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Adsorption of water on the pristine and defective semiconducting 2D CrPX3 monolayers (X: S, Se)

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Abstract

The effect of vacancy and water adsorption on the electronic structure of semiconducting 2D trichalcogenide material CrPX3 (X: S, Se) is studied using state-of-the-art density functional theory (DFT) approach. It is found that chalcogen vacancies play a minor role on the electronic structure of CrPX3 in the vicinity of the Fermi level leading to the slightly reduced band gap for these materials, however, inducing strongly localised defect states which are placed in the energy gap formed by the valence band states. Our DFT calculations show that the interaction of water molecules with CrPX3, pristine and defective, can be described as physisorption and the adsorption energy for H2O is insensitive to the difference between pristine and chalcogen-defective surface of trichalcogenide material. These results are the first steps for the theoretical description of the ambient molecules interaction with 2D semiconducting CrPX3 material, that is important for its future experimental studies and possible applications.
Adsorption of water on the pristine and defective
semiconducting 2D CrPX3monolayers (X: S, Se)
Sifan Xu1, Zhicheng Wu1, Yuriy Dedkov1,2,, and
Elena Voloshina1,2,
1Department of Physics, Shanghai University, 99 Shangda Road, 200444 Shanghai,
China
2Institut f¨ur Chemie und Biochemie, Freie Universit¨at Berlin, Arnimallee 22, 14195
Berlin, Germany
Abstract.
The effect of vacancy and water adsorption on the electronic structure of
semiconducting 2D trichalcogenide material CrPX3(X: S, Se) is studied using state-of-
the-art density functional theory (DFT) approach. It is found that chalcogen vacancies
play a minor role on the electronic structure of CrPX3in the vicinity of the Fermi level
leading to the slightly reduced band gap for these materials, however, inducing strongly
localised defect states which are placed in the energy gap formed by the valence band
states. Our DFT calculations show that the interaction of water molecules with CrPX3,
pristine and defective, can be described as physisorption and the adsorption energy for
H2O is insensitive to the difference between pristine and chalcogen-defective surface of
trichalcogenide material. These results are the first steps for the theoretical description
of the ambient molecules interaction with 2D semiconducting CrPX3material, that is
important for its future experimental studies and possible applications.
1. Introduction
The class of the pure 2D and quasi-2D materials is rapidly developing [1, 2, 3, 4] regularly
bringing new exciting phenomena, like observation of the 2D magnetic order [5, 6, 7],
superconductivity [8, 9], and exciting optical properties [10, 11]. Among these materials,
quasi-2D transition metal trichalcogenides (MPX3, M: transition metal, X: S, Se)
recently attracted increased attention because of their possible applications in many
areas. It was proposed that they can be used as low-dimensional spin-polarised
conductors which spin character can be tuned by the applied bias [12], in photocatalysis
for the efficient water splitting and hydrogen production [13, 14, 15], as efficient materials
for the Li storage [16], and, for example, the tuning of the vacancy state can lead to the
low-dimensional ferromagnetic state [17].
From the crystallographic point of view, these materials are similar to, e. g., MoS2,
where one third of the metal atoms is substituted by P–P dimers and in this case the
metal layer in MPX3is encapsulated by both chalcogens and phosphorus atoms (Fig. 1).
arXiv:2112.12712v1 [cond-mat.mtrl-sci] 23 Dec 2021
2
Diversity in transition metals and two different chalcogens can lead to a wide variation
in the electronic and magnetic properties of these materials. Also, the simultaneous
presence of sulphur and phosphorus in these compounds can cause a synergetic effect
on the electronic structure of the central metal atoms. Moreover, due to the layered
structure of MPX3, they can be easily prepared as two-dimensional nanostructures
having a large surface area with large number of active sites. Surprisingly, the electronic
structure of these materials is mainly addressed only from the theory side and the
experimental studies are very rear and sporadically appear in the literature [18],
moreover not always correctly interpreting the obtained experimental data [19, 20].
Also, the influence of vacancies as well as ambient adsorbates on the magnetic and
electronic properties of MPX3are not studied at all.
