# Spectral evidence for NiPS3 as a Mott-Hubbard insulator

Yifeng Cao  Department of Physics, Boston University, Boston, Massachusetts,
02215, USA.  Advanced Light Source, Lawrence Berkeley National Laboratory,
Berkeley, California, 94720, USA.  Nicholas Russo  Department of Physics,
Boston University, Boston, Massachusetts, 02215, USA.  Advanced Light Source,
Lawrence Berkeley National Laboratory, Berkeley, California, 94720, USA.
Qishuo Tan  Department of Chemistry, Boston University, Boston, Massachusetts,
02215, USA.  Xi Ling  Department of Chemistry, Boston University, Boston,
Massachusetts, 02215, USA.  Jinghua Guo  Advanced Light Source, Lawrence
Berkeley National Laboratory, Berkeley, California, 94720, USA.  Yi-de Chuang
Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley,
California, 94720, USA.  Kevin E. Smith<EMAIL_ADDRESS>Department of Physics,
Boston University, Boston, Massachusetts, 02215, USA.

###### Abstract

The layered van der Waals trichalcogenide NiPS3 has attracted widespread
attention due to its unique optical, magnetic, and electronic properties. The
complexity of NiPS3 itself, however, has also led to ongoing debates regarding
its characteristics such as the existence of self-doped ligand holes. In this
study, X-ray absorption spectroscopy and resonant inelastic X-ray scattering
have been applied to investigate the electronic structure of NiPS3. With the
aid of theoretical calculations using the charge-transfer multiplet model, we
provide experimental evidence for NiPS3 being a Mott-Hubbard insulator rather
than a charge-transfer insulator. Moreover, we explain why some previous XAS
studies have concluded that NiPS3 is a charge-transfer insulator by comparing
surface and bulk sensitive spectra.

##  I Introduction

Van der Waals (vdW) materials, including grapheneNovoselov  _et al._ (2012),
transition metal dichalcogenidesNicolosi  _et al._ (2013); Xu  _et al._
(2015), and boron nitrideWatanabe  _et al._ (2004) are a promiment class of
two-dimensional (2D) crystals. The reduced dimensionality of these systems
often leads to exceptional physical properties, resulting from enhanced
quantum effects and increased correlations due to the reduction of available
phase space and diminished screeningAjayan  _et al._ (2016). In this study, we
focus on NiPS3, a type of 2D vdW metal phosphorus trichalcogenides (MPX3).
NiPS3 is monoclinic, with space group $C2/m$; it can be visualized as layered
NiS2 crystals with P-P pairs substituting for one third of the Ni sitesWang
_et al._ (2018); Klingen  _et al._ (1973) as shown in FIG. 1. NiPS3 exhibits
intriguing properties in electronicsKim  _et al._ (2018); Lane and Zhu (2020);
Tan  _et al._ (2022),spintronicsWang  _et al._ (2021); Basnet  _et al._
(2021); Scheie  _et al._ (2023), magnetismWildes  _et al._ (2015); Kim  _et
al._ (2019a); He  _et al._ (2024), and opticsLiu  _et al._ (2019); Wang  _et
al._ (2022). NiPS3 stands out among the 2D crystals due to its ultrasharp
photoluminescence (PL) peak at 1.47 eV, induced by a spin-orbit-entangled
exciton stateKang  _et al._ (2020); Wang  _et al._ (2021); Hwangbo  _et al._
(2021). Understanding the properties of the exciton state requires an
investigation of both the occupied and unoccupied states of NiPS3; although
the exciton of NiPS3 has been extensively studiedBelvin  _et al._ (2021); Ho
_et al._ (2021); Klaproth  _et al._ (2023); Kim  _et al._ (2023), many
fundamental electronic properties of NiPS3 have still remained controversial.

