Robust half-metallicity and tunable ferromagnetism in two-dimensional VClI 2

Abstract

Recent theoretical and experimental discoveries of two-dimensional (2D) ferromagnetic (FM) materials have sparked intense interest for their potential applications in spintronics. 2D FM materials with high spin polarization are extremely desirable for future low-dimensional spintronics. Half-metallicity plays a key role in the development of such devices. Here, we reported a new 2D nanomagnet VClI[Formula: see text] using the first-principles based density functional theory calculations. VClI[Formula: see text] shows an exciting half-metallic character with a wide half-metallic gap of 0.4 eV. The ground state favors ferromagnetic coupling with a Curie temperature [Formula: see text] of 21 K. The half-metallicity with a FM ground state is further achieved by the application of an external strain and by the combined effects of the strain and the electric field. A phase transition from a half-metallic [Formula: see text] semiconductor [Formula: see text] metal was further observed under different stimuli with an antiferromagnetic ground state. At [Formula: see text] V/nm and in the presence of [Formula: see text] strain, the calculated [Formula: see text] is estimated at 35 K, which shows a 67% increment than the [Formula: see text] observed in the unstrained condition. The fascinating and unique properties suggest that VClI[Formula: see text] is a promising two-dimensional ferromagnetic half-metal, which can be useful for applications in future memory devices to enrich the 2D magnetic materials library.