Here, we present state-of-the-art density functional theory (DFT) studies of Cr-
based phosphorus trichalcogenides (CrPS3and CrPSe3). These materials were recently
synthesised and studied with respect to their electrochemical sensing and energy
applications [20]. In our work we address many aspects of these materials, like stability,
chalcogen defects formation and adsorption of water molecules on pristine and defective
2D CrPX3layer. We found that in all cases, the electronic structure around the top of the
valence band of CrPX3remains insensitive and main modifications are connected with
the valence states redistributions at large binding energies. These results demonstrate
that CrPX3are robust to the external factors, like chalcogen defects formation and
ambient molecules adsorption, that can be utilised in future applications of these
materials as, e. g., protective coatings or inert barriers for molecules.
2. Computational details
Spin-polarised DFT calculations based on plane-wave basis sets of 500eV cutoff energy
were performed with the Vienna ab initio simulation package (VASP). [21, 22, 23] The
Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional [24] was employed. The
electron-ion interaction was described within the projector augmented wave (PAW)
method [25] with Cr (3p, 3d, 4s), P (3s, 3p), S (3s, 3p) and Se (4s, 4p) states treated
as valence states. The Brillouin-zone integration was performed on Γ-centred symmetry
reduced Monkhorst-Pack meshes using a Gaussian smearing with σ= 0.05 eV, except
for the calculation of total energies. For these calculations, the tetrahedron method with
Bl¨ochl corrections [26] was employed. The 12×12×4 and 24×24×1k-meshes were used
for the studies of bulk and monolayer CrPX3, respectively, and the 12 ×12 ×1k-mesh
was used for the (2 ×2) supercells consisting of 4-fold unit monolayers. The DFT+ U
scheme [27, 28] was adopted for the treatment of Cr 3dorbitals, with the parameter
Ueff =UJequal to 4 eV. Dispersion interactions were considered adding a 1/r6atom-
atom term as parameterised by Grimme (“D2” parameterisation) [29]. This approach
yields structural parameters, which are in good agreement with available experimental
data [20].
When modelling CrPX3monolayers, the lattice constant in the lateral plane was
3
set according to the optimised lattice constant of bulk CrPX3. A vacuum gap was set to
approximately 26 ˚
A. During structure optimisation, the convergence criteria for energy
and force were set equal to 105eV and 102eV/˚
A, respectively.
The cleavage energy was calculated as
Ecl = (Ed0→∞ E0)/A, (1)
where d0is the van der Waals gap of bulk crystal and Ais the in-plane area.
To extract the exchange interaction parameters between Cr ions spins, the
Heisenberg Hamiltonian was considered
H=X
hi,ji
J1~
Si·~
Sj+X
hhi,jii
J2~
Si·~
Sj+X
hhhi,jiii
J3~
Si·~
Sj,(2)
where ~
Siis the net spin magnetic moment of the Cr ions at site i, three different distance
magnetic coupling parameters were estimated, considering one central Cr ions interacted
with three nearest neighbouring (NN, J1), six next-nearest neighbouring (2NN, J2), and
three third-nearest neighbouring (3NN, J3) Cr ions, respectively. Here, the long-range
magnetic exchange parameters (J) can be obtained as [30]
J1=(EsAFM EzAFM)+(EnAFM EFM)
16S2,
J2=(EzAFM +EsAFM)(EnAFM +EFM )
32S2,(3)
J3=3 (EzAFM EsAFM)+(EnAFM +EFM)
48S2,
where Sis the calculated magnetic moment of the Cr ion and EFM,EnAFM,EzAFM ,EsAFM
are the total energies in ferromagnetic, N´eel antiferromagnetic, zigzag antiferromagnetic,
and stripy antiferromagnetic configurations, respectively.
To estimate TNtemperature, Monte Carlo simulations were performed within the
Metropolis algorithm with periodic boundary conditions [31]. The three exchange
parameters J1,J2and J3were used in a 64 ×64 superlattice containing a large enough
amount of magnetic sites to accurately evaluate the value. Upon the heat capacity
Cv(T) = (hE2i − hEi2)/kBT2reaching the equilibrium state at a given temperature, the
TNvalue can be extracted from the peak of the specific heat profile.
The electrically neutral vacancies were created by removing one or two X atoms
from the (2 ×2) supercells. Thereby, the distance between repeated vacancies in the
nearest-neighbour cells is larger than 10 ˚
A. The defect formation energy is defined as
follows
Edef =1
n[E(CrPX3n) + n µXE(CrPX3)] ,(4)
where nis a number of defects, E(CrPX3n) and E(CrPX3) are the energies of the 2D
CrPX3with and without vacancy, respectively, µXis the chemical potential of X atom
(µS=4.1279 eV and µSe =3.4895 eV).
