# Room temperature relaxometry of single nitrogen-vacancy centers in proximity
to $\alpha$-RuCl3 nanoflakes

Jitender Kumar  [  Dan Yudilevich  [  Ariel Smooha  [  Inbar Zohar  [  Arnab
K. Pariari  [  Rainer Stöhr  [  Andrej Denisenko  [  Markus Hücker  [  Amit
Finkler<EMAIL_ADDRESS>[

###### Abstract

Investigating spin and charge noise in strongly correlated electron systems is
a valuable way to analyze their physical properties and unlock new phases of
matter. In this context, nitrogen-vacancy (NV) center-based magnetometry has
been proven to be a versatile sensor for various classes of magnetic materials
in broad temperature and frequency ranges. Here, we use longitudinal
relaxation time $T_{1}$ of single NV centers to investigate the spin dynamics
of nanometers-thin flakes of $\alpha$-RuCl3 at room temperature. We observe a
significant reduction in the $T_{1}$ in the presence of $\alpha$-RuCl3 in
proximity to our NVs, which we attribute to paramagnetic spin noise confined
in the 2D hexagonal plane. Furthermore, the $T_{1}$ time exhibits an almost
linear increase with an applied external magnetic field. We associate this
trend with the alteration of spin and charge noise in $\alpha$-RuCl3 under an
external magnetic field. These findings suggest that the influence of the
room-temperature spin dynamics of $\alpha$-RuCl3 on the longitudinal
relaxation time of the NV center can be used to gain information on the
material itself and the technique to be used on other 2D materials.

###### keywords:

NV center, quantum sensing, $T_{1}$ relaxometry, quantum spin-liquid, 2D
materials

SI WIS1] Department of Chemical and Biological Physics, Weizmann Institute of
Science, Rehovot, Israel WIS1] Department of Chemical and Biological Physics,
Weizmann Institute of Science, Rehovot, Israel WIS1] Department of Chemical
and Biological Physics, Weizmann Institute of Science, Rehovot, Israel WIS1]
Department of Chemical and Biological Physics, Weizmann Institute of Science,
Rehovot, Israel WIS2] Department of Condensed Matter Physics, Weizmann
Institute of Science, Rehovot, Israel USTUTT]3. Physikalisches Institut,
Universität Stuttgart, Stuttgart, Germany USTUTT]3. Physikalisches Institut,
Universität Stuttgart, Stuttgart, Germany WIS2] Department of Condensed Matter
Physics, Weizmann Institute of Science, Rehovot, Israel WIS1] Department of
Chemical and Biological Physics, Weizmann Institute of Science, Rehovot,
Israel

##  1 Introduction

The NV center is a defect in the diamond lattice that forms an electronic
qubit with a sufficiently long coherence time for a variety of applications,
ranging from quantum computing and quantum information to quantum sensing 1,
2, 3, 4, 5. In the realm of sensing, the NV center serves as a highly
sensitive sensor for many physical quantities, including temperature,
rotation, electric and magnetic fields, and pressure 6, 7. In magnetic field
sensing, the NV center is susceptible not only to AC and DC fields but also to
magnetic fluctuations across a broad frequency spectrum 8. For instance, the
transverse coherence times $T_{2}^{*}$ and $T_{2}$ of the NV center are
susceptible to DC to MHz magnetic noise, depending on the pulse sequences
used, such as Ramsey, Hahn echo, and CPMG 9. Complementing this, noise
generated from fluctuations in the GHz regime affects the longitudinal
relaxation time or spin-lattice relaxation time $T_{1}$ of the NV center 10.

Magnetic noise sensing finds a useful application in the study of 2D
materials. Indeed, intense research has been directed toward van der Waals
(vdW) strongly correlated materials in condensed matter physics. A weak
interlayer vdW coupling and strong anisotropic magnetic interactions allow 2D
materials to host interesting quantum properties in exfoliated single to few
atomic layers such as layer-dependent magnetism (ferro/anti), multiferroicity,
superconductivity and quantum spin liquid state 11, 12, 13, 14. Conventional
experimental techniques widely used to explore low-dimensional magnetic
systems include spin-polarized scanning tunneling microscopy 15, scanning
SQUID magnetometry 16, X-ray magnetic circular dichroism 17, and neutron
scattering 18. Common to these techniques are the requirement of low
temperatures and limited detection bandwidth for magnetic fluctuations.
Moreover, in some, for instance the routinely used magnetic probe neutron
scattering technique, a relatively large amount of sample is required, and it
is also susceptible to high absorption in heavy elements, such as iridium. In
recent studies on 2D magnetic materials, single NV center $T_{1}$ relaxometry
has emerged as a vital noninvasive experimental tool for exploration of
diverse physical properties at the nanoscale 19, 7, 20, 21, 22, 23, 24.

