# Topological Quasi-2D Semimetal Co3Sn2S2: Insights To Electronic Structure
From NEXAFS and Resonant Photoelectron Spectroscopy

Mouhui Yan  [  Yichen Jin  [  Xiaofei Hou  [  Yanfeng Guo  [  Arshak Tsaturyan
[  Anna Makarova  [  Dmitry Smirnov  [  Yuriy Dedkov  [
<EMAIL_ADDRESS>Elena Voloshina  [<EMAIL_ADDRESS>
###### Abstract

The electronic structure of the natural topological semimetal Co3Sn2S2
crystals was studied using near-edge x-ray absorption spectroscopy (NEXAFS)
and resonant photoelectron spectroscopy (ResPES). Although, the significant
increase of the Co $3d$ valence band emission is observed at the Co $2p$
absorption edge in the ResPES experiments, the spectral weight at these photon
energies is dominated by the normal Auger contribution. This observation
indicates the delocalised character of photoexcited Co $3d$ electrons and is
supported by the first-principle calculations. Our results on the
investigations of the element- and orbital-specific electronic states near the
Fermi level of Co3Sn2S2 are of importance for the comprehensive description of
the electronic structure of this materials, which is significant for future
applications of this material in different areas of science and technology,
including catalysis and water splitting applications.

SHU] Department of Physics, Shanghai University, 200444 Shanghai, China SHU]
Department of Physics, Shanghai University, 200444 Shanghai, China STech]
School of Physical Science and Technology, ShanghaiTech University, 201210
Shanghai, China STech] School of Physical Science and Technology, ShanghaiTech
University, 201210 Shanghai, China SFedU] Institute of Physical and Organic
Chemistry, Southern Federal University,
344090 Rostov on Don, Russia FU] Institut für Chemie und Biochemie, Freie
Universität Berlin, Arnimallee 22,
14195 Berlin, Germany TUD] Institut für Festkörper- und Materialphysik,
Technische Universität Dresden,
01069 Dresden, Germany E3] Centre of Excellence ENSEMBLE3 Sp. z o. o., ul.
Wolczynska 133, 01-919 Warsaw, Poland [SHU] Department of Physics, Shanghai
University, 200444 Shanghai, China E3] Centre of Excellence ENSEMBLE3 Sp. z o.
o., ul. Wolczynska 133, 01-919 Warsaw, Poland [FU] Institut für Chemie und
Biochemie, Freie Universität Berlin, Arnimallee 22,
14195 Berlin, Germany [SHU] Department of Physics, Shanghai University, 200444
Shanghai, China

During the past decade in condensed matter physics, chemistry and materials
science a huge interest arose to the new topological phases of solids and
their connection to new exciting phenomena 1, 2, 3, 4. Here, the natural
topological semimetal Co3Sn2S2, which can be considered as a quasi-two-
dimensional material, attracts a lot of attention in the last years due to its
interesting crystallographic structure and electronic properties 5, 6, 7.
Initially, this material was identified as a ferromagnetic (FM) material with
a Curie temperature ($T_{C}$) of $177$ K 8, followed by its theoretical
description as a half-metallic ferromagnet (HMF) 9, 10, 11. Here, during the
transition from the paramagnetic (PM) to the HMF state the band gap around the
Fermi level ($E_{F}$) is formed for the spin-down channel, leaving the spin-up
channel metallic. Following the systematic description of HMF materials,
Co3Sn2S2 was described as Type IA HMF 12, 13.