To study the adsorption of a single molecule, a (2 ×2) supercell was used with one
water molecule added. Adsorption energies were calculated as
Eads =E(A/CrPX3)[E(A) + E(CrPX3)] ,(5)
4
where E(CrPX3) and E(A) are he energies of the isolated 2D CrPX3and an adsorbate,
and E(A/CrPX3) is the energy of their interacting assembly.
3. Results and Discussion
3.1. 3D CrPX3(X = S, Se)
3D bulk MPX3crystals usually adopt either an AAA stacking in C2/m space group space
or ABC stacking in R¯
3 space group. Both of them can be represented in hexagonal unit
cells (Fig. 1 a). Then every unit cell contains three MPX3single layers which have D3d
symmetry (see Fig. 1 b,c), which are stacked in a different way. Each single-layer are
held together by van der Waals forces. The lattice parameters of hexagonal 3D CrPX3
were fully relaxed in nonmagnetic (NM), ferromagnetic (FM) and N´eel antiferromagnetic
(nAFM) states and they are listed in Table 1 with the respective total energies. Thus,
both CrPX3(X = S, Se) prefer the C2/m symmetry, that is in agreement with available
experimental data [32]. For both CrPS3and CrPSe3, the energetically most favourable
structure corresponds to the nAFM configuration (Tab. 1). The band structure and
density of states (DOS) calculated for the ground-state structures of 3D CrPS3and
CrPSe3are shown in Figure 2 (a) and (b), respectively. From these results one can see,
that the both systems under study are indirect band gaps semiconductors. The band
gaps obtained by the PBE+Umethod are 1.11 eV for bulk CrPS3and 0.70 eV for bulk
CrPSe3. The upper valence bands (VBs) are mainly formed by S/Se pand equal to
that by the Cr 3dorbitals; the lower conduction bands (CBs) are composed of Cr 3d
states with somewhat contribution from S/Se p. The partial contributions from P p
orbitals are very small in VBs as well as CBs. These results are very different from the
respective data known for MnPX3[33] and NiPX3[18, 34], where the contribution of
metal 3dstates in VBs was insignificant.
It is expected that individual CrPX3layers can be isolated by mechanical
exfoliation. In this regard, the cleavage energy (Ecl) of a layered material is an essential
property that need to be considered. The calculated values, Ecl(CrPS3) = 0.18 J m2
and Ecl(CrPSe3) = 0.23 J m2(Fig. 3, left panel), are smaller than that of a bulk
graphite (0.36 J m2) [35], which is used as an indicator for the feasibility of exfoliation
of materials in experiments. The obtained values are in the same range as recently
published for MnPX3and NiPX3[33, 34].
3.2. 2D CrPX3(X = S, Se) monolayers
Four possible magnetic configurations were investigated to evaluate the ground state
of 2D CrPX3monolayers: The mentioned above FM (Fig. 4 a), and nAFM (Fig. 4 b)
were supplemented by a zig-zag AFM (zAFM, Fig. 4 c) and a stripy AFM (sAFM,
Fig. 4 d). The obtained results are listed in Table 2. It can be seen that the lowest
energy configurations for the 2D CrPX3(X = S, Se) monolayers are the N´eel AFM
states.
5
The 2D CrPS3and CrPSe3in their ground states keep an indirect semiconductor
behaviour (Fig. 2c,d). Due to the quantum confinement effects, the band gaps are
slightly larger than the values calculated for the bulk phases and are 1.52 eV and 1.11 eV
for the 2D CrPS3and CrPSe3, respectively. As for the bulk materials, the bands in the
vicinity of Fermi energy are mostly composed of Cr-dand S/Se-porbitals.
The exchange-coupling parameters (J1,J2,J3) describing the magnetic interactions
between Cr2+ ions were calculated according to eqn. (3) and are listed in Tab. 2.
According to the Goodenough-Kanamori-Anderson (GKA) rules [36, 37], the origin
of the nAFM ground state can be attributed to the competition between the NN AFM
direct Cr–Cr (dd) exchange interactions and the indirect Cr–Se· · · Se–Cr (pd)
superexchange interactions [38]. The calculated Jparameters were used in the Monte-
Carlo simulations of N´eel temperatures of CrPX3monolayers. The estimated TNis
190 K for 2D CrPS3and 119 K for 2D CrPSe3(Fig. 3, right panel). These results
are in very good agreement with the experimental result available for CrPSe3, that is:
TN= 136 K [20].