Recently, the 2D magnetic insulator, ruthenium trichloride ($\alpha$-RuCl3),
was proposed as a potential candidate to host an exotic state of matter: a
quantum spin liquid (QSL) state. In QSLs, strong quantum fluctuations inhibit
long-range spin order down to very low temperatures and instead form an
unconventional ground state exhibiting long-range spin entanglement and
topological order 25, 26, 27, 14. In 2006, Kitaev proposed an exactly solvable
model for the QSL ground state in a honeycomb lattice, which supports the
existence of fractional excitations like Majorana fermions and
$\mathbb{Z}_{2}$ gauge fluxes 28. Besides the exciting physics of QSLs, they
also have application potentials. For instance, long-range entangled spins
have the potential to establish a quantum communication network, and Majorana
fermions may serve as error-protected qubits in a future quantum computing
technology 29, 30.
While $\alpha$-RuCl3 displays intriguing magnetic phases at low temperatures,
its high-temperature spin dynamics, particularly under external perturbation,
is equally fascinating. For instance, the collapse of the Mott state and
magnetic susceptibility has been observed at room temperature under external
pressure31, 32. In addition, a scattering continuum, argued to be associated
with fractional excitations has been observed in room temperature
polarization-resolved Raman spectra of $\alpha$-RuCl3 single crystals 33.
Considering the NV center’s excellent sensitivity to magnetic and electric
field noise and drawing inspiration from recent theoretical proposals to
employ $T_{1}$ relaxometry for exploring different phases of magnetic systems
34, 35, 24, there is significant interest in utilizing NV relaxometry to
explore nanoflakes of $\alpha$-RuCl3.

In this work, we performed room temperature $T_{1}$ relaxometry on single NV
centers to investigate the magnetic noise originating from nanometers-thin
layers of $\alpha$-RuCl3. Our results reveal a significant reduction in
$T_{1}$ in the presence of these flakes. Additionally, we examined $T_{1}$
under varying external magnetic fields. Our findings illustrate that external
magnetic fields alter the noise profile of $\alpha$-RuCl3 and appear to
enhance the $T_{1}$ of the proximate NV center.

Figure 1: (a) Schematic of our experiment depicting, a quantum sensor located
at distance $z$ from a 2D $\alpha$-RuCl3 spin bath. Ruthenium trichloride
acquires a monoclinic structure (space group C2/m) at room temperature, where
Ru3+ ions form a 2D hexagonal honeycomb lattice in the ab plane 36. (b)
Depiction of the projection of 2D noise, with the external magnetic field
$B_{\parallel}$ aligned parallel to the NV quantization axis, for an NV center
located in the diamond pillar.

##  2 Results and discussion

Figure 2: (a) 45-degree tilted SEM image of one of the thin $\alpha$-RuCl3
flakes transferred on diamond outlined by dotted yellow line; the flake forms
a tent-like structure over the nanopillars (encircled by a red dashed line).
(b) A confocal microscope image of the same flake which shown in (a). The
region covered with the flake exhibits less fluorescence, indicating quenching
of the fluorescence in the presence of the atomically thin flake. (c) Optical
microscope image of a $\sim$ 100 nm thick flake on the pillars, outlined by
dotted line. (d) Confocal image of the  $\sim$ 100 nm thick flake shown in
(c). The pillars beneath the flake are brighter than the pillars outside of
the flake, which may result from the interaction between the flake and the
fluorescing defect.

All fluorescence experiments were performed using a custom-built confocal
microscope. Illustrated in Fig. 1a, a spin qubit is positioned at a distance
$z$ from a 2D dimensional material, while Fig. 1b depicts an optically
accessible shallow NV center qubit in a diamond nanopillar. We start out with
diamond membranes with shallow single NV centers (see SI for details); by
using e-beam lithography, nanopillars which increase the photon collection
efficiency are etched in the diamond. Since placing flakes on top of
nanopillars is challenging, we developed a method of a hybrid bulk-nanopillar
diamond structure to explore atomically thin flakes using single NV centers in
pillars. In this hybrid structure, we created oval-shaped regions of
nanopillars covering nearly 25$\%$ of the flat diamond surface area. Hence,
one can enjoy the benefits of both cases, i.e., the flat areas providing
strong adhesion, helping the flakes to adhere to and encircle the nanopillars
seamlessly, while the nanopillars can host a single NV center and offer high
photon counts per second. An SEM image of bare diamond pillars is provided in
the SI (Fig. LABEL:Fig.S1).

To investigate $\alpha$-RuCl3 using single NV center $T_{1}$ relaxometry, we
exfoliated thin flakes from a sufficiently large single crystal (see SI for
details on crystal growth). These flakes were then transferred onto a $(100)$
diamond membrane patterned with nanopillars hosting NV centers using the
Scotch tape dry exfoliation method. In Fig. 2a, the SEM image illustrates that
the transferred flake adopts a tent-like structure over the nanopillars. This
pattern is similar to h-BN flakes transferred onto diamond nanopillars for
artificial manipulation of curvature and strain 37. The thickness of the
transferred flakes, as determined by atomic force microscopy (AFM), ranges
from approximately 10 nm to several hundred nm. The AFM height profile of the
thinnest flake ($\sim$ 11 nm) examined in this study is provided in Fig.
LABEL:Fig.S3c of the SI. Optical microscope images reveal the thickness-
dependent contrast of the transferred flakes. A relatively thick flake,
approximately 100 nm in thickness, is easily distinguishable atop the pillars
in optical microscope images, as illustrated in Fig. 2c.

In our experimental setup, we observed up to approximately five times
enhancement in the collection efficiency for nanopillars compared to flat
diamond38, 39, 40. High photon collection efficiency improves sensitivity and
shortens measurement times for sequences incorporating $T_{1}$ 5. Another
advantage of using pillars is that they allow us to pass the laser through the
bottom of the diamond to illuminate the NV centers, which minimizes the laser
impact on the material on top. This becomes particularly important in the case
of atomically thin materials, where the higher laser power can damage the
material 41. Thus, the utilization of nanopillars reduces the total irradiated
energy on the sample due to the combined effects of faster measurements,
reduced transmission to the sample, and lower laser powers.