In X-ray absorption spectroscopy (XAS), a core electron is excited to an empty
state, thereby probing the unoccupied states of the system, with information
about the occupied states being inferred indirectlyFuggle  _et al._ (1992).
Meanwhile, in resonant inelastic X-ray scattering (RIXS), photons are
scattered inelastically off matter, and we measure the excitations
corresponding to the changes that occur during the scatteringAment  _et al._
(2011). Both XASKim  _et al._ (2018, 2019b); Kang  _et al._ (2020); Yan  _et
al._ (2021) and RIXSKang  _et al._ (2020); DiScala  _et al._ (2023); He  _et
al._ (2024) have been applied to NiPS3, yet they have yielded differing
results. The major controversy is whether NiPS3 is a charge transfer insulator
or Mott-Hubbard insulator. A charge-transfer insulator is defined by a charge-
transfer energy $\Delta$ (the energy cost of transferring an electron from the
$p$ level of a ligand to the metal ion) that is smaller than the Coulomb
repulsion energy between two $d$ electrons $U_{dd}$ (the energy cost of a $d$
electron hopping to another already occupied $d$ site); by contrast, when
$\Delta$ is greater than $U_{dd}$, the standard Hubbard model will be applied,
resulting in a Mott-Hubbard insulatorKhomskii (2014). The simplified energy
levels for these two types of insulatorsSahiner  _et al._ (1996) are shown in
FIG. 2: although both have a dominant ground state of $d^{8}$, the Mott-
Hubbard insulator’s lowest excited state is $d^{9}$, while the charge-transfer
insulator’s lowest excited state is $d^{9}\underline{L}$, where
$\underline{L}$ represents a ligand hole. Kim et al. first applied XAS to the
Ni L-edge of NiPS3 and compared with calculated spectra corresponding to
different values of $\Delta$Kim  _et al._ (2018). They found that NiPS3 is a
self-doped charge transfer insulator with a negative value of $\Delta$. With a
negative $\Delta$, the charge transfer from the ligand will occur
spontaneously, resulting in a dominant ground state $d^{9}\underline{L}$. This
claim, however, was directly challenged by a subsequent calculation which
showed that NiPS3 would be a metal rather than an insulator with
$d^{9}\underline{L}$ ground stateKim  _et al._ (2019b). They confirmed the
presence of the paramagnetic Mott phase and the dominant ground state $d^{8}$
for NiPS3. Following XAS studiesKang  _et al._ (2020); Yan  _et al._ (2021),
although challenging NiPS3 as having negative $\Delta$ with self-doped
behavior, they still concluded that NiPS3 has a small but positive $\Delta$
and belongs to the category of charge-transfer insulator. The exciton of NiPS3
probed by RIXS is also a subject of debate. Initially, the exciton has been
described as a Zhang-Rice singletKang  _et al._ (2020). However, this does not
explain the extremely narrow PL peak of the excitonHe  _et al._ (2024) and its
mismatch in response to an applied magnetic fieldJana  _et al._ (2023).
Instead of the Zhang-Rice mode, a most recent RIXS studies have revealed the
dominant Hund’s character in NiPS3He  _et al._ (2024).

In this study, we compared XAS measurements of an as-grown single crystal of
NiPS3 to an exfoliated sample of NiPS3 in order to reconcile the controversy
regarding the value of $\Delta$ for NiPS3. XAS was applied using both total
electron yield (TEY) mode and total fluourescence yield (TFY) mode for surface
sensitive ($<10$ nm) and bulk sensitive ($>100$ nm) measurements,
respectivelyYang  _et al._ (2021). Therefore, the surface and bulk features of
NiPS3 were simultaneously collected, enabling us to capture the most subtle
details of the electronic structure. By comparing the XAS results in TEY mode
and TFY mode, we obtained different spectra from previous XAS studiesKim  _et
al._ (2018); Kang  _et al._ (2020); Yan  _et al._ (2021) on NiPS3.
Furthermore, by comparison with calculations using the charge-transfer
multiplet model we are led to conclude that, contrary to the previously held
belief that NiPS3 has a very small value of $\Delta$, it actually has a
relatively large value of $\Delta$. Further analysis was conducted to explain
why previous XAS results concluded that NiPS3 belongs to the charge-transfer
insulator. Moreover, we also applied RIXS to NiPS3 and found that $dd$
excitations are dominant, while charge-transfer excitations were too weak to
be observed. Combined with the conclusion from XAS that NiPS3 has a relatively
large $\Delta$, we provide strong evidence that NiPS3 is a Mott-Hubbard
insulator.