Experimental studies of bulk Co3Sn2S2 confirmed its ferromagnetic state below
$T_{C}$ and the measured value of magnetic moment
$0.93\,\mu_{B}/\mathrm{f.u.}$ is very close to the theoretical value of
$1\,\mu_{B}/\mathrm{f.u.}$ obtained within the framework of the local spin-
density approximation (LSDA) 9, 10, 11. This material was experimentally found
to be strong ferromagnet with an $\langle 001\rangle$ easy magnetisation axis
and the signature of the HMF state with an energy gap of $\approx 300$ meV
around $E_{F}$ was measured in spin-resolved scanning tunnelling microscopy
(STM) experiments 14. Furthermore, the recent interest to the new topological
phenomena in condensed matter and the extended analysis of the electronic
structure of Co3Sn2S2 identified this material as the first magnetic Weyl
semimetal with broken time-reversal symmetry demonstrating giant anomalous
Hall effect and topologically protected surface states 5, 6, 7, 15, 16. First
photoelectron spectroscopy experiments on Co3Sn2S2, which are more than a
decade old 9, 10, were devoted to the identification of chemical state of
elements in poly- and single-crystalline samples and comparison to the
available theoretical data obtained using LSDA, and good agreement between
them was found. These works also indicate the existence of surface-derived
contributions in x-ray photoelectron spectra (XPS) of core levels. Further
detailed angle-resolved photoelectron spectroscopy (ARPES) and STM studies
revealed the existence of the topological surface states and the respective
surface Fermi arcs states around the $\overline{\mathrm{K}}$ point in the
electronic structure of Co3Sn2S2(001) with different atomic terminations 16,
6. Also the nontrivial surface states theoretically identified for PM and FM
states at $0.23$ eV above $E_{F}$ for all surface terminations of
Co3Sn2S2(001) were shown to be effective for the water splitting processes 15.

Despite the recent progress in the studies of this new interesting material,
the full description of its electronic structure using electron spectroscopy
methods is not complete, missing the detailed investigations of the element-
and orbital-specific electronic states near $E_{F}$. Here, we present the
systematic studies of the electronic structure of bulk Co3Sn2S2 using near-
edge x-ray absorption spectroscopy (NEXAFS) and resonant photoelectron
spectroscopy (ResPES). These experimental methods being element specific allow
to discriminate between atomic partial contributions in the valence band
states around $E_{F}$. Our results demonstrate that the spectral weight in
ResPES measurements at the Co $2p$ absorption edge is dominated by the strong
Auger contribution. These observations indicate the delocalised character of
the valence band states above $E_{F}$. All photoelectron spectroscopy results
are accompanied by the detailed density functional theory (DFT) calculations
supporting experimental findings.

The crystal structure of bulk Co3Sn2S2 has a rhombohedral symmetry of the
$R\overline{3}m$ space group (shandite structure isostructural to the mineral
Ni3Pb2S2, see Fig. 1(a)). This structure can be considered and described using
a hexagonal symmetry (marked in the figure) with experimentally obtained
lattice parameters $a=b=5.3680$ Å and $c=13.1830$ Å, which are very close to
the values obtained within the general gradient approximation (GGA) (5.3785 Å
and 13.1594 Å, respectively) (see Supporting Information for the corresponding
data files for the experimentally derived and theoretically optimised
crystallographic structures). Here, the inclusion of the van der Waals
correction in the DFT calculations leads to the slightly reduced values of
lattice constants (5.3125 Å and 13.0009 Å, respectively) and to decreasing the
magnetic moment of Co atoms ($0.347\,\mu_{B}$ for GGA+D3 vs. $0.353\,\mu_{B}$
for GGA), however, does not significantly influencing the band structure of
Co3Sn2S2. After sample was cleaved and annealed in vacuum the clear hexagonal
LEED spots (Fig. 1(b)) characteristic for the 3-fold symmetry of the
Co3Sn2S2(001) surface were obtained, indicating the correctness of the
description of this material in a hexagonal structure as well as the high
quality of the studied material.

Bulk Co3Sn2S2 crystals in our study were synthesised using Sn-flux method from
the stoichiometric amounts of elements and obtained several-mm2 samples were
characterised using different bulk- and surface-sensitive techniques. Figs. S1
and S2 summarises the results of structural, magnetic and transport
measurements. These results confirm the high quality of the studied samples
and strong ferromagnetic state of Co3Sn2S2 with Curie temperature of
$T_{C}=172\pm 1$ K, similar to previous results 11, 5, 14. The GGA calculated
total and atom-projected density of states (DOS) for the FM and PM states of
Co3Sn2S2 are shown in Fig. 1(c,d), respectively and these results are in very
good agreement with previous works 9, 11, 14 (see also Fig. S3 for calculated
band structures). The valence band states are spread down to
$E-E_{F}\approx-10\,\mathrm{eV}$. As previously reported, in the FM state this
material is HMF with only spin-up electrons at $E_{F}$ and the band gap of
$0.340$ eV for spin-down electrons. In the PM state the density of states at
$E_{F}$ is significantly increased. At low binding energies (close to $E_{F}$)
they are dominated by the Co $3d$ states weakly hybridised with Sn and S
states. Below $E-E_{F}\approx-3.5\,\mathrm{eV}$ the Sn $5s$ and S $3p$ start
to contribute to DOS where they effectively hybridise with Co $3d$ states.