Figure 3: (a) Basic pulse sequence for a typical $T_{1}$ measurement: The spin
state $m_{s}=0$ is polarized with a laser pulse. The state interacts with
noise bath during the waiting time and read out by the second laser pulse (b)
Comparison of the $T_{1}$ relaxation time decay of a single NV center measured
in the presence (blue circles) and absence (red squares) of an 11 nm thick
flake of $\alpha$-RuCl3. Solid lines are stretched exponential fits explained
in the text. (c) $T_{1}$ relaxation time measured for a set of single NV
centers in the presence (blue) and absence (red) of thick (100 nm, NV12 to
NV14) and thin flake ($\sim$ 11 nm, NV1 to NV11) of $\alpha$-RuCl3. The values
of NV4 and NV14 are multiplied by a factor of 10 to make them visible on the
$y$ scale.

To explore magnetic noise from $\alpha$-RuCl3 flakes, we performed $T_{1}$
relaxometry of thin flakes of $\alpha$-RuCl3 using a single NV center. The NV
is polarized in the spin state $m_{s}=0$ using a 520 nm laser, and this state
freely decays to a thermal admixture of $m_{s}=0,\pm 1$. The decay rate of the
polarized state depends on the coupling of the NV center to its environment.
In general, the relaxation time of the NV center in the presence of spin noise
has been described as10

$\displaystyle\frac{1}{T_{i}}=\left(\frac{1}{T_{i}}\right)_{\mathrm{int}}+\int\gamma^{2}\left\langle
B\right\rangle^{2}S\left(\omega,T,E_{a}\right)F_{i}\left(\omega\right)d\omega,$

where $\left(T_{i}^{-1}\right)_{\mathrm{int}}$ refers to intrinsic relaxation
mechanisms, $\gamma$ is the gyromagnetic ratio of the NV center, and ${B}$ is
the root mean square value of the effective magnetic field at the NV position
produced by the proximate spin bath configuration. $E_{a}$ is the energy of
magnetic anisotropy. $S(\omega)$ is the spectral density of the spin noise
environment, and $F(\omega)$ is a filter function, which depends on the pulse
sequence used (the filter function for $T_{1}$ is provided in the SI). The
relaxation rate of an NV center [$\Gamma$=1/$T_{1}$], proximate to a
conductive or insulating magnetic environment, is governed by spin noise
associated with the imaginary part of the magnetic susceptibility
($\chi^{{}^{\prime\prime}}$) — in other words, the imaginary part of the
magnetic field auto-correlation function, 7, 19, 42, 34, 35.

$\displaystyle\frac{1}{T_{1}}=\frac{\mu_{B}^{2}}{2\hbar}\coth\left(\frac{\beta\hbar\omega}{2}\right)\mathrm{Im}\chi_{B_{Z}B_{Z}}\left(z,\omega\right),$

where $z$ is the distance of the noise source to the NV center, and $\omega$
is the transition frequency of the NV center (the concept is schematically
depicted in Fig. 1a). The amplitude of the imaginary part of the magnetic
susceptibility may be modified by different factors, e.g., orbital diamagnetic
susceptibilities of spinon, chargon and the diamagnetic susceptibility of the
emergent gauge field 42, 34, 35. The $T_{1}$ relaxation time of the NV center
is susceptible to magnetic noise in the GHz regime ($\sim$3 GHz) 10, which is
suitable for detecting the magnetic field’s autocorrelation function (magnetic
noise) generated by spin liquids 35, metals 43 and magnetic insulators24, 19.

In Fig. 3b, we compare collected room temperature photoluminescence signals of
a single NV center against the variation in waiting time $\tau$ in the
presence and absence of $\sim$ 11 nm thick flake of $\alpha$-RuCl3. The
signals show an exponential decay trend, indicating a relaxation of the NV
center polarized state $m_{s}=0$ to mixed $m_{s}=0,\pm 1$ states. The
characteristic decay time $T_{1}$ is calculated by fitting the signal with a
stretched exponential function 44.

$\displaystyle{S}=\tau_{0}\exp\left(-\frac{\tau}{T_{1}}\right)^{\eta},$

where $S$ is the signal, $\tau_{0}$ is the prefactor, $\tau$ waiting time,
$\eta$ refers to the stretching parameter, and $T_{1}$ is the longitudinal
relaxation time. For NV4, the fits yield $T_{1}$Ru=13.2$\pm{2.6}$ $\upmu$s and
$T_{1}$= 472$\pm{37}$ $\upmu$s with and without flake, respectively (the
fitting procedure is given in the SI). The ratio of $T_{1}$/$T_{1}$Ru $\sim$
35; such a significant reduction of $T_{1}$ in the presence of a flake
indicates a strong coupling of the NV spin dynamics to magnetic noise of
$\alpha$-RuCl3. Similar reductions in $T_{1}$ have been observed in the case
of proximate magnetic noise sources; such as superparamagnetic Fe3O4
nanoparticles 45, paramagnetic Gd3+ spins 46, and ferritin nanomagnets 47, 10.
At room temperature, $\alpha$-RuCl3 is in a paramagnetic state, confirmed by
fitting the Curie-Weiss law to the inverse dc magnetic susceptibility (Fig.
LABEL:Fig.S5 of the SI). The notable reduction in $T_{1}$ in the presence of
$\alpha$-RuCl3 suggests that the paramagnetic noise bath of $\alpha$-RuCl3
couples to the NV center. The incoherent dipole-dipole interaction between the
NV center and the nearby thermally fluctuating spin bath accelerates the
relaxation rate of the NV center. Furthermore, in polarized Raman spectroscopy
of $\alpha$-RuCl3, a broad scattering continuum with asymmetric Fano-line
shapes is recorded, arising from two-dimensional magnetic scattering at room
temperature 48, 33. In general, asymmetric Fano-line shapes typically
originate from a coupling between discrete phonon modes and electronic states,
signifying metallicity in phase-separated systems 48, 49, 50. Therefore, we
argue that there is noise, similar to that in metals, being present in
$\alpha$-RuCl3, which can account for the reduction of $T_{1}$ of a single NV
center.

