# Charge-spin interconversion in graphene-based systems from density
functional theory

M. Rassekh1,2<EMAIL_ADDRESS>Hernán Santos3 A. Latgé4 Leonor
Chico5,6 S. Farjami Shayesteh1 J. J. Palacios2<EMAIL_ADDRESS>1Department of Physics, University of Guilan, 41335-1914 Rasht, Iran
2Departamento de Física de la Materia Condensada, Condensed Matter Physics
Center (IFIMAC), and Instituto Nicolás Cabrera (INC), Universidad Autónoma de
Madrid, Cantoblanco 28049, Spain
3Dept. de Matemática Aplicada, Ciencia e Ingeniería de Materiales y Tecnología
Electrónica, ESCET, Universidad Rey Juan Carlos, C/ Tulipán s/n, Móstoles
28933, Madrid, Spain
4Instituto de Física Universidade Federal Fluminense, Niterói, Av. Litorânea
24210-340, RJ-Brazil
5GISC, Departamento de Física de Materiales, Facultad de Ciencias Físicas,
Universidad Complutense de Madrid, 28040 Madrid, Spain
6Instituto de Ciencia de Materiales de Madrid, Consejo Superior de
Investigaciones Científicas, C/ Sor Juana Inés de la Cruz 3, 28049 Madrid,
Spain

(September 3, 2024)

###### Abstract

We present a methodology to address, from first principles, charge-spin
interconversion in two-dimensional materials with spin-orbit coupling. Our
study relies on an implementation of density functional theory based quantum
transport formalism adapted to such purpose. We show how an analysis of the
$k$-resolved spin polarization gives the necessary insight to understand the
different charge-spin interconversion mechanisms. We have tested it in the
simplest scenario of isolated graphene in a perpendicular electric field where
effective tight-binding models are available to compare with. Our results show
that the flow of an unpolarized current across a single layer of graphene
produces, as expected, a spin separation perpendicular to the current for two
of the three spin components (out-of-plane and longitudinal), which is the
signature of the spin Hall effect. Additionally, it also yields an overall
spin accumulation for the third spin component (perpendicular to the current),
which is the signature of the Rashba-Edelstein effect. Even in this simple
example, our results reveal an unexpected competition between the Rashba and
the intrinsic spin-orbit coupling. Remarkably, the sign of the accumulated
spin density does not depend on the electron or hole nature of the injected
current for realistic values of the Rashba coupling.

##  I  Introduction

Modern spintronics relies not only on the generation, manipulation and
detection of spin-polarized currents through ferromagnetic materials but also
on the increasingly important phenomena related to the interconversion of spin
and charge currents. This conversion can be made by an external electric field
via the magnetoelectric coupling or, most importantly, via the spin-orbit
coupling (SOC) Sinova  _et al._ (2015); Manchon  _et al._ (2015); Sander  _et
al._ (2017); Garello  _et al._ (2018, 2018). The latter approach is typically
associated with the Bychkov-Rashba or the Dresselhaus effects Bychkov and
Rashba (1984); Dresselhaus (1955), which consist of a momentum-dependent
splitting of spin bands. The Bychkov-Rashba splitting occurs in low-
dimensional systems, such as semiconductor heterostructures or metal surfaces
Koroteev  _et al._ (2004); Ast  _et al._ (2007); Bihlmayer  _et al._ (2007);
Mirhosseini  _et al._ (2010), whereas the Dresselhaus effect takes place in
non-centrosymmetric bulk materials Nikolaev and Solovyev (2020).

In the paradigmatic spin Hall effect (SHE) Valenzuela and Tinkham (2006);
Sinova  _et al._ (2015) a charge current flowing in a given direction
generates a transverse spin current flowing in the perpendicular direction.
The generation of this spin current leads to spin accumulations with opposite
magnetizations at the edges of the sample. This phenomenon, which appears in
electrically conductive and non-magnetic materials with a sizable SOC, can be
experimentally measured through different techniques Sinova  _et al._ (2015);
Valenzuela and Tinkham (2006). In the Rashba-Edelstein effect (REE) Edelstein
(1990); Inoue  _et al._ (2003) (or inverse spin galvanic effect), a non-
equilibrium spin density is generated instead of spin current on account of a
charge current. Likewise, a finite SOC is an essential ingredient. Both spin
currents and densities can be used, for instance, to manipulate the
magnetization of ferromagnets. Their reciprocal effects, the inverse SHE
(ISHE) Saitoh  _et al._ (2006) and inverse REE (IREE) Sánchez  _et al._
(2013); Isasa  _et al._ (2016); Ganichev  _et al._ (2002); Khokhriakov  _et
al._ (2020)), consist of the conversion of spin currents or spin densities,
respectively, into charge currents.

Many classes of materials are being explored in this context, including heavy
element metals such as Au and Bi, oxides, and topological insulators (TIs)
Manchon  _et al._ (2019); Mendes  _et al._ (2017). Of increasing relevance are
two-dimensional (2D) crystals that essentially consist of atomically thin
layers obtained from van der Waals materials Novoselov  _et al._ (2016) and
whose electrical, optical, and spin properties can be easily modified by
proximity. Among these, graphene has played a prominent role in these
investigations. Graphene presents the longest spin-relaxation length ever
measured at room temperature Ingla-Aynés  _et al._ (2015), in part due to
carbon being a light element with a relatively small intrinsic SOC Min  _et
al._ (2006). However, this property precludes graphene from being able to play
an active role in charge-spin interconversion. In order to enhance its
efficiency in this respect, there is an ongoing quest to increase the SOC
splitting by external means, including mechanical deformation of the graphene
lattice, applied electric fields, defects, addition of heavy adatoms that can
increase the $d$-orbital contribution to SOC, as well as magnetic atoms that
can induce an exchange-mediated spin splitting Weeks  _et al._ (2011); Eremeev
_et al._ (2014); Ma  _et al._ (2012); Marchenko  _et al._ (2012); Avsar  _et
al._ (2014); Santos  _et al._ (2016, 2017).

One of the most promising strategies consists of placing graphene in contact
with other materials that can transfer their SOC by proximity. In fact, the
observation of the SHE was originally reported in graphene decorated with
adatoms and in contact with WS2 Avsar  _et al._ (2014). However, further
studies have questioned the spin-related interpretation of the measured
effects Kaverzin and Van Wees (2015); Wang  _et al._ (2015a); Van Tuan  _et
al._ (2016). More recently, the ISHE was observed in heterostructures
comprising multilayer graphene and MoS2 Safeer  _et al._ (2019). Even though
the observation of the ISHE was unequivocal, it was not easy to discriminate
between proximity-induced SOC in graphene or in bulk MoS2 because the latter
is believed to be conductive. This debate, however, seems to have been
clarified in a recent work Benítez  _et al._ (2020). Moreover, recent
experiments have demonstrated the spin galvanic effect (or IREE) in
graphene/TI heterostructures Khokhriakov  _et al._ (2020).