Fig. 2 shows the representative XPS and NEXAFS spectra for Co3Sn2S2 crystal.
XPS lines of (a) Co $2p$, (b) Sn $3d$, and (c) S $2p$ are in very good
agreement with previously published results 10, 15 and confirm the respective
chemical states of elements (Co0)3(Sn2+)2(S2-)2 (see Fig. S4 for the survey
spectra measured after annealing of the crystal in vacuum). This is supported
by the energy positions of the respective core-level lines:
$E_{B}(\mathrm{Co}\,2p_{3/2})=777.9$ eV corresponds to the metallic state of
Co0 (additional lines at $780.5$ eV and $786.2$ eV can be attributed to the
surface oxidation and satellite structure, respectively, appearing due to the
sample treatment), $E_{B}(\mathrm{Sn}\,3d_{5/2})=486.1$ eV and
$E_{B}(\mathrm{S}\,2p_{3/2})=161.7$ eV. Both S $2p$ and Sn $3d$ spectra
demonstrate the existence of emission at lower binding energies, that can be
attributed to the surface-derived contributions and can be assigned to the
simultaneous existence of different surface terminations for the cleaved
Co3Sn2S2(001) surface, which were observed experimentally 15, 6.

NEXAFS spectrum measured at the Co $L_{2,3}$ absorption edge (Fig. 2(d))
corresponds to the metallic state of Co0 with the position of the main peak at
$779.8$ eV. Additionally, two distinct shoulders at $780.6$ eV and $782.5$ eV
on the higher energy side of the main line can be seen. As was pointed in Ref.
15 the Co-atoms, which form the Kagome lattice, can be considered as placed in
the strongly distorted S2-Co-Sn4 face-shared octahedra (see Fig. S5). Due to
the metallic state of Co0, metallic character of Co3Sn2S2 and the relatively
large distances between Co and chalcogen atoms, the splitting between $t_{2g}$
and $e_{g}$ is small favouring filling the $d$-states according to the Hund’s
rule and giving high-spin state for Co-atoms (although magnetic moments are
strongly suppressed and screened by valence electrons). This is also confirmed
by our DFT calculations. The existing electric field of the strongly distorted
octahedra consisting of Sn and S can lead to the splitting of unoccupied Co
states resulting the observed Co $L_{2,3}$ NEXAFS spectra. These shoulders
also correlate with the positions of broad features in the unoccupied Co-
projected $3d$ DOS shown in Fig. 1(c,d). The satellite structure observed at
$\approx 786.8$ eV can be assigned to changes in the hybridisation of the $sp$
orbitals between the initial and final states or a mixed ground state effect.

In case of the Sn $M_{4,5}$ NEXAFS spectra (Fig. 2(e) and Fig. S6) the
electron transitions occur from the spin-orbit split $3d_{3/2,5/2}$ core
levels onto the unoccupied $p$ and $f$ shells (according to the selection
rules $\Delta l=\pm 1$) 17, 18, 19. The main $M_{5}$ peak ($487.7$ eV) is
split and additionally two intensity shoulders can be observed at the lower
and higher energies at $\approx 486.1$ eV and $\approx 488.7$ eV,
respectively. In Co3Sn2S2 bulk crystal two types of Sn atoms are identified
(Sn1 are located in the same plane as Co atoms and Sn2 are placed between the
planes formed by S atoms). For both types of atoms their valence band orbitals
effectively hybridise with the orbitals of S and Co atoms as can be deduced
from the atom projected DOS in Fig. 1(c,d). The formed hybrid bands can be
seen just above $E_{F}$, at $E-F_{F}\approx 2$ eV and $E-F_{F}\approx 3.5$ eV.
These bands with the significant Sn-atoms projected DOS can be assigned to the
observed features of the Sn $M_{4,5}$ NEXAFS spectra. At the same time the Sn-
atom projected DOS at $E-F_{F}\approx 2$ eV is split that can explain the
observed small splitting of the Sn $M_{5}$ main line. The description and
interpretation of the S $L_{2,3}$ NEXAFS spectra (Fig. 2(f)) is not certain as
the spin-orbit splitting of the S $2p$ level is small ($\approx 1.1$ eV)
leading to the overlapping of the respective absorption transitions. However,
the main absorption band peaked at $158.9$ eV and the respective low- and
high-energy shoulders can be assigned to the hybrid bands formed by the
respective valence orbitals (Fig. 1(c,d)).