Figure 4: $T_{1}$ Magnetic field effect: Relaxation time of single NV center
measured in the presence (a) and absence (b) of $\alpha$-RuCl3 flake for two
different fields aligned parallel to the NV quantization axes. (c) $T_{1}$
relaxation versus magnetic field measured in the presence (blue) and absence
(red) of the $\alpha$-RuCl3 flake.

We have also collected $T_{1}$ data for NV centers covered by a relatively
thick flake (100 nm), incorporated in Fig. 3c as NV12, NV13, and NV14. The
results closely resemble those observed under a thin flake. This behavior
suggests that varying the thickness does not significantly alter the noise
profile of the NV center. This is likely because the NV center is a highly
localized probe, sensitive to its environment within 15 to 20 nm radius. To
validate this observation, we conducted $T_{1}$ experiments on a total of 14
individual NV centers, both with and without the presence of flakes. The
results are shown in Fig. 3c, with NV1 to NV11 representing thin flake
conditions and NV12 to NV14 under thick flake conditions. The results
consistently demonstrate a reduction of $T_{1}$ for each NV center in the
presence of a flake. Investigating magnetic noise in the MHz regime, we
utilized spin-echo spectroscopy ($T_{2}$ measurement), and the results are
illustrated in Fig. LABEL:Fig.S4 of the SI. The experiment was conducted on
the same NV center as our $T_{1}$ relaxometry measurements in Fig. 3b.
Intriguingly, the transverse coherence time $T_{2}$ is barely affected by the
presence of the flake, probably due to the low noise amplitude within this
specific frequency range.

To gain more insight into the magnetic behavior of the material at room
temperature, we performed $T_{1}$ relaxometry under the application of an
external magnetic field along the quantization axis of the NV center. This
method is sometimes referred to as cross-relaxometry 51. In a cross-
relaxometry experiment, applying a magnetic field leads to Zeeman splitting,
resulting in a linear opening of the energy gap between NV states $m_{s}=-1$
and $m_{s}=+1$. Each state exhibits distinct decay rates determined by the
comparability of its energy with the transition rate of the nearby noise bath.

Figure 4a displays the $T_{1}$ of a single NV center, for two values of
applied fields (2 and 383.5 Gauss) in the presence of flake. $T_{1}$ shows a
stretched exponential decay and notably increases approximately 18-fold at the
higher field. In contrast, the change was negligible when we collected data
for different fields without the flake (Fig. 4b). In Fig. 4c, we summarize our
field-dependent data for $T_{1}$. In the absence of the flake, the change in
$T_{1}$ with respect to field variation is almost negligible, or the change is
within the error. Remarkably, in the presence of the flake, $T_{1}$ exhibits
an almost linear increase as the magnetic field strength increases, and at
high field values, it nearly returns to the value observed in the absence of
the flake. Such a significant increment of $T_{1}$ with magnetic field at room
temperature is unusual due to the incompatible energy scales, i.e.,
$k_{B}T=25\,\mathrm{meV}$ and exchange interaction ($J\sim 3\,\mathrm{meV}$)
52, and so its origin is not immediately apparent. We discuss two possible
mechanisms.
A. Diamagnetism. It has been observed that a diamagnetic electrolyte near the
NV center reduces both electric and magnetic noise, consequently improving
$T_{1}$ 53. A theoretical calculation for the $T_{1}$ relaxation time of an NV
center proximate to a 2D spin liquid shows similar effects of a diamagnetic
state on the $T_{1}$ 34. It is worthwhile noting that a Curie-Weiss fit of the
magnetic susceptibility gives a magnetic moment of 2.31 $\mu_{B}$. The inverse
susceptibility data is fitted with a Curie-Weiss formula at a high-temperature
regime to calculate the total paramagnetic moment (Fig. LABEL:Fig.S5 in the
SI). This value is significantly larger than the spin-only contribution of
Ru3+ in its low-spin state, which is 1.73 $\mu_{B}$54, and indicates a
significant contribution from the orbital moment. Interestingly, the
calculated orbital moment is nearly one-third of the spin moment, resembling
the free electron model, where the Landau diamagnetic response of the orbitals
is precisely one-third of the Pauli paramagnetic response 55. In their recent
theoretical work, Zin et al. 56. explored the intertwining of spin and orbital
magnetization in $\alpha$-RuCl3 using multiorbital spin-orbit model for Mott
insulators such as $\alpha$-RuCl3. They formulate that local current loops are
induced when an external magnetic field is applied in such Mott insulators.
This generates magnetization opposite to the applied field as a diamagnetic
response similar to Landau diamagnetism in metals. Due to the substantial
orbital moment present in $\alpha$-RuCl3, we propose that applying an external
magnetic field could induce a diamagnetic-like response in $\alpha$-RuCl3,
potentially leading to an enhancement in $T_{1}$.
B. Charge redistribution. In a recent work, a noticeable enhancement in the
transverse coherence time of a NV centers has been observed in the presence of
a superconductor 57. The effect is tentatively rationalized as a change in the
electric noise due to the superconductor (diamagnetic)-induced redistribution
of charge carriers near the NV center. $\alpha$-RuCl3 is a small band-gap
semiconductor with room temperature resistivity of the order of 10-1 $\Omega$
cm58. In $\alpha$-RuCl3, due to the onsite Coulomb repulsion, a gap opens
within the Ru $4d$ band and splits it into two sub-bands, the upper Hubbard
band and the lower Hubbard band, and an inter-site
$d^{5}$$d^{5}$$\rightarrow$$d^{4}$$d^{6}$ charge transfer between neighboring
Ru3+ ions governs the hopping conduction mechanism 59. Along parallel lines as
those of the change in transverse coherence time due to charge fluctuations,
we therefore suggest that these could be an additional source of noise at room
temperature. Charge fluctuations are sensitive to external perturbations, such
as magnetic fields, especially in poor conductors. An external magnetic field
may reduce the mobility of charges, leading to a decrease in charge
fluctuations, and could enhance the $T_{1}$. The electrical conductivity of
single crystal $\alpha$-RuCl3 is highly anisotropic, with a reported
conductivity almost four orders of magnitude higher in a plane perpendicular
to the $c$ axis compared to the plane parallel to the $c$ axis60. The
longitudinal relaxation time of an NV center is sensitive to noise projected
perpendicular to its quantization axis. In the presence of magnetic noise
coupled to an NV center, the longitudinal relaxation rate can be expressed as
61.