Figure 1: (Color online). Schematic view of our proposed graphene setup for
zigzag (a), and armchair (b) orientations. An infinite graphene flake is
divided into three regions, the central one (of length $L$ and shown in
yellow) being subject to a strong electric field to induce a Rashba effect
therein. Black boxes show the unit cells used as the units of this length in
the text. The lateral areas are SOC-free zones. The red and blue arrows
represent how opposite spin carriers (along the $x$-quantization axis) deviate
in opposite directions resulting in the SHE.

On the theoretical side, density functional theory (DFT) studies have
supported the possibility that proximity-induced SOC can enhance the graphene
charge-spin interconversion efficiency Gmitra  _et al._ (2016); Wang  _et al._
(2015b); Gmitra and Fabian (2015); Offidani  _et al._ (2017); Milletarì  _et
al._ (2017). The information obtained from the DFT calculations can be
transferred to effective models, which can then be used to compute charge-spin
related quantities. These calculations are typically based on Kubo formalism
Garcia  _et al._ (2017) or non-equilibrium Green’s function formalism Nikolić
_et al._ (2005a, b), all of them being real-space methodologies. Since the
subtle proximity effects induced, e.g., by transition metal dichalcogenides
(TMD) on graphene can only be captured by DFT calculations, it would be
desirable to make a direct connection between these calculations and charge-
spin interconversion-related quantities without the need of an effective
model, not always at hand.

In this work we present a DFT-based quantum transport methodology to
quantitatively address charge-spin interconversion in 2D crystals. The novelty
here relies on the $k$-dependent evaluation of the spin polarization of the
current, where $k$ is the crystal momentum perpendicular to the direction of
the current. This allows us to obtain the charge-spin fingerprint in
reciprocal space for any material or combination of materials directly from
DFT. We have tested our methodology on free-standing graphene with Rashba
coupling induced by the presence of a strong perpendicular electric field. For
this paradigmatic system a simple tight-binding (TB) model is available which
we use to verify the results obtained from our DFT implementation and to aid
in the interpretation of these.

##  II  Theoretical approach

###  II.1 Methodology: k-dependent spin polarization

A schematic view of the proposed graphene-based device is shown in Fig. 1. The
system consists of a single and infinite layer of graphene with a central
region where the Rashba coupling is induced either by a perpendicular electric
field, the presence of heavy adatoms or by proximity to other materials. This
way, the graphene flake is divided into three regions: the central SOC active
region, where the charge-spin interconversion takes place and that here is
infinite in the $y$ direction, and the left and right semi-infinite regions,
which inject and collect the current, respectively. Since the system is
infinite in the direction perpendicular to the current, which flows in the $x$
direction, the wavevector $k_{y}$ (parallel to the interface) is a good
quantum number. This magnitude, combined with the knowledge of the band
structure, can be used to single out the left-going and right-going
contributions to the total current.

Figure 2: (Color online).Schematic representation of the origin of the SHE (a)
and REE (b) in graphene for transport along the positive $x$ axis. The Fermi
level is set to positive energies (electrons) and, therefore, only states with
positive velocities on the right semicircles are considered. The blue arrows
indicate the spin of the injected carriers.

Charge-spin interconversion mechanisms (SHE and REE) can be easily identified
and quantified by the spin polarization of the $k_{y}$-dependent current, as
discussed below; notwithstanding, a simple picture for the origin of these
effects can already be anticipated from the schematics in Fig. 2. There we
show two situations giving rise to the SHE (a), and the REE (b), respectively,
for the simplest Rashba coupling scenario. The Fermi surface of the graphene
region injecting the current is depicted on the left of the figures, whereas
the spin-split Fermi surface of the graphene region with Rashba coupling is
shown on the right (we only present one valley, since both valleys behave
identically with respect to the spin splitting of the bands Rashba (2009)).
The green arrows connect the sections of the Fermi surfaces between which the
current is expected to be significant for different spin orientations of the
incoming electrons. From panel (a) (SHE) one anticipates a predominant current
for positive (negative) $k_{y}$ and parallel (antiparallel) orientation of the
injected spins along $x$ Dyrdał  _et al._ (2009). In panel (b) (REE), there is
no left-right asymmetry in the injected current, but this is expected to be
polarized due to the different transmission of opposite-spin injected carriers
Dyrdał  _et al._ (2014). When the spin polarization of the injected current is
perpendicular to the plane, a SHE may also emerge, but such a simple picture
is no longer available.

To properly quantify both effects we define the spin polarization of the
current at a given energy $E$ as in Ref. Chico  _et al._ , 2015,

$P=T_{\upuparrows}+T_{\downarrow\uparrow}-T_{\uparrow\downarrow}-T_{\downdownarrows}\,\,,$
(1)

where the spin-conserved ($T_{\upuparrows}$, $T_{\downdownarrows}$) and the
spin-flip ($T_{\uparrow\downarrow}$, $T_{\downarrow\uparrow}$) transmission
functions are obtained with the help of the Green’s function of the SOC-active
region and the coupling matrices to left (L) and right (R) regions Jacob and
Palacios (2011); Chico  _et al._ (2015)

$T_{\sigma\sigma^{\prime}}=\operatorname{Tr}\left[\bm{\Gamma}_{\sigma}^{L}\bm{G}_{\sigma\sigma^{\prime}}\bm{\Gamma}_{\sigma^{\prime}}^{R}\bm{G}_{\sigma\sigma^{\prime}}^{\dagger}\right].$
(2)

Therefore, more specifically, we must compute

$\begin{split}P=&Tr\left[\bm{\Gamma}_{\uparrow}^{L}\bm{G}_{\upuparrows}\bm{\Gamma}_{\uparrow}^{R}\bm{G}_{\upuparrows}^{\dagger}+\bm{\Gamma}_{\downarrow}^{L}\bm{G}_{\downarrow\uparrow}\bm{\Gamma}_{\uparrow}^{R}\bm{G}_{\downarrow\uparrow}^{\dagger}-\right.\\\
&\left.-\bm{\Gamma}_{\uparrow}^{L}\bm{G}_{\uparrow\downarrow}\bm{\Gamma}_{\downarrow}^{R}\bm{G}_{\uparrow\downarrow}^{\dagger}-\bm{\Gamma}_{\downdownarrows}^{L}\bm{G}_{\uparrow\downarrow}\bm{\Gamma}_{\downarrow}^{R}\bm{G}_{\downdownarrows}^{\dagger}\right].\end{split}$
(3)

As such, these equations imply that spin is conserved in the electrodes, with
$\uparrow$ and $\downarrow$ denoting spin eigenstates along an arbitrary
direction (here $x,y,$ and $z$). We will refrain from integrating in energy
since a small bias voltage is assumed and we are only interested in linear
effects.