Figure 3 summarises the result of the ResPES studies of Co3Sn2S2 performed at
the Co $L_{2,3}$ absorption edge: (a) Co $L_{2,3}$ spectrum with marked photon
energies used to acquire PES spectra presented in (b) and (c), where in the
later panel all spectra were normalised to the maximum intensity for every
line in order to emphasise the respective spectral features. A huge increase
in the photoemission intensity by factor of $\approx 35$ is observed at the Co
$L_{3}$ absorption edge (compare spectra 1 and 6). This enhancement of the Co
$3d$ intensity, which photon energy dependence in this case is described by
the Fano profile, is expected by the resonant photoelectron process described
by the interference of two photoemission channels: (i) a direct photoemission
$2p^{6}3d^{n}+h\nu\rightarrow 2p^{6}3d^{n-1}+e$ and (ii) a photoabsorption
process followed by a participator Coster-Kronig decay
$2p^{6}3d^{n}+h\nu\rightarrow 2p^{5}3d^{n+1}\rightarrow 2p^{6}3d^{n-1}+e$,
where the initial and final states are identical 20. At the same time the
intensity enhancement can also occur due to the normal Auger decay described
by $2p^{6}3d^{n}\rightarrow 2p^{5}3d^{n+1}\rightarrow 2p^{6}3d^{n-2}+e$. Here,
the resonance peak stays at the same binding energy, while the normal Auger
line linearly shifts to higher binding energies with increasing the photon
energy. The same description of the resonant processes is also valid for the
spin-orbit counterpart Co $L_{2}$.

PES spectra of bulk Co3Sn2S2 crystals measured with pre- and post-absorption-
edge photon energies (spectrum 1 – $h\nu=770$ eV and spectrum 20 – $h\nu=810$
eV, respectively) reflect the total DOS dominated by the Co $3d$ states (see
Fig. 1(c,d)) and these results are in very good agreement with previous
results obtained for polycrystalline samples 9. At photon energies
corresponding to the Co $L_{3}$ absorption edge (spectra $4-10$) a large
increase of intensity is observed. The intensity maximum of the enhanced
features linearly shifts to large binding energies as photon energy is
increased. This behaviour indicates the normal Auger decay character of these
emission lines (this consideration is valid for both spin-orbit split
absorption edges). At the same time we can indicate the increase of the
photoemission intensity for spectral features with no shift of the binding
energy (marked by vertical arrows in Fig. 3(b,c)). However, the intensity of
the first feature at $E-E_{F}\approx=-0.75$ eV is increased by factor of
$6.5$, compared to factor $35$ for the increase of intensity associated with
the normal Auger decay.

In ResPES, the resonance excitations with constant binding energy are observed
when the intermediate electronic state (i. e., the final state for the
photoabsorption) in the resonant process is relatively localised, that leads
to the direct recombination of photoexcited electron. Opposite to this, for
the case of normal Auger decay, if the photoexcited electron on the $3d$
orbital is delocalised, then it will relax to the other orbital before
returning to the inner $2p$ shell 21, 22. Therefore the observation of the
strong intensity for the normal Auger decay compared to the resonant behaviour
in the ResPES spectra for Co3Sn2S2 can be considered as a sign of the
delocalisation of photoexcited electrons on the Co $3d$ unoccupied states.
Considering the atom-projected band structure and DOS of Co3Sn2S2 (Fig. 1(c,d)
and Fig. S2) one can identify two types of valence band states above $E_{F}$.
For the PM state the flat bands in the range of $0-1$ eV give two sharp peaks
in DOS and can be responsible for the resonating behaviour of valence band
features marked by arrows in Fig. 3. At energies above $1$ eV the dispersive
Co $3d$ bands are present and the photoexcited electrons (Co $2p\rightarrow
3d$) exhibit strong itinerancy and do not remain at the same atomic site. As
shown above, such behaviour leads to the strong enhancement of the normal
Auger emission. These observations clearly explain the delocalisation of
electrons in Co3Sn2S2 and reduction the effective magnetic moments of Co
atoms.