3.3. Chalcogen defects
Mechanical exfoliation used for monolayers production, can lead to formation of
chalcogen vacancies. Therefore, we consider three different kinds of defects: (i) one
vacancy at X-site, named as VX@1L with a defect concentration about 2.5 % (Fig. 1 c);
(ii) two vacancies at the neighbouring X-sites of the same chalcogen sublayer named
as VX2@1L with a concentration about 5 % (Fig. 1 d); (iii) two vacancies at X-sites of
the different chalcogen sub-layers named as VX2@2L with a concentration about 5 %
(Fig. 1 e). The defect formation energies (Tab. 3) are of the same order that is known
for the other MPX3family members [33, 34] and are rather low in all cases presumably
indicating a feasibility of formation of these kinds of defects in experiments. According
to the defect formation energies, it is found that VX@1L defects are the most favourable
to form, followed by V2X@2L and V2X@1L. Also, we can observed that for the same
defect type, Se vacancy is more likely to occur than S vacancy, which correlates with
the respective electronegativity values. Although the rather low ∆Edef obtained for
all considered cases, we expect that in experimental conditions the formation of single
chalcogen defects is more feasible and from now on we will focus on detailed consideration
of VX@1L.
Removal of chalcogen atom leads to some modifications of the local lattice and
electronic structures. As compared to the pristine CrPX3monolayer, the phosphorous
dimers tend to moving closer to the vacancy. The angle, which P–P dimer forms with
the vertical direction is 2.5and 3.9for X = S and Se, respectively. The dimer is
pulled out from a monolayer. This leads to somewhat increase of the P–S bond length
(by 0.05 ˚
A), while the P–P bond lengths remain basically unchanged.
The electrons left behind upon removal of a chalcogen atom, occupy the easily
available electronic states of a (P2X5) entity. The magnetic moments of the Cr2+-ions
6
nearby the vacancy are coupled antiferromagnetically. Similarly to the data recently
published for MnPX3[33], there are no well-localised defect state generated within the
band gap in the DOS (Fig. 5). As a result, the energy gap width of the defective
monolayers stays almost unchanged regarding the pristine CrPX3:Eg= 1.41 eV
and 1.02 eV for the defective CrPS3and CrPSe3, respectively. At the same time, at
EEF≈ −0.55 eV a new state appears, which is formed by S/Se pand equal to that
by the Cr 3dorbitals.
The estimated TNvalue for the defective trichalcogenide monolayers is reduced to
158 K and 69 K for CrPS3and CrPSe3, respectively (Fig. 3). This effect is generally
expected because the X-vacancy formation leads to the drastic reduction of the J
exchange-coupling parameters (J1=2.76 meV, J2= 0.03 meV, J3= 0.20 meV for
CrPS3x;J1=1.59 meV, J2= 0.02 meV, J3= 0.28 meV for CrPSe3x). At the same
time the strongly localised magnetic moments of Cr2+ ions remain the same.
3.4. Adsorption of H2O
The effect of adsorption of molecular water plays an important role in various
applications and technological processes, since they are present in the environment of
any device. Thus in the next step we investigate how adsorption of H2O affects the
electronic properties of CrPX3monolayers.
Various high-symmetry adsorption sites and adsorption orientations are taken into
account. Considering the pristine monolayers, all adsorption configurations have similar
adsorption energies which range from 133 meV to 153 meV and from 148 meV to
166 meV for 2D CrPS3and 2D CrPSe3, respectively. In the relaxed structures water
stays almost parallel to the substrate and the vertical distance between the molecule
and the CrPX3monolayer is always above 3.2˚
A.
For pristine monolayers, in the most stable adsorption structure (AS1, Fig. 6a), a
water molecule attaches with its oxygen atom to an P atom [d(P-O) = 3.23 ˚
A and
3.32 ˚
A for CrPS3and CrPSe3, respectively] and the H atoms are directed towards
the neighbouring X atoms. In accordance with the weak interaction, the structural
parameters of H2O as well as of the studied monolayer undergo insignificant changes.