$\displaystyle\frac{1}{T_{1}}=\frac{1}{T_{0}}+3\gamma^{2}\sqrt{\left\langle
B^{2}\right\rangle_{\perp NV}},$

where $\gamma$=28 GHz/Tesla is the electron gyromagnetic ratio, and $B$ is the
magnetic field noise component perpendicular to the NV quantization axis. The
schematic of experimental geometry is shown in Fig. 1b. The noise bath
comprising of electronic spins and charge fluctuation lies in the ${ab}$
plane. The component of this noise perpendicular to the quantization axis of
the NV center will be

$\displaystyle\sqrt{\left\langle B^{2}\right\rangle_{\perp
NV}}=\sqrt{\left\langle B^{2}\right\rangle}\sin\theta,$

where $\theta$ is the angle between the noise bath and NV quantization axis.
Considering the two-dimensional nature of the spin-spin interactions in the
hexagonal ${ab}$ plane, we believe that applying the magnetic field parallel
to the NV quantization axis will diminish the angle $\theta$ and the noise
component perpendicular to the NV quantization. This suggestion further
validates our observation of $T_{1}$ recovery at a high field.

In conclusion, we have investigated nanometers-thick flakes of $\alpha$-RuCl3
using the longitudinal spin relaxation time $T_{1}$ of single NV centers in
diamond. We observed a significant reduction of NV relaxation time by the
proximity of $\alpha$-RuCl3, which signifies the coupling of noise
fluctuations of $\alpha$-RuCl3 with the NV. The reduction in $T_{1}$ is almost
independent of variations in the flake thickness, confirmed with 11-nm and
100-nm thick flakes. A gradual increment of $T_{1}$ time as a function of
magnetic field in the flake’s presence was observed. We hypothesize that the
increase in $T_{1}$ is associated with the suppression of spin and charge
fluctuations in atomically thin flakes due to the magnetic field. These
results indicate that $T_{1}$ relaxometry with a single NV center is a
promising technique to explore the spin dynamics of nanoflakes of potential
quantum spin liquid candidate $\alpha$-RuCl3 and similar systems . A
comprehensive low-temperature $T_{1}$ relaxometry study, along with supporting
experiments such as magneto-resistance, are required to corroborate our
interpretation. We also propose exploiting a (111) oriented scanning NV center
to study the out-of-the-plane spin dynamics confined in the ab hexagonal plane
62. Furthermore, unlike neutron scattering in iridium containing compounds,
the NV qubit does not suffer from issues related to flux absorption and amount
of the sample, rendering it a desirable sensor for the family of iridium-based
QSLs.

We heartily appreciate comments from I. Sodemann on our manuscript. We thank
N. Bar-Gill’s group for allowing us to use their setup and H. Steinberg’s
group for showing us how to handle vdW materials. We also thank A. Cohen and
O. Yaffe for running Raman characterization of our flakes. MH is incumbent of
the Henry and Gertrude F. Rothschild Research Fellow Chair and acknowledges
support of the Leona M. and Harry B. Helmsley Charitable Trust grant no.
2018PG-ISL006. AKP acknowledges postdoctoral fellowship support from the
Council for Higher Education, Israel, through the Study in Israel program. The
authors acknowledge the historical support of the Perlman family as well as
the Kimmel Institute for Magnetic Resonance Research. AF is the incumbent of
the Elaine Blonde Career Development Chair in Perpetuity and acknowledges
financial support from the Minerva Stiftung (grant no. 714131) and the Israel
Science Foundation (grant no. 418/20).

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Nailton Silva, José Moura and Patrick Terremattelogo_ttlM. Antonia Huertas,
João Marcos, María Manzano, Sophie Pinchinat,
François Schwarzentruber54th International Conference on Tools for Teaching
Logic11207TTL2015

# ARG: A Virtual Tool for Teaching Argumentation Theory

Nailton Silva  José Moura  Patrick Terrematte  Federal University of Rio
Grande do Norte (UFRN)
Metropole Digital Institute (IMD)
Group of Logic, Language, Information, Theory and Applications (LoLITA)
Natal – RN – Brazil
<EMAIL_ADDRESS>
###### Abstract.