##  II Methodology

NiPS3 single crystals were synthesized by the chemical vapor transport method.
Pure elements, in a stoichiometric ratio of Ni:P:S $=$ 1:1:3 (2 g in total),
along with 40 mg iodine as transport agent, were enclosed in quartz ampules
under vacuum of 1$\times$10$-$4 Torr. Subsequently, the ampules underwent
heating in a two-zone furnace with the temperature range of 650 $-$ 600 ∘C for
1 week, followed by cooling to room temperature. Bulk crystals were harvested
from the lower temperature zone of the ampules. The as-grown NiPS3 single
crystal was directly mounted on the sample holder with conductive copper tape.
The exfoliated sample was prepared by removing the top layers using Scotch
tape under an argon atmosphere in a glovebox, and was transferred to the
analysis chamber using a vacuum suitcase to prevent oxidation.

The nickel L3,2-edge XAS spectra were measured at Advanced Light Source (ALS)
beamline 7.3.1 at Lawrence Berkeley National Laboratory (LBNL). Both TEY and
TFY modes were collected simultaneously. The XAS photon energy was calibrated
using a Li(Ni1/3Mn1/3Co1/3)O2 reference sample. O K-edge XAS spectra with both
TEY and TFY modes were also collected to determine the extent of O
contamination in the sample.

The theoretically calculated XAS spectra were obtained using the Crispy
software for the Quanty libraryRetegan (2019). A charge-transfer multiplet
model is applied to the system, described by a semi-empirical Hamiltonian that
includes atomic and crystal-field interactionsde Groot  _et al._ (2021). In
this study, nickel L3,2-edge XAS spectra were calculated by Crispy for various
values of $\Delta$. For simplicity, the symmetry is set to $O_{h}$. The
applied parameters are: $F_{k}$=0.8, $G_{k}$=0.8, $\zeta$=1.0, $U(3d,3d)$=4.0
eV, $U(2p,3d)$=6.0 eV, $10Dq(3d)$=1.0 eV, $Ve_{g}(3d,L1)$=1.4 eV,
$Vt_{2g}(3d,L1)$=1.0 eV. The broadening full width at half maximum parameters
(eV) are set to be 0.48, 0.52 for Lorentzian and 0.3 for Gaussian. The values
of $\Delta$ range from -1 eV to 5 eV.

The RIXS spectra of nickel L3-edge were obtained at beamline 8.0.1 at the ALS.
The RIXS photon energy was calibrated by an undulator.

##  III Results and discussion

XAS was first applied to nickel L3,2-edge of as-grown NiPS3 single crystal as
shown in FIG. 3(a). Surprisingly, the spectrum from TEY mode (blue solid line)
and TFY mode (red solid line) exhibited different features. In TEY mode, both
the L3-edge and L2-edge show a single peak feature with a satellite peak
indicated by the blue arrow around 856.6 eV. This is precisely the feature
corresponding to the small $\Delta$ observed in previous literature through
experiments and calculations, indicating a charge-transfer insulator. However,
as mentioned earlier, the TEY signal primarily reflects the surface electronic
structure of a sample. In contrast, the TFY spectra reveal that the satellite
splits into two peaks at 855.8 eV and 857.2 eV. Furthermore, distinguishable
double peak features appear at both L3-edge (854.4 eV) and L2-edge (871.0 eV),
as indicated by the red arrows.