As follows from the electron density redistribution plot (Fig. 6a), upon adsorption the
main charge rearrangement takes place between O and P atoms. Charge accumulation
in the p-orbital of P on the side of the adsorbate indicates that it is the main orbital
participating in the bonding. This charge accumulation is accompanied with a depletion
at the hydrogen positions. These observation are in line with the effects arising in DOS
due to the interaction between H2O and CrPX3(Fig. 6e): Hybridisation between pstates
of P and the water lone pair [3a1molecular orbital (MO) of H2O] takes place, that results
in broadening of the respective water derived states. Besides, a slight upward shift with
respect to the MO of gas phase water molecule is observed. The obtained results on the
adsorption of H2O on pristine CrPX3are in general trend observed for graphene and for
the other 2D chalcogenides. The adsorption energies for H2O on graphene, MoS2, and
7
WS2are 0.12... 0.14 eV, 0.15 eV, and 0.15 eV, respectively [39, 40, 41], indicating
the physisorption nature of interaction.
Considering the defective monolayers, the situation is more interesting. Firstly, the
adsorption structure similar to AS1 exists. It is abbreviated as AS2 and presented
in Figure 6b. In this case, the interaction between H2O and the substate is stronger
(Eads =219 meV and Eads =224 meV), which is reflected by the reduced distance
d(P-O) = 2.85 ˚
A and 2.98 ˚
A for CrPS3and CrPSe3, respectively. In the rest, the
electronic structures of the molecule and substate undergo qualitatively similar changes
as in the case of AS1 (Fig. 6f).
In addition to AS2, a structure, called AS3 was investigated, where water molecule
is coordinated between two Cr ions as it is shown in Figure 6c. (Similar configuration
was found to be the energetically most favourable when studying water adsorption on
NiPX3x[34]). Charge accumulation is observed between O and two Cr atoms as well
as between H and P atom, which lost the chalcogen neighbour (Fig. 6c). Significant
contribution of the the 1b1and 3a1MOs to the bonding with the monolayer is expressed
in their substantial broadening due to hybridisation with P-psates. The healing of
vacancy is accompanied by shift of the the defect derived state from its original position
to lower binding energies where it is mixed with the valence band states.
The interaction between between H and P atoms in AS3 has one important effects
on the geometric structure: A significant elongation of the H–O bond from 0.97 ˚
A for
the gas-phase molecule to 1.06 ˚
A and 1.04 ˚
A for the adsorbed molecule on CrPS3xand
CrPSe3x, respectively. A further H–O bond elongation up to d(O-H) = 2.02 ˚
A leads to
structure AS4 (Fig. 6d), which is slightly higher in energy as compared to AS3. Here
the P–H bond is formed (d(P-H) = 1.40 ˚
A). Similarly to recently published results for
NiPX3[34], the corresponding structure was found to be unstable for CrPSe3x. The
weaker adsorbate-substrate interaction in the case of AS4 is reflected by less pronounced
changes in the DOS of the interacting species. By that the qualitative tendency of the
induced modifications in AS4 is similar to AS3.
4. Conclusions
In conclusions, we performed systematic DFT studies of pristine and chalcogen-
defective 2D CrPX3(X: S, Se). It is shown that both pristine materials are wide
gap semiconductors in the ground state with a band gap of 1.52 eV and 1.11 eV,
respectively. The chalcogen vacancies are characterised by very strongly localised defect
states located at 0.5 eV below the valence band maximum and in the gap formed by
valence band states, indicating the minimal influence of such defects on the optical and
transport properties of CrPX3. The adsorption of H2O on the pristine and chalcogen-
defective 2D CrPX3layers is always described as a physisorption, with possible water
splitting. However, the clear preferential adsorption of H2O on all kinds of surfaces
of CrPX3, molecular or dissociative, is not observed. It is found that in all cases
of the surface modifications (chalcogen vacancies or ambient molecules adsorption),
8
the electronic structure of CrPX3remains robust against these factors, indicating the
possible application of these materials as effective protecting coatings.
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Table 1. Results obtained for the different magnetic states of 3D CrPS3and CrPSe3
with PBE+U+D2: E(in eV) is the total energy per unit cell, a, c (in ˚
A) are the
optimised lattice parameters, d0(in ˚
A) is the van der Waals gap of bulk crystal.