For the DFT implementation of the quantum transport calculation presented in
this work, the Green’s function (with spin indices omitted here) is defined as

$\bm{G}(E)=[z\bm{S}-\bm{H}_{\rm C}-\bm{\Sigma}_{T}(E)]^{-1}\,\,,$ (4)

with $z=E+i\eta$ and $\eta$ being an infinitesimal number. $\bm{H}_{\rm C}$ is
the Hamiltonian of the central part where SOC is present, $\bm{S}$ the
corresponding overlap matrix for the basis functions, which are assumed not
necessarily orthogonal, and $\bm{\Sigma}_{T}(E)$ is the summation of right and
left self-energies from which the coupling matrices in Eq. 2 are obtained:

$\begin{split}&\bm{\Gamma}^{L}(E)=i\left(\bm{\Sigma}_{L}(E)-(\bm{\Sigma}_{L}(E))^{\dagger}\right),\\\
&\bm{\Gamma}^{R}(E)=i\left(\bm{\Sigma}_{R}(E)-(\bm{\Sigma}_{R}(E))^{\dagger}\right).\end{split}$
(5)

The right and left self-energies, which are identical here, are calculated
from the on-cell Hamiltonian, $\bm{H}_{0}$, and corresponding overlap matrix,
$\bm{S}_{0}$, by the following Dyson equations:

$\displaystyle\begin{split}&\bm{\Sigma}_{L}(E)=(\bm{H}_{1}^{\dagger}-z\bm{S}_{1}^{\dagger})(z\bm{S}_{0}-\bm{H}_{0}-\bm{\Sigma}_{L}(E))^{-1}(\bm{H}_{1}-z\bm{S}_{1})\\\
&\bm{\Sigma}_{R}(E)=(\bm{H}_{1}-z\bm{S}_{1})(z\bm{S}_{0}-\bm{H}_{0}-\bm{\Sigma}_{R}(E))^{-1}(\bm{H}_{1}^{\dagger}-z\bm{S}_{1}^{\dagger}),\end{split}$

where $\bm{H}_{1}$ and $\bm{S}_{1}$ are the forward hopping and overlap
matrices, respectively.

In the transmission calculations the area where SOC is active can cover all
the central region defined through $H_{C}$ in Eq. 4 or just part of it to
allow for SOC-free buffer zones and a smoother or perfect electronic match
with the SOC-free self-energies (see Fig. 1). Although we have not appreciated
differences between these two possibilities in the results, including buffer
zones is safer and our DFT spin polarization results are obtain in this way.
Also, in order to conserve spin in the electrodes, we remove SOC from them,
but we keep the effect of the electric field. When SOC is absent from $H_{\rm
C}$, the transmission is perfect and no spin polarization or interference
effects appear.

The above-presented methodology is standard in quantum transport, but the
infinite nature of our system along the parallel ($y$) direction allows to
replace the Hamiltonian and overlap matrices with their lattice Fourier
transform only in the $y$ direction, so $\bm{H}_{0}$ and $\bm{H}_{1}$ are
actually given by (see Fig. 3)

Figure 3: Schematic illustration of Hamiltonian/overlap matrix partitioning.
Figure 4: DFT and TB bands near one of the Dirac points, without electric
field (a), with an external electric field of 4 V/nm (b), and 20 V/nm (c). The
color bar indicates the $y$-component of the spin expectation value.

$\begin{split}&\bm{H}_{0}=...+\bm{H}_{0,-1}e^{-ik_{y}R_{y}}+\bm{H}_{0,0}+\bm{H}_{0,1}e^{ik_{y}R_{y}}+...\\\
&\bm{H}_{1}=...+\bm{H}_{1,-1}e^{-ik_{y}R_{y}}+\bm{H}_{1,0}+\bm{H}_{1,1}e^{ik_{y}R_{y}}+...\end{split}$
(6)

or in general

$\bm{H}(R_{x},k_{y})=\sum_{R_{y}}H(R_{x},R_{y})e^{ik_{y}R_{y}}\,\,,$ (7)

where $\bm{R}$ are Bravais lattice vectors. Similarly,

$\bm{S}(R_{x},k_{y})=\sum_{R_{y}}S(R_{x},R_{y})e^{ik_{y}R_{y}}\,\,.$ (8)

These equations finally result in a $k_{y}$-dependent spin polarization
function $P(E,k_{y})$ that contains all the needed information. We note that a
related methodology was proposed in Ref. Dolui and Nikolić, 2017, although in
a different context where the focus was on the spectral function, not the spin
polarization.

###  II.2 Atomistic Modelling

The matrices needed for the evaluation of Green’s functions, as explained in
the previous section, are obtained from the DFT implementation of the OpenMX
code Ope ; Ozaki (2003); Ozaki and Kino (2004, 2005); Lejaeghere  _et al._
(2016); Lee and Ozaki (2019). This code is based on the norm-conserving
pseudo-potential method Bachelet  _et al._ (1982); Troullier and Martins
(1993); Vanderbilt (1990); Blöchl (1990); Morrison  _et al._ (1993) with a
partial core correction and pseudo atomic orbitals (LCPAO) as basis functions
Ozaki (2003); Ozaki and Kino (2004) here specified by
$C(6.0)-s^{2}p^{2}d^{1}$. Where $C$ is the atomic symbol for Carbon, 6.0 is
the cutoff radius in units of Bohr, and $s^{2}p^{2}d^{1}$ indicates that two
primitive orbitals for each of $s$ and $p$ components and one primitive
orbital for $d$ components are employed. The fully relativistic effects,
including spin-orbit coupling (SOC), have been included in the non-collinear
DFT calculations via the j-dependent pseudo-potentials scheme MacDonald and
Vosko (1979); Bachelet  _et al._ (1982); Theurich and Hill (2001). The
exchange-correlation functional chosen here is the spin-polarized GGA-PBE
Perdew  _et al._ (1996). All calculations were performed until the change in
total energy between two successive iteration steps converged to less than
10-6 Hartree. A cutoff energy of 220 Ry and a $7\times 7\times 1$ $k$-grid
have been used in all results presented below. A vacuum spacing of 20 Å in the
$z$ direction is used to prevent the interaction between periodic images.
Atomic SOC in the presence of a perpendicular electric field, adatoms, or
other materials in proximity, gives rise to both intrinsic and Rashba
couplings.In our implementation we remove the SOC terms from the lateral
buffer zones and obtain the matrices to compute the self-energies from there.
Since the effect of the electric field remains, the electronic mismatch with
the SOC-active region is reduced to a minimum.