Researchers look for new virtual instruments that can improve and maximize
traditional forms of teaching and learning. In this paper, we present the ARG
system, a virtual tool developed to help the teaching/learning process in
argumentation theory, especially in the field of Law. ARG was developed based
on Araucaria by Reed and Rowe, Room 5 by Ronald P. Loui, as well on systems
such as Argue!-System and ArguMed by Bart Verheij. ARG is a platform for
online collaboration and applies the theory of Stephen Toulmin to produce
arguments that are more concise, precise, minimally structured and more
resistant to criticism.

###### Key words and phrases:

Teaching Argumentation Theory; Juridical Argumentation; Toulmin’s Layout;
Didactic Software.

###### 1991 Mathematics Subject Classification:

K.3.1 Computer Uses in Education.

##  1\. Introduction

_“The use of argumentation implies that one has renounced resorting to force
alone, that value is attached to gaining the adherence of one’s interlocutor
by means of reasoned persuasion, and that one is not regarding him as an
object, but appealing to his free judgment. Recourse to argumentation assumes
the establishment of a community of minds, which, while it lasts, excludes the
use of violence.”_

— Chaim Perelman

This study was initiated in mid-2010 to help undergraduate students understand
the argumentative structures used by magistrates in the justification of their
judicial decisions, adopting the accurate analysis of judgments pronounced by
judges of the Rio Grande do Norte State Court as their methodology.

Following the senior thesis presented by Nailton Silva [6], this study ccome
to three findings, which were crucial to the development of ARG. The first
being (i) identification of fragility in the composition of those Magistrates’
arguments which were uncritical and did not observe rules pertinent to any
argumentation theory.

Further, it was also observed that the substantiation of judicial decisions
were being organized based on the same patterns that were already used in the
very beginning of juridical rhetoric which accentuates, as an argumentative
structure, the “Legal Syllogism”, creating the illusion of certainty in a
sphere of uncertainty. Finally, it was noted that (iii) some arguments make
use of assumptions and occult inference rules, establishing conclusions by
implication. There are an obstacle for complete exercising of jurisdiction, of
constitutional warrantees and credibility of the decisions and judicial
institutions. Such conclusions served to be the justification for the search
of higher rigor and consistency in the judicial determinations, and thus led
to the development of the tool presented here.

We have analyzed how students of law are taught critical thinking and
argumentation, focusing on argumentative structures used in the Brazilian
legal practice. This analysis has led to the development of an
electronic/virtual tool to assist in the task of argument construction. The
aim of this work is to present the ARG system111The ARG is available at
http://assistentearg.herokuapp.com/ with a video presentation at
http://youtu.be/BB0YDiOPam8., a system designed to be a multilingual online
tool able to assist in the production and improvement of practical arguments –
not only those juridical in nature.

Our solution adopts Stephen Toulmin’s theory of argumentation [7, 8], and we
consider the value of his “layout” of argument, which enables us to visualize
and follow the moves necessary for the construction of an argument of
juridical practice. Toulmin’s theory of argumentation, it is important to say,
was already applied to compound electronic tools of representation and to
helping in the composition of arguments222See
http://www.phil.cmu.edu/projects/argument_mapping/., fitting very well when
applied in numerous experiences of Artificial Intelligence and Argumentation
and Law. This may be due to its heuristic properties, which is exploitable in
information systems.

##  2\. State-of-the-art argumentation tools

_“We can’t understand where we are now, without understanding how we got
there. And of course, once we recognize the need to understand how we get to a
particular point, we have to recognize also that the work of our successors
will supersede our own ideas, and we must be modest in recognizing that the
best we can do is indeed the best we can do.”_

— Stephen Toulmin. Reasoning in Theory and Practice, 2006

There are well-known uses of informatics in Law333About the subject see:
http://austhink.com/critical/pages/argument_mapping.html and
http://www.phil.cmu.edu/projects/argument_mapping/., such as in the Mechanical
Jurisprudence, CCLIPS - Civil Code Legal Information Processing System,
JUDITH, British Nationality Act, HYPO, Zeno, Room 5, PROSUPPORT, Araucaria and
ArguMed projects. All of them essentially focus on the comprehension,
representations and/or reproduction of judicial arguments. However, none of
these serves as a solution for the problem highlighted in the previous
section.

Four of these tools were the main tool available and have some of the
functions of ARG. The first one was Room 5, developed by Ronald P. Loui, Jeff
Norman, Joe Altepeter, Dan Pinkard, Dan Craven, Jessica Linsday and Mark
Foltz, from Washington University. It was a website that provided a mechanism
to represent, in a structured way, juridical argumentation, allowing visitors
to make moves like those made by cases decided on the Supreme Court of the
United States of America, inserted into a format that structures the
discussion as either pro-author or pro-defendant [3].

The second and third systems that inspired us were ARGUE!-SYSTEM and
ArguMed444Available at: http://www.ai.rug.nl/~verheij/aaa/., which were
systems developed by Bart Verheij [9, 10, 11], from the University of
Maastricht in order to mediate the process and the argumentation of one or
more users. In ARGUE!, the user provides argument data, such as assumptions,
questions and reasons, and the system determines the status of the
justification: whether they were justified, unjustified, or neither [9]. Its
successor, ArguMed, with a more transparent subjacent argumentation theory and
a more intuitive interface, provides the user with the gradual construction of
arguments, through the filling-in of patterns, each of them corresponding to
an “argument move”, such as adducing a reason or making a declaration [9].

Lastly, Araucaria555Available at:
http://araucaria.computing.dundee.ac.uk/doku.php., developed in 2001 by Chris
Reed and Glenn Rowe [5] from the University of Dundee, is a tool that helps in
(re)construction, typesetting and evaluation of arguments through a graphical
interface (“point-and-click”).