X Symmetry Magnetic state E a c d0
SC2/m NM 150.706 5.75 19.35 3.32
FM 167.336 6.01 19.48 3.27
nAFM 168.501 6.01 19.48 3.21
R¯
3 NM 150.083 5.75 19.35 3.33
FM 167.300 6.01 19.48 3.26
nAFM 166.507 6.01 19.48 3.21
Se C2/m NM 134.846 6.16 19.44 3.30
FM 153.804 6.35 19.94 3.26
nAFM 154.568 6.35 19.94 3.20
R¯
3 NM 134.901 6.16 19.44 3.32
FM 153.137 6.35 19.94 3.25
nAFM 153.141 6.35 19.94 3.20
11
Table 2. Results obtained for the different magnetic states of 2D CrPS3and CrPSe3
with PBE+U+D2: Etot (in eV per (2 ×2) unit cell) is the total energy; ∆E(in meV)
is the difference between the total energy calculated for the magnetic states and the
total energy calculated for the nAFM state. Band gap (Eg, in meV), Cr2+ magnetic
moment (M, in µB), the exchange coupling parameters between two local spins (J, in
meV), and N´eel temperature (TN, in K) are given for the lowest-energy structure.
X Magn. state Etot E EgM J1J2J3TN
S FM 223.260 480
nAFM 223.740 0 1.52 3.83.10 0.14 0.32 190
sAFM 223.587 153
zAFM 223.351 389
Se FM 204.172 294
nAFM 204.466 0 1.11 3.82.06 0.15 0.36 119
sAFM 204.375 91
zAFM 204.194 272
12
Table 3. Defect formation energies (∆Edef , in eV) obtained for the CrPX3x
monolayers.
Defect type X = S X = Se
VX@1L 1.069 0.810
VX2@1L 1.222 1.120
VX2@2L 1.098 0.863
13
Figure 1. (Left panel) (a) Crystal structure of 3D MPX3. Dashed line denotes the
hexagonal unit cell used in the present work. The in-plain and out-of-plane lattice
constants are indicated with letters aand c, respectively. Shaded area denotes a
primitive unit cell. Distance d0corresponds to the van-der-Waals gap. Spheres of
different size/colour represent ions of different type. (Middle panel) Top (b) and side
(c) views of a single layer of MPX3. (Right panel) The considered chalcogen defects:
(d) VX@1L; (e) VX2@1L; (f ) VX2 @2L.
14
Figure 2. Band structure and site-pro jected density of states for (a) 3D CrPS3bulk,
(b) 3D CrPSe3bulk, (c) 2D CrPS3monolayer, and (d) 2D CrPSe3monolayer.
15
Figure 3. (Left panel) Cleavage energy of 3D CrPX3(Ecl) as a function of the van
der Waals gap (d0). (Right panel) Specific heat capacity per spin with respect to
temperature for 2D CrPX3and CrPX3x.
16
Figure 4. Four different magnetic configurations of 2D CrPX3: (a) ferromagnetic
(FM), (b) N´eel antiferromagnetic (nAFM), (c) zigzag antiferromagnetic (zAFM), and
(d) stripy antiferromagnetic (sAFM).
17
Figure 5. Site-projected density of states for the defective monolayers: (a) 2D
CrPS3xand (b) 2D CrPSe3x.
18
Figure 6. (a-d) Top and side views of the relaxed structures obtained after
water adsorption on pristine and defective CrPX3(cf. text for details). Side
view are superimposed with electron density redistribution maps. Electron density
accumulation (depletion) is shown in red (blue). Blue, violet, and orange spheres
represent Cr, P, and X atoms, respectively. The water molecule is shown with
red and light-blue spheres, for O and H, respectively. The adsorption energies are
given above each adsorption structure for X=S (X=Se). (e-h) Site-projected density
of states obtained for the structures presented in (a-d) where X = S. In (e), the
molecular orbitals of a gas-phase H2O molecule are indicated by horizontal dashed
lines. These are obtained by aligning the 2a1core level of the gas-phase and adsorbed
H2O molecules.
... Usually, several types of vacancies are considered. According to our previous studies, the so-called V X @1L defects (one vacancy at X-site) are the most favourable to form [32,55,56] and in the present study we restricted ourselves to this kind of defects. The defect formation energy in this case is found to be 1.23 eV and 1.02 eV for X = S and Se, respectively, and this is in trend with the previously calculated values for the other MPX 3 monolayers [32,55,56]. ...
... According to our previous studies, the so-called V X @1L defects (one vacancy at X-site) are the most favourable to form [32,55,56] and in the present study we restricted ourselves to this kind of defects. The defect formation energy in this case is found to be 1.23 eV and 1.02 eV for X = S and Se, respectively, and this is in trend with the previously calculated values for the other MPX 3 monolayers [32,55,56]. Removal of chalcogen atom leads to some modifications of the local lattice and electronic structures. ...