To test our DFT implementation and elucidate the role of the two SOC
contributions, we have also considered a simple TB model for graphene-based on
four atomic orbitals ($s,p_{x},p_{y},p_{z}$). SOC effects are included by
adding the atomic term $H_{\text{SOC }}$ to the TB Hamiltonian Santos  _et
al._ (2013). With the usual assumption that the most important contribution of
the crystal potential to the SOC is close to the cores, $H_{\text{SOC }}$ is
given by

$H_{\mathrm{SOC}}=\sum_{i}\frac{\hbar}{4m^{2}c^{2}}\frac{1}{r_{i}}\frac{dV_{i}}{dr_{i}}\bm{L}\cdot\bm{S}=\lambda_{I}\bm{L}\cdot\bm{S},$

where $V_{i}$ is assumed to be spherically symmetric; $r_{i}$ is the radial
coordinate with origin at the $i$-th atom; $\bm{L}$ is the electron orbital
angular momentum operator, and $\bm{S}$ is the spin operator. The parameter
$\lambda_{I}$ is a renormalized atomic SOC constant that depends on the
angular momentum. Note that $H_{\text{SOC }}$ only couples $p$ orbitals in the
same atom. Since spin is included, the Hamiltonian matrix has $8N_{a}\times
8N_{a}$ elements, where $N_{a}$ is the number of carbon atoms in the unit
cell, and 8 corresponds to the four orbitals per spin of the basis set.
Therefore, the total Hamiltonian in the $2\times 2$ block spinor structure is

$H=\left(\begin{array}[]{cc}H_{0}+\lambda_{I}L_{z}&\lambda_{I}\left(L_{x}-iL_{y}\right)\\\
\lambda_{I}\left(L_{x}+iL_{y}\right)&H_{0}-\lambda_{I}L_{z}\end{array}\right).$

As in the DFT description, the presence of a perpendicular electric field can
be directly added to the four-orbital Hamiltonian. However, we choose to take
its effect into account through the effective one-orbital Hamiltonian Zhang
_et al._ (2014); Chico  _et al._ (2015); Santos  _et al._ (2020)

$H_{\rm R}=\frac{i\lambda_{R}}{a_{cc}}\sum_{\begin{subarray}{c}<i,j>\\\
\sigma,\sigma^{\prime}\end{subarray}}c_{i\sigma}^{\dagger}\big{[}(\bm{\sigma}\times\mathbb{d}_{ij})\cdot\mathbb{e}_{p}\big{]}_{\sigma\sigma^{\prime}}\
c_{j\sigma^{\prime}}\,\,,$ (9)

acting only on $p_{z}$ orbitals with $\bm{\sigma}$ being the Pauli spin
matrices in vector notation, $\mathbb{d}_{ij}$ the position vectors between
atoms $i$ and $j$, $\lambda_{R}$ the Rashba strength, and $\mathbb{e}_{p}$ the
unitary vector perpendicular to the plane of graphene. The nearest-neighbor
carbon-carbon distance in graphene is $a_{cc}=1.42$ Å. The values of the
hopping parameters in our TB model, $\lambda_{I}$, and $\lambda_{R}$ are
chosen to fit the DFT bands. The fitted values are $\lambda_{I}=9.2$ $\mu$eV,
and $\lambda_{R}=18.1$ and $93.3$ $\mu$eV for 4 and 20 V/nm electric fields,
respectively. These values are in good agreement with those reported in Refs.
Gmitra  _et al._ (2009); Abdelouahed  _et al._ (2010). Notice that, strictly
speaking, the Rashba parameter $\lambda_{R}$ depends on $\lambda_{I}$ since we
have included the full atomic SOC, $H_{\rm SOC}$, in our TB Hamiltonian.
However, in our single-orbital model 9, $\lambda_{R}$ can be independently
fitted. Alternatively, one could have used a one-orbital effective Hamiltonian
all along as in Ref. Gmitra  _et al._ (2009). As illustrated in Fig. 4, where
the bands and their $y$-component of the spin expectation value (encoded in
the color of the lines and dots) are shown near one of the Dirac points, the
coincidence between DFT and TB results is excellent up to the highest values
considered for the electric field. The gaps also follow the evolution with the
field previously reported Gmitra  _et al._ (2009).

Figure 5: (Color online) Polarization for the armchair orientation. DFT and TB
results are shown on the left and right columns, respectively. Results on (a),
(b) and (c) correspond to the polarization for injected electrons with spin
along the $x$, $y$, and $z$ directions, respectively. The length of the Rashba
region is L-12 (L-n being the number of n unit cells, where the length of one
unit cell (L-1) is 2.46 Å) and the value of the electric field is 4 V/nm.
Figure 6: (Color online) Polarization for the zigzag orientation. DFT and TB
results are shown on the left and right columns, respectively. Results on (a),
(b) and (c) correspond to the polarization for injected electrons with spin
along the $x$, $y$, and $z$ directions, respectively. The length of the Rashba
region is L-12 (L-n being the number of n unit cells, where the length of one
unit cell (L-1) is 4.26 Å) and the value of the electric field is 4 V/nm.
Figure 7: (Color online) DFT Fermi surface and spin texture for graphene in a
perpendicular electric field of E=4 V/nm. Four different values of the Fermi
energy near the Dirac point have been selected. The color bar refers to the
$z$-spin projection which is too small to visibly reflect in the length of the
arrow. Figure 8: (Color online) Integrated spin polarization values over
$k_{y}$, as a function of energy for armchair orientation of DFT for the
injected electrons with spin along the x, and z directions.

##  III Results and discussion

Polarization results for graphene in a perpendicular electric field, obtained
from the TB model and from DFT, are shown in Fig. 5 and Fig. 6. We consider
two orientations of the graphene plane, that we label armchair and zigzag,
respectively; the orientation refers to the direction of the interface, which
is perpendicular to that of the current, injected here in the $x$-direction,
as mentioned before (see insets of Figs. 5 and 6). For instance, the setup
shown in Fig. 1(a) corresponds to the zigzag orientation. A large value of the
electric field of 4 V/nm has been chosen, which gives rise to a significant
splitting of the bands, as shown in the middle panel in Fig. 4. It is
important to mention that electric field values of this order correspond, in
fact, to realistic situations. We can mention that a large interfacial
electric field equal to 5 V/nm (or 0.5 V/Å) have been reported on liquid/solid
interfaces with high-density carrier accumulation Yuan  _et al._ (2013). Also,
an out-of-plane electric field of 1 V/Å = 10 V/nm was addressed by Houssa et
al. Houssa  _et al._ (2015) and there are many references on electric fields
of such magnitude applied on 2D materials Gmitra  _et al._ (2016); Rong  _et
al._ (2015). The three orthogonal spin components have been explored as
indicated in the corresponding panels of Figs. 5 and 6. The energy origin has
been set to the Dirac point in both, TB and DFT cases. The wave vector $k_{y}$
runs over the whole Brillouin zone.