These tools, however, are limited to English speakers. Such applications do
not include an interactive guide centered in on gradual composition and
evaluation of arguments with the criterion of evaluation and improvement. They
also do not provide an environment of discussion where students are able to
explore the collective knowledge with technical support in theories of
argumentation.

With analysis of the systems of automation, mediation and representation of
reasoning encountered, it is possible to formulate the following conclusions
that also serve the as basis of the new system: (i) arguments can be
represented graphically through systems of electronic data processing; (ii)
representation of arguments make their dialectical structure more evident; and
(iii) theories of argumentation can be used in addition to an electronic tool
to construct arguments.

In all argumentation situations we can use a methodology to clarify the
structure of the arguments at stake. These tools previously mentioned took
into account or created a theory of argumentation subjacent to their own
judicial system. For similar purposes, ARG (abbreviation of “ _argumentum_ ”)
was developed: with the clear objective of helping in the composition and
management of arguments, and to address the root of the problem of
inconsistency and fragility in argumentation that occur in Brazilian judicial
practice. As a secondary objective, our tool also intends on supporting the
teaching of critical thinking to students of philosophy, literature and
science, helping their comprehension of theories of argumentation.

##  3\. The Argumentation Assistant: ARG

_“Arguments are human interactions through which such trains of reasoning are
formulated, debated, and/or thrashed out.”_

— Stephen Toulmin. An Introduction to Reasoning, 1979.

The aim was to construct and make public an online a multilingual teaching
tool on the theory of argumentation based on participatory methodology with
open source-code that could make it possible to store arguments and to
visualize them in a clear and concise way. We planned on making available
interactive guides to help users learn the techniques of arguing well by
providing them with problems that stimulate them to think and produce good
arguments. For this, we used the following technologies: (i) Ruby 1.9.3p125;
(ii) Ruby on Rails 3.2.3; (iii) PostgreSQL 9.1.3; (iv) Github; and (v) Heroku.
These tools were suitable for the development of multilingual information
systems, are integrated with social media, and also have a large repository of
documentation available online.

Figure 1. ARG’s homepage.

ARG is able to implement many functions. Some of them will be laid out briefly
in this work, particularly the functions of (i) stimulation, (ii) evaluation,
(iii) help/instruction and (iv) improving arguments.

The first function, stimulation, consists of prompting argument through cases
provided by managers and/or professor-moderators of the system or by other
academic students. Every week, for example, a new case might be introduced or
a new problem regarding a previous case, opening a discussion where the users
and moderators evaluate the arguments used, assigning a grade that it deems
fitting, taking into account suggested criteria.

In ARG it is possible to post the abstract of a factual situation, attach
elements of a police investigation and/or show a video and request, for
example, that the users elaborate arguments that they have to compose. This
could be an accusatory exordial (complaint) presented by the Prosecutor, for
instance. After this, users could be asked to formulate the main argument of
the answer to the accusation.

All the arguments posted are stored in an external data bank and accessible in
real time, with daily indexation. We have also created a repository of
arguments oriented to cases and specific themes.

Regarding the second function, in the evaluation system, each user or
moderator can, besides comment, attribute a maximum grade of five stars or a
minimum of one star to any argument according to the quality of reasoning
presented, ideally observing the presence of the following properties:

> 1\. Clarity about what is considered in the argument; 2. Necessary and
> sufficient data to support the conclusion; 3. Relevant support and proof of
> the case under discussion; 4. Strength of the conclusion explicitly gained
> and the possible refutations. [8, 2]

In order to evaluate the arguments, it is necessary to observe that the
following are avoided: “1. Absent data; 2. Irrelevant data; 3. Deficient data;
4. Unjustified suppositions; 5. Ambiguity”[8].

In regards to the third function, in ARG it is possible to teach users the
basics of any theory of argumentation, as it offers an interactive guide
oriented by the theory of Toulmin (see Fig. 2). Through this guide, it is
requested that the user fills in the fields to generate a “skeleton” of an
argument, treated by ARG as a “draft” or “sketch”.

Figure 2. ARG’s page to guide the argumentative construction.

Finally, the fourth function focuses on improving arguments. ARG intends to
help the prevention of eventual mistakes or neglect during its elaboration,
disposing of a group of schemes of argumentation with many critical questions
[12]. Usually argument schemes have a number of critical questions that must
be answered satisfactorily when there is its application in a particular case.
Some of those questions refer to the acceptability of the premises and other
issues related to the exceptional circumstances in which the scheme cannot be
applied [4].

##  4\. Solving a case with ARG: the Speluncean Explorers

_“The true revolution will arrive when computer systems now in development
begin to perform or assist in the process of legal reasoning.”_

— Computers and Legal Reasoning. Garry S. Grossman and Lewis D. Solomon, 1983.

As a hypothetical scenario, let us suppose that we introduced on ARG the case
of the Speluncean Explorers666The work describes the judgment of an
appellation resource where the accused were processed and condemned to death
by the Court of Jury that recognized the practice of homicide. In synthesis,
the victim was sacrificed by the accused to enable their survival, since they
had been without any resources or food, involuntary and unpredictably for more
than twenty days because of a landslide at the only access to a cave [1]., and
that the character J. Keen, Magistrate of the Supreme Court, needs help in
constructing an argument for his vote.