Although many studies indicate that NiPS3 is stable in airLu  _et al._ (2020);
Fang  _et al._ (2021), exposure to air may still cause surface oxidation and
affect its TEY signalFrati  _et al._ (2020). This can be inferred from the
different features exhibited by the TEY and TFY signals in FIG. 3(a). To
chracterize the surface oxidation, we also applied XAS in the oxygen K-edge
region for the same sample used in FIG. 3(a) as presented in FIG. 4. As we
previously inferred, the surface-sensitive TEY signal in the oxygen range
exhibited very distinct signals, with characteristic peaks appearing in both
the X-Ray absorption near edge structure (XANES) region (532 eV and 537 eV)
and extended X-ray absorption fine structure (EXAFS) region (558 eV). This
indicates that the oxygen on the surface of NiPS3 is not merely adsorbed free
oxygen from the air, but has chemically bonded with the Ni cations. The
spectrum in TFY mode, on the other hand, shows a very weak signal-to-noise
ratio (SNR) in oxygen range compared to the spectrum in TEY mode. The
appearance of an oxygen peak in the bulk-sensitive TFY mode does not mean that
the entire NiPS3 sample is oxidized. Instead, it is because the TFY signal
detection range covers the entire region to a depth of about 100 nanometers,
including the few nanometers of the oxidized surface. It is precisely because
the SNR of the TFY signal is significantly lower than that of the TEY signal
that it proves the oxidation is only present on the surface of the NiPS3
sample (occupying only a small portion of the TFY detection depth). This is
reasonable, as the bulk NiPS3 should not retain oxygen and should be air-
stable.

Further investigation into the structure of the O K edge XAS has found that it
is likely that nanoscaled NiO appear on the surface of NiPS3, evidenced by the
similarity to the O K edge XAS from NiO nanowires as shown by Wu et al.Wu  _et
al._ (2005); these nanoscaled NiO exhibit very different features in the XAS O
K-edge region compared to bulk NiO. By comparing with their XAS results, we
find that the characteristic peaks in the TEY mode in FIG. 4 are perfectly
consistent with those of NiO nanowires in both the XANES and EXAFS regions.
The TEY probe depth shows that the nanoscaled NiO once again demonstrates that
oxidation occurs only on the surface of the NiPS3 sample.

To eliminate the impact of surface oxidation on the experimental results, the
most straightforward method is to directly remove the outermost few layers. As
a vdW material, NiPS3 can be easily exfoliated using Scotch tape. The XAS
spectrum was remeasured for the Ni L3,2-edge of exfoliated NiPS3 sample [FIG.
3(b)]. After exfoliation, we observed the following: (1) The TEY and TFY
spectra exhibited excellent consistency, as indicated by the blue and red
arrows, respectively; compared to the untreated sample, (2) the TEY signal
showed significant changes, with the most notable being that both the Ni L2
peak and L3 peak split into a double peak structure, with more distinct
features appearing in the satellite peak next to the L3 peak; (3) the TFY
signal did not show obvious changes. These observations indicate that: (1)
Exfoliation successfully removed the surface oxidation layers, making the TEY
signal after exfoliation more likely to reflect the true sample signal; (2)
The presence of the surface oxidation layers have a significant impact on the
TEY signal; (3) The oxidation layers have a minimal impact on the TFY signal,
allowing the TFY signal to remain reliable throughout the entire study.

To determine the $\Delta$ of NiPS3, we performed theoretical calculations
using the charge-transfer multiplet model. The comparison between the
experimental data for the exfoliated sample and the theoretical calculation is
presented in FIG. 5. From the calculated results, it can be observed that with
the increase in $\Delta$, the most noticeable change is that the Ni L3 and L2
absorption edges transition from a single peak structure to a double peak
structure, accompanied by a shift in the peak positions and changes in the
satellite peaks. This trend is consistent with previous calculationsKim  _et
al._ (2018); Kang  _et al._ (2020); Yan  _et al._ (2021). When determining the
$\Delta$ of NiPS3 by comparing the features with calculations, however, the
main focus and point of contention has been around the L3 edge. By contrast,
the most noticeable feature here, which differs from previous studies, is that
the L2 peak also splits into a double peak structure. The best match to the
experimental results is the calculated spectra with $\Delta$=3 eV, yet the
spectra with $\Delta$=2.5 eV and $\Delta$=3.5 eV also match some features of
the experimental results very well. Therefore, we have obtained a relatively
large $\Delta$ for NiPS3, suggesting it is highly likely that NiPS3 falls
within the regime of a Mott-Hubbard insulator.