Blue and red colors represent positive and negative values of the spin
polarization, respectively. From the sign of the spin polarization in Fig.
5(a), we conclude that spin-up and spin-down electrons (in the $x$-direction)
are preferentially deflected in opposite spatial directions since the spin
polarization sign follows that of the transverse group velocity (for this
orientation the two Dirac cones are superimposed and behave identically in
this regard). This result was already anticipated and discussed with the help
of Fig. 2(a) and is the basis of the SHE. The same number of spin-up and spin-
down electrons are moving in opposite directions while the total transmission,
$T=T_{\upuparrows}+T_{\downarrow\uparrow}+T_{\uparrow\downarrow}+T_{\downdownarrows}$,
not shown here, is $k_{y}$-symmetric. Therefore, the net transverse charge
current is 0, while a finite spin $S_{x}$ current flows in the transverse
direction. In an actual sample with boundaries, this spin current would result
in a spin accumulation of opposite signs on the lateral edges. Notably, the TB
and DFT results are qualitatively coincident, which gives us confidence in our
DFT-based implementation. In all cases, the spin polarization is maximum for
the largest values of $|k_{y}|$ and zero for $k_{y}=0$ (as expected from the
schematics in Fig. 2), but shows a sub-structure that originates from
interference due to the finite length of the SOC-active area (more clearly
seen in the TB results). Also, not surprisingly, similar results are obtained
when choosing the zigzag orientation, as shown in Fig. 6. Now the two Dirac
cones can be differentiated, becoming clear that they contribute in the same
manner to the spin polarization.

When the spin projection of the injected current is perpendicular to the
graphene plane ($z$-direction), a similar $k_{y}$-dependent spin polarization
can be seen in our results, albeit with reversed sign [see Figs. 5(c) and
6(c)], being visibly smaller in absolute value than that of the
$x$-projection, but not zero. The small spin polarization found in this case
is understandable, since the $S_{z}$ component of the spin is only (and
barely) appreciable near the Dirac point, as shown in the panels of Fig. 7 for
quite small energy values. This is in contrast with the results in more
experimentally relevant situations Safeer  _et al._ (2019), but is in
agreement with previous theoretical works of Nikolić et al. on a two-
dimensional electron gas Nikolić  _et al._ (2005a, b). Our methodology does
not allow us to make a direct comparison with experimental observations or
with the spin conductance as defined, e.g., by Nikolić et al. Nikolić  _et
al._ (2005a, b), but we can get some intuition defining the quantity

$P_{v}=\sum_{k_{y}}P(k_{y},E)v_{y}(k_{y},E),$

which is shown in Fig. 8. This quantity reflects now the overall lateral
separation of the spin polarization as a function of energy in close analogy
with the spin current. Notice the lack of electron-hole symmetry expected in
an simple TB model, but absent in the DFT calculations.

As far as the $y$ spin component of the injected current is concerned, this
shows spin accumulation [Figs. 5(b) and 6(b)] since the spin polarization is
symmetric with respect to $k_{y}$ (as is the total transmission, not shown).
This result is at the heart of the REE. Naively, according to our simple
picture discussed above (see Fig. 2), the spin accumulation should change sign
as the energy of the injected electrons crosses the Fermi level. However, this
is not the case in either type of calculation, DFT or TB. (The fact that both
DFT and TB results are essentially similar rules out any implementation
problem or lack of accuracy of the DFT calculations as the origin of this
unexpected result.) We attribute this result to the competing effect of the
intrinsic and extrinsic (Rashba) couplings, which are still comparable in
magnitude for the value of the electric field we have considered Dyrdał  _et
al._ (2009); Correa  _et al._ (2020). Our DFT results in Figs. 5 and 6 show
that the sign of the spin polarization actually changes for electrons
(positive energies), but away from the Fermi energy and only for states with
wave vectors almost parallel to the interface. This change becomes more clear
for larger values of the electric field such as 20 V/nm and larger SOC-active
areas (results not shown here).

In order to explore more in detail how the naive picture (the spin
accumulation changing sign at the Dirac point) may be recovered, we have
carried out TB calculations for systems up to $\approx 0.25\,\mu$m in length
and for unrealistic large values of the Rashba coupling, equivalent to
electric fields up to 2000 V/nm. Results for the armchair orientation are
presented in Fig. 9. Top panels show the TB spin polarization including only
the Rashba term. In this case one can see the expected sign change in the spin
polarization. The other panels show how the “expected” result starts to appear
at values of 20 V/nm when SOC is fully included. However, this requires a
minimum length of the SOC-active region of $\approx 0.25\,\mu$m. As a summary,
only for extremely large electric fields, the sign change can be observed for
any length. This is a mesoscopic effect that can only be unveiled by resorting
to calculations based on TB effective models.

Figure 9: (Color online) Polarization results for the armchair orientation and
injected electrons with spin along the $y$-direction following the tight-
binding approach. Increasing electric field values are considered from top to
bottom panels, from E = 20 to 2000 V/nm (E-20, E-200, and E-2000). Wider SOC
areas are considered from left to right panels, L-n being the number of n unit
cells, where the length of one unit cell (L-1) is 2.46 Å. First row is
calculated with $\lambda_{I}=0$, the others with the two SOC contributions,
$\lambda_{I}$ and $\lambda_{R}$.

##  IV Conclusions

We have studied the charge-spin interconversion capabilities of graphene from
spin-orbit effects by means of DFT calculations. As expected, non-polarized
spin currents injected in a region with Rashba SOC produce lateral spin
accumulation at opposite edges (SHE) for the out-of-plane and longitudinal
spin components and pure spin accumulation (REE) for the perpendicular spin
component.

To obtain the quantitative information we use a $k$-dependent spin
polarization map obtained from DFT where the Rashba SOC was induced by an
electric field applied perpendicular to the graphene plane. A TB approach was
additionally employed to verify our methodology, as an aid in the
interpretation of the aforementioned charge-spin processes, and to overcome
size limitations, inherent to DFT calculations, when deemed necessary. We have
found that the longitudinal and perpendicular spin-projected current
components are greater in absolute value than the out-of-plane component due
to the nature of the Rashba effect.