In summary, we performed systematic studies of the electronic properties of
natural topological quasi-2D semimetal Co3Sn2S2 using electron spectroscopy
methods XPS, NEXAFS and ResPES. Our spectroscopic studies reveal that
octahedrally coordinated, by S and Sn, Co atoms are in the high-spin state.
However, the strong delocalisation of the Co $3d$ states and the itinerant
character of valence electrons lead to the strong reduction of magnetic moment
of Co atoms to $0.3\,\mu_{B}$. This description is strongly supported by the
ResPES measurements at the Co $L_{2,3}$ absorption edge. The spectral weight
of ResPES spectra is dominated by the normal Auger decay indicating the
delocalised nature of the photoexcited Co $3d$ electrons. The present results
give the presentation of the atom- and orbital-specific electronic states near
$E_{F}$ and are of importance for the complete description of the electronic
structure of Co3Sn2S2 and of the localisation character of electronic states
in this material. Such information is important for the future using of this
material in different areas of science and technology, including catalysis and
water splitting applications.

Y. D. and E. V. thank the “ENSEMBLE3 - Centre of Excellence for nanophotonics,
advanced materials and novel crystal growth-based technologies” project (GA
No. MAB/2020/14) carried out within the International Research Agendas
programme of the Foundation for Polish Science co-financed by the European
Union under the European Regional Development Fund and the European Union’s
Horizon 2020 research and innovation programme Teaming for Excellence (GA. No.
857543) for support of this work. A. T. acknowledges the Ministry of Science
and Higher Education of the Russian Federation No. 0852-2020-0019 (State
assignment in the field of scientific activity, Southern Federal University,
2020 Project No. BAZ0110/20-1-03EH). A. M. acknowledges the BMBF (grant No.
05K19KER). D. S. acknowledges the BMBF (grant No. 0519ODR). We thank HZB for
the allocation of synchrotron radiation beamtime and for support within the
bilateral Russian-German Laboratory program. The HPC Service of ZEDAT, Freie
Universität Berlin, is acknowledged for computing time.

The following files are available free of charge

  * •

Additional theoretical and experimental data can be downloaded via link:
https://pubs.acs.org/doi/10.1021/acs.jpclett.1c02790

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Figure 1: (a) Hexagonal crystal structure of Co3Sn2S2 with the rhombohedral
primitive cell highlighted by grey colour. (b) LEED image obtained from the
Co3Sn2S2(001) surface. (c) and (d) Total and atom-projected density of states
calculated for the FM and PM states of bulk Co3Sn2S2, respectively.

Figure 2: XPS spectra of Co3Sn2S2 collected at $h\nu=1000$ eV: (a) Co $2p$,
(b) Sn $3d$, and (c) S $2p$. In case of the S $2p$ spectra we used spin-orbit
split lines presented by red and green lines for the bulk- and surface-derived
emission, respectively. NEXAFS spectra of Co3Sn2S2 collected in the TEY mode:
(d) Co $L_{2,3}$, (e) Sn $M_{4,5}$, and (f) S $L_{2,3}$.

Figure 3: Results of ResPES experiments for Co3Sn2S2: (a) the reference Co
$L_{2,3}$ NEXAFS spectrum and (b,c) a series of photoemission spectra taken at
the particular photon energies marked by the corresponding vertical lines in
panel (a). Spectra in panel (c) are normalised by the maximum intensity for
every emission line. All ResPES spectra are shifted in the vertical direction
for clarity.