Thus far, we have determined the $\Delta$ of NiPS3 with XAS and theoretical
calculation. To further confirm that such a $\Delta$ categorizes NiPS3 as a
Mott-Hubbard insulator, we employed mapping of RIXS as shown in FIG. 6. It can
be observed that parallel to the elastic peak (yellow solid line), two
resonant X-ray Raman features (red dashed line) were found with energy-loss of
1.2 eV and 1.8 eV. Based on the scale of energy-lossAment  _et al._ (2011) and
previous optical spectra resultsKim  _et al._ (2018), both resonant X-ray
Raman features were assigned to $dd$ excitations. Therefore, we found that the
$dd$ excitations are dominant, with the charge-transfer features being too
weak to be observed. This indicates that standard Hubbard model applies to
NiPS3, with transitions occurring only among $d$-electrons themselves, rather
than the $p-d$ model as in the case of charge-transfer insulator. Moreover,
these energy-loss features match the previous RIXS resultHe  _et al._ (2024),
except that we did not find the ultrasharp PL peak due to the limitation of
resolving power. With the aid of calculations, they determined the expectation
values describing the NiPS3 wavefunction and revealed that NiPS3 has a
dominant Hund’s character with a ground state $d^{8}$, instead of
$d^{9}\underline{L}$ as in the Zhang-Rice scenario. This further proves that
NiPS3 belongs to a Mott-Hubbard insulator rather than a charge-transfer
insulator.

##  IV Conclusion

In this study, we used XAS and RIXS to investigate the electronic structure of
NiPS3. By comparing experimental data from as-grown and exfoliated samples
with theoretical calculations, we found that NiPS3 has a relatively large
$\Delta$ (about 3 eV), indicating it is a Mott-Hubbard insulator.
Additionally, we observed surface oxidation on as-grown samples, which may
have contributed to the previous debates over the XAS results and was
mitigated by exfoliation. RIXS data showed dominant $dd$ excitations with weak
charge-transfer features, further supporting this classification. These
findings resolve previous controversies, contribute to the broader knowledge
of NiPS3, and emphasize the importance of controlling surface adsorption in
studies of the electronic structure of vdW materials.

##  V Acknowledgement

This research used resources of the Advanced Light Source, which is a
Department of Energy (DOE) Office of Science User Facility under contract no.
DE-AC02-05CH11231. Work done by Q.T. and X.L. was supported by National
Science Foundation (NSF) under Grant No. 2216008 and No. 1945364, and the U.S.
DOE, Office of Science, Basic Energy Science (BES) under Award Number DE-
SC0021064. Q.T. also acknowledges the support of the Laursen Fellowship at
Boston University.

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##  VI Figures

Figure 1: The crystal structure of NiPS3 seen along the $c$ axis (top) and $a$
axis (bottom). Generated by VESTAKlingen  _et al._ (1973). Figure 2:
Simplified electronic energy levels for NiPS3 assuming it is a charge-transfer
insulator (left) and assuming it is a Mott-Hubbard insulator (right)Sahiner
_et al._ (1996). Figure 3: Nickel L3,2-edge XAS spectra with TEY mode (blue)
and TFY mode (red) for (a) an untreated NiPS3 sample and (b) a NiPS3 sample
after exfoliation of the surface layers in an air-isolated environment. Figure
4: Surface oxidation check: O K-edge XAS spectra with TEY mode (blue) and TFY
mode (red) for the untreated NiPS3 sample used in FIG. 3(a). Figure 5:
Experimental (Exp.) nickel L3,2-edge XAS spectra and calculated spectra from
the charge-transfer multiplet model by Crispy softwareRetegan (2019). The top
of the figure shows the experimental XAS data for the exfoliated NiPS3 sample
with TEY signal (blue) and TFY signal (red). The subsequent spectra from top
to bottom represent the calculated spectra corresponding to $\Delta$
decreasing from 5.0 eV to -1.0 eV. Figure 6: Nickel L3-edge mapping of RIXS of
NiPS3. Yellow solid line: elastic peak. Red dashed line: energy lost features.