Moreover, we have found a competition between the intrinsic effect of the
atomic SOC and the Rashba effect (atomic SOC + broken inversion symmetry)
which determines the sign of the pure spin accumulation for electrons. This
can be changed by the length of the SOC active area or by the relative
strength of the couplings. Our approach to these $k$-dependent studies can be
applied to determine the different charge-spin interconversion processes in
more complicated scenarios, such as when SOC effects are induced by proximity
with other materials.

###### Acknowledgements.

We acknowledge financial support through the “María de Maeztu” Programme for
Units of Excellence in R&D (CEX2018-000805-M), the Spanish MCIU and AEI and
the European Union under Grants No. PID2019-109539GB-C43, PID2019-107874RB-I00
and PGC2018-097018-B-I00 (MCIU/AEI/FEDER, UE), the EU Graphene Flagship
funding through JTC2017/2D-Sb&Ge) and the Comunidad Autónoma de Madrid through
Grants S2018/NMT-4321 (NanomagCOST-CM) and P2018/NMT-4411 (ADITIMAT-CM).
J.J.P. and H.S. acknowledge the computer resources and assistance provided by
the Centro de Computación Científica of the Universidad Autónoma de Madrid and
the Red Española de Supercomputación. A.L. thanks the financial support of
Brazilian CAPES/PrInt/UFF.

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# Cross-lingual Offensive Language Identification for Low Resource Languages:
The Case of Marathi

Saurabh Gaikwad1, Tharindu Ranasinghe2, Marcos Zampieri1, Christopher M.
Homan1
1Rochester Institute of Technology, USA
2University of Wolverhampton, UK
<EMAIL_ADDRESS>

###### Abstract

The widespread presence of offensive language on social media motivated the
development of systems capable of recognizing such content automatically.
Apart from a few notable exceptions, most research on automatic offensive
language identification has dealt with English. To address this shortcoming,
we introduce MOLD111MOLD is available at: https://github.com/tharindudr/MOLD,
the Marathi Offensive Language Dataset. MOLD is the first dataset of its kind
compiled for Marathi, thus opening a new domain for research in low-resource
Indo-Aryan languages. We present results from several machine learning
experiments on this dataset, including zero-short and other transfer learning
experiments on state-of-the-art cross-lingual transformers from existing data
in Bengali, English, and Hindi.

##  1 Introduction

The presence of hate speech, cyber-bullying, and other forms of offensive
language in online communities is a global phenomenon. Even though thousands
of languages and dialects are widely used in social media, most studies on the
automatic identification of such content consider English only, a language for
which datasets and other resources such as pre-trained models exist Rosenthal
et al. (2021). In the past few years researchers have studied this problem on
languages such as Arabic Mubarak et al. (2021), French Chiril et al. (2019),
and Turkish Çöltekin (2020) to name a few. In doing so, they have created new
datasets for each of these languages. Competitions such as OffensEval Zampieri
et al. (2020) and TRAC Kumar et al. (2020a) provided multilingual datasets,
which enabled the use of data augmentation methods Ghadery and Moens (2020),
multilingual word embeddings Pamungkas and Patti (2019), and cross-lingual
contextual word embeddings Ranasinghe and Zampieri (2020) to tackle this
problem.

In this paper, we revisit the task of offensive language identification for
low resource languages, focusing on Marathi, an Indo-Aryan language spoken by
over 80 million people, most of whom live in India. Even though Marathi is
spoken by a large population, it is relatively low-resourced compared to other
languages spoken in the region. We collect and annotate the first Marathi
offensive language identification dataset to date and we train a number of
monolingual models on this dataset. Finally, we explore state-of-the-art
cross-lingual learning methods to project predictions to Marathi from Bengali,
Hindi, and English. We address two research questions in this paper:

RQ1: What is the impact of the dataset size in monolingual and cross-lingual
models for offensive language identification? While the Marathi dataset is
relatively small, cross-lingual transfer learning methods allow us to take
advantage of larger available datasets in other languages.

RQ2: What is the influence of language similarity in cross-lingual predictions
for offensive language identification? Previous work used English as the base
language to make predictions in lower resourced languages. In this paper we
use two Indo-Aryan languages, Bengali and Hindi, to project predictions into
Marathi.

Our main contributions are the following:

  1. 1.

We release MOLD, the Marathi Offensive Language Dataset, with nearly 2,500
annotated tweets. MOLD is the first dataset for offensive language
identification in Marathi.

  2. 2.

We evaluate the performance of several traditional machine learning models
(e.g. SVMs) and deep learning models (e.g. LSTM) trained on MOLD.

  3. 3.

We apply cross-lingual transformers to offensive language identification in
Marathi. We take advantage of existing data in English and in two Indo-Aryan
languages, Hindi and Bengali, to project predictions to Marathi and we compare
the results of these strategies. To the best of our knowledge, this is the
first paper to study closely-related languages in transfer learning for
offensive language identification.

  4. 4.

In addition to MOLD, we make the code and the models freely available to the
community.

##  2 Related Work

The problem of offensive content online has been widely studied using
computational models. Researchers have trained system to recognize various
types of such content such as cyberbulling, hate speech, and many others. In
terms of computational approaches, early studies approached the problem using
feature engineering and classical machine learning classifiers, most notably
SVMs Dadvar et al. (2013); Malmasi and Zampieri (2017), while more recent work
applied deep neural networks combined with word embeddings Aroyehun and
Gelbukh (2018); Hettiarachchi and Ranasinghe (2019). With the development of
large pre-trained transformer models such as BERT and XLNET Devlin et al.
(2019); Yang et al. (2019), several studies have explored the use of general
pre-trained transformers in offensive language identification Liu et al.
(2019); Ranasinghe et al. (2019); Bucur et al. (2021) as well retrained or
fine-tuned models on offensive language corpora such as HateBERT Caselli et
al. (2020).

While the vast majority of studies address offensive language identification
using English data Yao et al. (2019); Ridenhour et al. (2020), several recent
studies have created new datasets for various languages and applied
computational models to identify such content in Arabic Mubarak et al. (2021),
Dutch Tulkens et al. (2016), French Chiril et al. (2019), German Wiegand et
al. (2018), Greek Pitenis et al. (2020), Hindi Bohra et al. (2018), Italian
Poletto et al. (2017), Portuguese Fortuna et al. (2019), Slovene Fišer et al.
(2017), Spanish Plaza-del Arco et al. (2021), and Turkish Çöltekin (2020). A
recent trend is the use of pre-trained multilingual models such as XLM-R
Conneau et al. (2019) to leverage available English resources to make
predictions in languages with less resources Plaza-del Arco et al. (2021);
Ranasinghe and Zampieri (2020, 2021c, 2021b); Sai and Sharma (2021). This is
made possible by the availability of the aforementioned datasets as well
multilingual datasets made available at shared tasks such as HASOC 2019 Mandl
et al. (2019), TRAC 2018 and 2020 Kumar et al. (2018, 2020a), and two tasks at
SemEval: HatEval 2018 Basile et al. (2019) and OffensEval 2020 Zampieri et al.
(2020).