There is a page in the system that provides a guide for argumentation and an
argument “constructor/builder”. In this case, the user is asked to fill in the
appropriate fields with elements that, according to Toulmin, compound any
argument. So, Keen, stimulated by questions777I.e. “What are you trying to
prove?” or “Why do you have those assumptions?” and solicitations programmed
in ARG, will fill the elements in with his arguments in the following way:

  * •

Claim [C] = The sentence must be confirmed, with the maintenance of
condemnation of the accused.

  * •

Grounds [G] = (1) It is not of competence for the judge to measure if the act
was just or unjust, good or bad, but to apply the law and not their
convictions of morality; (2) The judiciary cannot create exceptions to the
application of the law; (3) The judge cannot search the purposes of the law.
In doing so, he legislates and, consequently usurps the competence of the
Legislative Power; And (4) the conduct perpetrated by the accused fits the
legal dispositive perfectly

  * •

Warrant [W] = The judge must be loyal to the written law and interpret its
evident meaning, without references to personal desire and its own concepts of
justice.

  * •

Backing [B] = Article 12-A of the criminal code.

The tool, considering the quantity of provided elements, will be able to
generate an automatic text for the argument following the aforementioned
guidelines:

> This is based on article 12-A [B] of the criminal code. We assume that [W]
> the judge is be loyal to the written law and interprets it on its evident
> meaning, without interferences or personal desires and own conceptions of
> justice. Given [G]: (1) it is not the duty of the judge to measure if the
> act was just or unjust, good or bad, but to apply the law and not its
> conceptions of morality; (2) the judiciary cannot create exceptions to the
> applications of the law; (3) it is not up to the judge to search the purpose
> of the law, but under the penalty of usurping the competence of the
> Legislative Power; and (4) the conduct perpetrated by the accused fits the
> legal dispositive, therefore, [C] it must confirm the sentence, keeping the
> condemnation of the accused ones.

Subsequently, offers the user a roll of verification 888With questions such
as: 1. Is it clear and sure the claim the argument tries to make? 2. Is there
clarity and certainty in what is implicitly purposed (is there any purpose)?;
3. Are the data/reasons relevant?; 4. Are the data/reasons enough?; 5. Are the
data/reasons justified?; among others. so that it is possible for the
improvement of the argument. This roll corresponds to the structured abstract
of what is necessary to compose a good argument, based on Toulmin [8] and
Hitchcock [2].

Thus, it is up to the user to verify the nature of the argument that it
intends to propose and to observe if it is proper to the form and to the main
proper questions. So, J. Keen, the judge in this example, could consult the
scheme “Argument from the Constitution of Causal Laws”999Available at:
http://araucaria.computing.dundee.ac.uk/downloads/schemesets/katzav-reed.scm
and http://assistentearg.herokuapp.com/en/schemes. and realize its task by
believing that this constitutes a good exercise to establish and comprehend
the structures and the cares one must have with each argument.

In ARG, arguments are not treated as the instantiation of an abstract
inference scheme, which would refer only to the evaluation of its formal
aspects. We want to provide arguments schemes and critical issues that allow
the user to make stronger arguments, resistant to criticism, and avoid the
incidence of reasoning faults - technical “argument-scheme approach” by
Prakken [4].

With the purpose of testing ARG, a pilot study was carried out in November
2014. The task was applied to 206 undergraduate law students of the Academic
Center of the Rio Grande do Norte State University (UNI-RN) and involved an
adaptation of the quoted case of “the Speluncean Explorers”. The students had
to give an argument, from the point of view of J. Keen, in favor of or against
the maintenance of the condemnation of the accused.

After this experiment, we compared the arguments before and after the use of
the ARG-system. The academics who used the tool made arguments remarkably more
concise, precise, minimally structured and more resistant to criticism. In
addition, the system has not received negative reviews by users, as they did
not report the occurrence of error in the application. However, we need more
tests for more accurate conclusions.

In sum, the advantages of ARG include: (i) being available in a scale that
goes beyond the classroom; (ii) being a useful tool for dissemination of
knowledge, exposing the argumentation process in a concise way; and (iii)
being a complement to face-to-face learning, as well as having online tasks,
as a “blended learning” strategy.

##  5\. Final Remarks

_“The best we can do, that is, is to consider when we live, where we live, how
we live, what the most reflective and best-informed experience of our
colleagues in different areas has been, and what options are open in the
future for the people who will come after us, and will revise and move beyond
our ideas. ”_

— Stephen Toulmin. Reasoning in Theory and Practice, 2006.

ARG presents a system that can be used in any area of knowledge as an
instrument of teaching critical thinking and argument production.

It is good to note that all the functionalities already implemented in ARG :
(i) storing of arguments; (ii) visualization of arguments in a clear and
concise way; (iii) interaction among users by tracking arguments of selected
users; (iv) assistance in compounding arguments and help in improving them;
(v) development of the intellectual faculties in argumentation theories; (vi)
availability of multilingual scheme structures of arguments; and (vii) an
evaluation system of arguments in two dimensions (community and moderators).

The system is available in two languages: English and Brazilian Portuguese,
and is currently being translated into Spanish and French. In the future we
aim to:

  * •

Adapt anti-plagiarism solutions with the processing of language to identify
similarities in the argumentative texts.

  * •

Automate an exportation and importation of arguments from the
professor/moderator.

  * •

Integrate with a virtual environment of learning, e.g. the Moodle.

With such modifications, we hope to improve and transform it to a strong
instrument for the learning of argumentation theory.

### Acknowledgements

The authors acknowledge all undergraduate law students who have contributed to
the project during the Logic and Techniques of Argumentation course at UNI-RN.
We would also like to acknowledge PIBIC/CNPq for their support of this
research.

## References

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