... (For the DOS of H 2 O/FePSe 3 , see Fig. S1(d)). The obtained results on the adsorption of H 2 O on pristine FePX 3 are in general trend known for the other MPX 3 materials [55,56]. ...
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... Usually, several types of vacancies are considered. According to our previous studies, the so-called V X @1L defects (one vacancy at X-site) are the most favourable to form [32,55,56] and in the present study we restricted ourselves to this kind of defects. The defect formation energy in this case is found to be 1.23 and 1.02 eV for X = S and Se, respectively, and this is in trend with the previously calculated values for the other MPX 3 monolayers [32,55,56]. ...
... According to our previous studies, the so-called V X @1L defects (one vacancy at X-site) are the most favourable to form [32,55,56] and in the present study we restricted ourselves to this kind of defects. The defect formation energy in this case is found to be 1.23 and 1.02 eV for X = S and Se, respectively, and this is in trend with the previously calculated values for the other MPX 3 monolayers [32,55,56]. Removal of chalcogenatom leads to some modifications of the local lattice and electronic structures. ...
... The bottom of the conduction band is composed of Co 3d states with low contribution from S 3p states, which is typical for the whole family of the MPX 3 materials. [20][21][22]33 The presented distribution of the electronic states in the DOS of CoPS 3 can be seen as an intermediate between the Our results confirm high crystallographic quality and purity of the studied crystals. As can be deduced from the XRD plot ( Fig. 3(a)), CoPS 3 bulk belongs to the C2/m space group 21,22,35 and the distance between single CoPS 3 layers is 6.327 Å and 6.545 Å, as extracted from the XRD and TEM data (see Fig. S5), respectively. ...
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... With U eff larger than 2.0 eV, our calculation results show that the ground-state magnetic order of the centrosymmetric phase is anti-ferromagnetic ST ordering. Recently, a theoretical study shows that monolayer and bulk PE phase of CrPSe 3 have NL order, while the ST order has an energy slightly higher than the NL order [49]. The discrepancy between this work and our study likely originates from different types of pseudopotentials (see Supplementary materials for more details). ...
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Two-dimensional (2D) multiferroic materials are ideal systems for exploring new coupling mechanisms between different ferroic orders and producing novel quantum phenomena with potential applications. We employed first-principles density functional theory calculations to discover intrinsic ferroelectric and anti-ferroelectric phases of CrPSe$_3$, which show ferromagnetic order and compete with the centrosymmetric phase with an antiferromagnetic order. Our analysis show that the electrical dipoles of such type-I multiferroic phases come from the out-of-plane displacements of phosphorus ions due to the stereochemically active lone pairs. The coupling between polar and magnetic orders creates the opportunity for tunning the magnetic ground state by switching from the centrosymmetric to the ferroelectric phase using an out-of-plane electric field. In ferroelectric and antiferroelectric phases, the combination of easy-plane anisotropy and Dzyaloshinskii-Moriya interactions (DMI) indicate they can host topological magnetic vortices like meron pairs.
... In our previous works 25,37,[39][40][41][42][43][44] we have shown that PBE+U +D2 performs very good when studying structure, electronic and magnetic properties of MPX 3 materials, including pristine FePS 3 and FePSe 3 . 25 Here we employ the same approach to get better insight into the properties of the mixed FePS 1.5 Se 1.5 material under study. ...
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... Note that the FM exchange couplings are obtained for the Mn and Ni nearest neighbors and Cr−Cr ions at the secondnearest-neighbor distance (see J 2 X in Table 3). The similar results for Cr have been recently reported in ref 90. In addition, the different values for J 1 MnNi (−1 meV) and J 1 NiMn (−0.7 meV) stems from the different lattice parameters of the hosts (see Table 3). ...
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... Still, the corresponding adsorption energy (E ads = −355 meV for NiPS 3 ) is lower in magnitude as compared with the value obtained for molecular adsorption structure, making the dissociative adsorption less favourable. The same trend was observed when studying adsorption of water on CrPX 3 monolayers [34]. All our attempts to find a local minimum corresponding to the dissociative adsorption structure similar to one presented in Figure 3c were failed, when NiPSe 3 is considered. ...
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