##  3 Datasets

We present MOLD and four other datasets used in this work: the Bengali dataset
Bhattacharya et al. (2020) used in the TRAC-2 shared task Kumar et al.
(2020a)—henceforth BE, the Hindi dataset Mandl et al. (2019) used in the HASOC
2019 shared task—henceforth HI, and the English datasets used in OffensEval,
SemEval-2019 Task 6 and SemEval-2020 Task 12—henceforth EN-OLID Zampieri et
al. (2019) and EN-SOLID Rosenthal et al. (2021), respectively.

To annotate MOLD, we followed OLID’s annotation scheme for English which has
been replicated in SOLID and in datasets in Greek Pitenis et al. (2020),
Turkish Çöltekin (2020) and many other languages. OLID’s taxonomy comprises
the following three levels:

Level A: Offensive language identification: offensive (OFF) vs. non-offensive
(NOT)

Level B: Categorization of offensive language: targeted insult or thread vs.
untargeted profanity.

Level C: Offensive language target identification: individual vs. group vs.
other.

This hierarchical taxonomy represents multiple types of offensive content in a
single annotation scheme (e.g. targeted insults to an individual are often
cyberbullying and targeted insults to a group are often hate speech) making it
a great fit for cross-lingual learning applied to low-resource languages like
Marathi. We used OLID level A labels to annotate MOLD and we map these labels
to those included in the Bengali and Hindi datasets.

#### MOLD

The Marathi dataset contains data collected from Twitter using the Twitter
API. We aimed to achieve a similar distribution of offensive vs. non-offensive
content present in OLID, which contains around 33% offensive and 67% non-
offensive tweets. To make sure that both classes were represented, we used
both offensive and non-offensive keywords. For the offensive content we used
22 common curse words in Marathi and for the non-offensive content we used
search phrases related to politics, entertainment, and sports along with the
hashtag #Marathi.

We collected a total 2,547 tweets that were annotated by 6 volunteer
annotators who are native speakers of Marathi with age between 20 and 25 years
old and a bachelors degree. The annotation task is a binary classification, in
which annotators assigned tweets as offensive (OFF) or not offensive (NOT).
The annotators could flag a tweet as invalid if it contained four or more non-
Marathi words. The final version of MOLD contains 2,499 annotated tweets
randomly split 75%/25% into training and testing sets, respectively. We used
Cohen’s kappa Carletta (1996) to measure agreement between pairs of
annotators. We provided a common set of 100 instances to each of the three
pairs of annotators and we report scores of 0.91 between A1 and A2, 0.79
between A3 and A4, and 0.77 between A5 and A6. Table 1 shows dataset
statistics, including class distribution.

Class | Training | Testing | Total
---|---|---|---
Not Offensive | 1,205 | 418 | 1,623
Offensive | 669 | 207 | 876
Total | 1,874 | 625 | 2,499

Table 1: Number of instances and class distribution of NOT and OFF tweets in
MOLD.

Code | Language | Dataset | Instances | Source |  Labels
---|---|---|---|---|---
BE | Bengali | TRAC | 4,000 | F |  overtly aggressive, covertly aggressive, non aggressive
EN-OLID | English | OLID | 14,100 | T |  offensive, non-offensive
EN-SOLID | English | SOLID | 120,758 | T |  offensive, non-offensive
HI | Hindi | HASOC | 8,000 | T |  hate offensive, non hate-offensive

Table 2: Instances, sources, and labels in all datasets. F stands for Facebook
and T for Twitter.

#### Other Datasets

In addition to the Marathi dataset, we used the four aforementioned publicly
available offensive language detection datasets presented in Table 2. OLID
(EN-OLID) is one of the most popular offensive language datasets for English
and we used its level A annotations (offensive vs. non-offensive) as labels.
We used EN-SOLID, the largest available dataset of its kind as our second
English dataset. EN-SOLID contains over nine million English tweets labeled in
a weakly supervised manner Rosenthal et al. (2021). EN-SOLID was created using
an ensemble of four different models and provides, along with the class
labels, the average and standard deviation of the confidence scores predicted
by each model. We included only training examples with average confidence
scores greater than 0.85 over all models, leaving us with 120,758 examples.
Using both EN-OLID and EN-SOLID allows us to investigate the impact of
training data size and help us answer RQ1.

To perform transfer learning from a closely-related language to Marathi, we
used HI Mandl et al. (2019). Both the English and Hindi datasets contain
Twitter data making them in-domain with respect to MOLD. BE, the Bengali
dataset Bhattacharya et al. (2020), is different than the other datasets as it
contain Facebook data and three classes, allowing us to compare the
performance of cross-lingual embeddings on off-domain data but in a a language
similar to Marathi. For Bengali we merged the classes overtly aggressive and
covertly aggressive and map them to EN-OLID’s offensive class. Using both BE
and HI in addition to the two English datasets allow us to investigate the
impact of language similarity aiming to answer our RQ2.

##  4 Methods and Results

###  4.1 Monolingual Models

We run several computational models on MOLD. We trained four classical machine
learning classifiers, available in Scikit-learn Pedregosa et al. (2011):
Decision Trees, Naive Bayes, Random Forest, and SVM using bag of words (BoW),
word unigrams, and word unigrams and bigrams combines using TF-IDF weighting.
We took several pre-processing steps before extracting features such as
removing numbers, extra spaces, special characters, and stop words.222Marathi
stop words are available on https://github.com/stopwords-iso/stopwords-
mr/blob/master/stopwords-mr.txt

We implemented several deep learning models, such as multi layer perceptron
(MLP), long short-term memory networks (LSTMs) with embedding layers, and bi-
LSTMs with attention and word embedding layers. We used the Marathi word2vec
embeddings released in Kumar et al. (2020b). We also experimented with several
SOTA transformer models that support Marathi: multilingual BERT (BERT-m)
Devlin et al. (2019) and XLM-Roberta (XLM-R) Conneau et al. (2019). XLM-R has
an additional advantage: the embeddings are cross-lingual. This helps
facilitate transfer learning across languages, as presented later in this
section. We followed the same architecture described in Ranasinghe and
Zampieri (2020) where a simple softmax layer is added to the top of the
classification ([CLS]) token to predict the probability of a class label. For
XLM-R, from the available two pre-trained models, we specifically used the
XLM-R large model.

