entity-
level distribution (entity spans) and token-level distribution (entity
tokens).

##  4 Related Work

Previous work has studied trend detection in online social media platforms
such as Twitter and Facebook (Benhardus and Kalita, 2013; Mathioudakis and
Koudas, 2010; Miot and Drigout, 2020). Benhardus and Kalita (2013) outlined
the methodologies for using the data from online platforms and proposed
criteria based on the frequency of words to identify trending topics in
Twitter. Mathioudakis and Koudas (2010) presented a system to detect bursty
keywords that suddenly appear in tweets at an unusually high rate. Recently,
Miot and Drigout (2020) investigated the efficiency of deep neural networks to
detect trends. However, these techniques are applied without taking named
entities into consideration.

Towards emerging named entities, recent work has mainly focus on
identification and classification of unusual and previously unseen named
entities. Derczynski et al. (2015) investigated the effects of data drift and
the evaluation of the NER models on temporally unseen data. Agarwal et al.
(2018) studied the disambiguation of named entities with explicit
consideration of temporal background. Rijhwani and Preotiuc-Pietro (2020)
reported improvements on performance for overlapping named entities under the
impact of temporal drift. Due to the limitation of resources and lack of
annotated data from social media, these NER models tend to have lower
performances on emerging named entities.

##  5 Conclusion

In this work, we propose a simple approach to update model parameters and
prevent degradation performance from temporal drifts. Our approach is inspired
by our observations of how Twitter data follows trends in topics that can
change very quickly. Experimentally, we show that leveraging emerging trends
can benefit the recognition of named entities and reduce performance
degradation, especially in low-resource scenarios. Our proposal is model
agnostic, and can potentially be adapted to other NLP tasks that target social
media and face the same problems of data evolution and temporal drift.

## Acknowledgements

This work was partially supported by the National Science Foundation (NSF)
under grant #1910192. We would like to thank the members from the RiTUAL lab
at the University of Houston for their invaluable feedback. We also thank the
anonymous reviewers for their valuable suggestions.

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(a) BiLSTM + CRF

(b) BERT + CRF

(c) BERTweet + CRF

Figure 4: Data can only be accessed year by year -  Each step represents a
year from 2014 to 2018. At each step, we add instances from its respective
year to the training set. For Temporal, we randomly select instances from that
given year. For Trend, we rank instances based on their trending score. We
experiment with 50 (Appendix B), 100 and 200 (Appendix B) instances per step
to show the impact of training size.

(a) BiLSTM + CRF

(b) BERT + CRF

(c) BERTweet + CRF

Figure 5: Data from all years is available - At each step, we add new
instances to our training set. For Random, we randomly select instances from
the available data. For Trend, we rank all available instances from most
trending to less trending based on their trending scores. We then use this
ranking to select the instances. At each step, we choose the instances with
the highest trending scores that have not yet been added to the training set.
We experiment with 50 (Appendix B), 100 and 200 (Appendix B) instances per
step to show the impact of training size.

(a) BiLSTM + CRF

(b) BERT + CRF

(c) BERTweet + CRF

Figure 6: Data can only be accessed year by year -  Each step represents a
year from 2014 to 2018. At each step, we add instances from its respective
year to the training set. For Temporal, we randomly select instances from that
given year. For Trend, we rank instances based on their trending score. We
experiment with 50 (Appendix B), 100 and 200 (Appendix B) instances per step
to show the impact of training size.

(a) BiLSTM + CRF

(b) BERT + CRF

(c) BERTweet + CRF

Figure 7: Data from all years is available - At each step, we add new
instances to our training set. For Random, we randomly select instances from
the available data. For Trend, we rank all available instances from most
trending to less trending based on their trending scores. We then use this
ranking to select the instances. At each step, we choose the instances with
the highest trending scores that have not yet been added to the training set.
We experiment with 50 (Appendix B), 100 and 200 (Appendix B) instances per
step to show the impact of training size.

##  Appendix A Details for Experimental Setup

For BiLSTM-CRF model, we use GloVe Twitter embeddings. The dimensions of
character embeddings and word embeddings are 50 and 100 respectively. We then
use 2-layer LSTM with 300 hidden units to encode sentences. The dropout rate
is 0.5. During training, we use stochastic gradient descent (SGD) with
learning rate 0.1, batch size 20, and momentum 0.9. The L2 regularization is
set to 0.001. For BERT and BERTweet, we do fine-tuning using AdamW optimizer
(Loshchilov and Hutter, 2017) with learning rate 5e-5, batch size 32, and
weight decay 0.01. We also use a gradient clipping of 1.0 and the dropout rate
is 0.1. In scoring function, $k$ is set as 0.1 for sample selection.

##  Appendix B Experiment with more data

In Figure 4 and Figure 5, we use 50 instances at each step. In Figure 6 and
Figure 7, we use 200 instances at each step. We repeat our experiment with
using different number of instances at each training step to study the impact
of dataset size.