For both classical and deep learning models we finetuned hyperparameters
manually to obtain the best results for the validation set created using a
0.8:0.2 split on the training data. As the deep learning models tend to
overfit, we evaluated the model on the validation set once in every 100
training batches. We performed early stopping if the validation loss did not
improve over 10 evaluation steps. All the deep learning experiments were run
on an Nvidia Tesla K80 GPU.

Figure 1: Text classification architecture with XLM-R Ranasinghe and Zampieri
(2020).

Table 3 shows the results obtained by all monolingual models on MOLD’s test
set in terms of both Macro F1 and Weighted F1. We use both metrics due to the
data imbalance in MOLD. With the exception of MLP, all of the deep learning
models outperformed the classical ones. This is somewhat surprising as
classical models tend to outperform deep models on relatively small datasets
like MOLD, but it corroborates the findings from recent competitions on this
topic Basile et al. (2019). Of the deep learning models, XLM-R transformers
provided the best results with a 0.91 macro F1 score.

Features | Model | M F1 | W F1
---|---|---|---
Embeddings | XLM-R | 0.9103 | 0.9210
Embeddings | BERT-m | 0.8852 | 0.8994
Embeddings | LSTM | 0.8400 | 0.84.09
Embeddings | Bi-LSTM | 0.8238 | 0.8251
BoW | Random Forest | 0.7686 | 0.7796
Embeddings | MLP | 0.7541 | 0.7830
BoW | SVM | 0.7489 | 0.7813
BoW | Naive Bayes | 0.7223 | 0.7597
BoW | Decision Tree | 0.7028 | 0.7395

Table 3: Monolingual results for Marathi ordered by macro (M) F1. We also
report weighted (W) F1 scores.

###  4.2 Cross-lingual Models

The main appeal of transfer learning is its potential to leverage models
trained on data from outside the domain of interest. This can be particularly
helpful for boosting the performance of learning on low-resource languages
like Marathi. The recent success of XLM-R cross-lingual transformers with
transfer learning in offensive language identification for low resource
languages Ranasinghe and Zampieri (2020) confirms that this is a feasible
approach. In these experiments, however, the transfer learning’s base language
was English whereas here we use two languages related to Marathi: Bengali and
Hindi, in order to evaluate the extent to which language similarity boosts
transfer learning performance.

#### Transfer Learning

We first trained the XLM-R model separately on the BE, HI, EN-OLID and EN-
SOLID datasets. Then we saved the weights of the transformer model and the
softmax layer and used these weights to initialize the weights of the
transformer-based classification model for Marathi. TL row in Table 4 shows
the results obtained by the cross lingual models with XLM-R. The use of
transfer learning substantially improved the monolingual results. With 8,000
and 4,000 training instances, respectively, the transfer learning model
achieved macro F1 scores of 0.9401 from Hindi and of 0.9345 from Bengali,
respectively, outperforming the results obtained using the two English
datasets, EN-OLID and, especially, EN-SOLID, each contain more instances than
either the Hindi or the Bengali dataset, yet they fail to outperform either as
the base dataset in our transfer learning experiments, suggesting that
language similarity played a positive role in transfer learning.

#### Zero shot learning

To further observe the impact of language similarity in transfer learning, we
performed Zero shot learning, where the XLM-R model was trained on the other
datasets and tested on the Marathi test set. According to the results in Zero-
shot row of Table 4 HI outperforms all the other languages in Zero shot too.

Methodology | Dataset | M F1 | W F1
---|---|---|---
| HI | 0.9401 | 0.9492
Transfer | BE | 0.9345 | 0.9422
Learning | EN-SOLID | 0.9321 | 0.9399
| EN-OLID | 0.9298 | 0.9385
| HI | 0.8396 | 0.8461
Zero-Shot | BE | 0.8115 | 0.8176
| EN-SOLID | 0.7954 | 0.8004
| EN-OLID | 0.7854 | 0.7901

Table 4: Transfer learning results ordered by macro (M) F1 for Marathi. We
also report weighted (W) F1 scores.

#### Few shot learning

Finally, we evaluated each of the languages performance in few shot learning
with Marathi. We retrained offensive language identification XLM-R models from
other languages on 100, 200, 300 etc. instances from Marathi. As shown in
Figure 2 HI tops other languages in all the few shot experiments making it
further clear that transfer learning from a more similar language is effective
in offensive language identification.

Figure 2: Macro F1 with different number of examples and with different
transfer learning strategies for Marathi

##  5 Conclusion and Future Work

This paper introduced MOLD, the first offensive language dataset for Marathi.
We evaluated the performance of several machine learning models trained to
identify offensive content in Marathi. Our results show that applying cross-
lingual contextual word embeddings substantially improved performance over
monolingual models. Furthermore, we showed that XLM-R with transfer learning
from Hindi outperforms all of the other methods we tested. The results
obtained by our models confirm that closely related languages provide an
advantage in our transfer learning experiments, answering our RQ2. This is
likely due to the fact that Hindi and Marathi are typologically related and
also because these languages are in a situation of language contact sharing
cultural background.

To the best of our knowledge, this paper is the first to address the question
of language similarity in cross-lingual learning for offensive language
identification. With respect to our RQ1, our results show that the difference
in performance between transfer learning strategies from OLID and from SOLID
is minimal. SOLID is more than eight times larger than OLID, suggesting that
beyond a certain point, more instances do not necessarily yield significant
performance improvements in transfer learning. Finally, we believe that the
findings presented in this paper can open a wide range of avenues to offensive
language identification applied to other low resource languages, particularly
from the Indo-Aryan family.

MOLD is the official dataset for Marathi at the HASOC
2021333https://hasocfire.github.io/hasoc/2021/index.html shared task on Hate
Speech and Offensive Content Identification in English and Indo-Aryan
Languages. We are expanding the annotation of this dataset to the levels B and
C of OLID’s annotation taxonomy. This will provide us with the opportunity to
test computational models to identify the type and target of offensive posts
in Marathi. As future work, we would like to evaluate the performance of
transfer learning from Dravidian languages spoken in India such as Tamil and
Telugu to analyze the interplay between language similarity and cultural
overlap in cross-lingual offensive language identification as in Ranasinghe
and Zampieri (2021a).

## Acknowledgment

We would like to thank the dataset annotators who helped us with the
annotation of MOLD. We further thank the anonymous RANLP reviewers for the
insightful feedback provided.

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