Full text

J. Appl. Phys. 133, 084303 (2023); https://doi.org/10.1063/5.0139843 133, 084303
© 2023 Author(s).
Robust half-metallicity and tunable
ferromagnetism in two-dimensional VClI2
Cite as: J. Appl. Phys. 133, 084303 (2023); https://doi.org/10.1063/5.0139843
Submitted: 23 December 2022 • Accepted: 02 February 2023 • Published Online: 27 February 2023
T. Mukherjee, P. Kumari, S. Kar, et al.
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Robust half-metallicity and tunable
ferromagnetism in two-dimensional VClI
2
Cite as: J. Appl. Phys. 133, 084303 (2023); doi: 10.1063/5.0139843
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Submitted: 23 December 2022 · Accepted: 2 February 2023 ·
Published Online: 27 February 2023
T. Mukherjee, P. Kumari, S. Kar, C. Datta, and S. J. Ray
a)
AFFILIATIONS
Department of Physics, Indian Institute of Technology Patna, Bihta 801106, India
a)
Author to whom correspondence should be addressed: ray@iitp.ac.in and ray.sjr@gmail.com
ABSTRACT
Recent theoretical and experimental discoveries of two-dimensional (2D) ferromagnetic (FM) materials have sparked intense interest for
their potential applications in spintronics. 2D FM materials with high spin polarization are extremely desirable for future low-dimensional
spintronics. Half-metallicity plays a key role in the development of such devices. Here, we reported a new 2D nanomagnet VClI2using the
first-principles based density functional theory calculations. VClI2shows an exciting half-metallic character with a wide half-metallic gap of
0.4 eV. The ground state favors ferromagnetic coupling with a Curie temperature Tcof 21 K. The half-metallicity with a FM ground state is
further achieved by the application of an external strain and by the combined effects of the strain and the electric field. A phase transition
from a half-metallic !semiconductor !metal was further observed under different stimuli with an antiferromagnetic ground state. At
Ez¼7:5 V/nm and in the presence of η¼5% strain, the calculated Tcis estimated at 35 K, which shows a 67% increment than the Tc
observed in the unstrained condition. The fascinating and unique properties suggest that VClI2is a promising two-dimensional ferromag-
netic half-metal, which can be useful for applications in future memory devices to enrich the 2D magnetic materials library.
Published under an exclusive license by AIP Publishing. https://doi.org/10.1063/5.0139843
I. INTRODUCTION
The progress and development of modern day information
technology is happening at a rapid pace. To cope with the require-
ments, high speed and low-power consuming information process-
ing devices are required.
1,2
In order to fulfill these conditions, one
way is to change the conventional charge-based micro-electronics
and spintronics. Spintronics, which manipulates the spin degree of
freedom of electrons, has attracted the attention of the scientific
community due to its superiority over charge-based electronics to
transfer data at a high speed in a low-power environment with high
integrating density. However, to design a productive spintronic
device, one requires completely spin-resolved current as demon-
strated in 2D nanomagnets.
3–6
To address this requirement, half-
metals can play a crucial role. Half-metallicity is a very special kind
of material property where only one type of spin channel contrib-
utes offering metallic character, while the other spin channel shows
insulating behavior. Such materials can provide completely spin-
polarized current and has attracted significant interest of material
scientists.
With several efforts, up to now, diverse half-metallic materials
are designed using transition-metal oxides, transition-metal
chalcogenides, double perovskites, Heusler alloys,
7
etc. Apart from
this, half-metallicity can be introduced through various external
doping as demonstrated for the case of graphene and MoS2sheets,
doped by transition-metal atoms.
8–10
However, to get ultra-thin,
flexible, and transparent next generation spintronics along with
high information processing speed and greater integration density,
we need intrinsically magnetic two-dimensional half-metals.
However, unfortunately, there are only few materials available in
which intrinsic half-metallicity is theoretically predicted. The
experimental discovery of low dimension half-metals is limited in
nature. Theoretically, half metallicity has been noted in several 2D
magnetic materials, such as Fe/MoS2,
11
Janus FeXY monolayers
12
(X,Y = Cl,Br,I; X=Y), Co9Se8nano-sheets,
13
MnX (X = P,As)
monolayers,
14
etc.
However, recently, a new group of 2D ferromagnets, called as
transition-metal trihalides (MX3, where M = V, Cr, Mn, Fe, Ni and
X = Cl, Br, I),
15,16
has attracted the interest of scientific community
due to their unique character, which includes semiconducting
properties,
17,18
high TC,
18,19
tunable magnetic properties,
16,19,20
and
many more.
16
Among them, few 2D transition-metal trihalides
have shown intrinsic half-metallic nature with a wide spin gap. For
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example, two exciting two-dimensional half-metallic materials are
recently reported from the group of transition-metal trichlorides,
which are TiCl3and VCl3.
21
The cleavage energy calculation of
these two materials shows that such 2D structures can easily be
obtained experimentally from their bulk configurations, having the
Curie temperature of 376 K (TiCl3) and 425 K (VCl3) with large
spin bandgaps. In addition to this, we also observed half-metallicity
with various tunable electronic and magnetic properties in different
2D MX3type of compounds, such as NiX3,
22
VI3,
23
MnI3,
24
etc.
Motivated by these recently discovered MX3monolayers, in
this article, we report new intrinsically ferromagnetic 2D half-metal
VClI2for the first time. The half-metallic gap is 0.4 eV with a
Curie temperature of 21 K, and furthermore, the half-metallicity
with ferromagnetic coupling is induced in it under the presence of
external perturbations. Additionally, on application of biaxial strain
and electric field, a phase transition from a half-metal to a metal
and a semiconductor with an antiferromagnetic (AFM) ground
state is noticed. Thus, the presence of intrinsic half-metallicity with
tunable properties makes VClI2a potential candidate for future
spintronic applications.
II. COMPUTATIONAL DETAILS
First-principles based density functional theory calculations
were performed to compute the electronic and magnetic properties
of monolayer VClI2using Quantum ATK.
25,26
In these calculations,
we considered the spin-polarized generalized gradient approximation
(SGGA) of the Perdew–Burke–Ernzerhof (PBE) exchange-correlation
functional.
27
A22 supercell of VClI2was constructed, and the
Brillouin zone was sampled with a 11 11 1Monkhorst–Pack
k-point grid mesh.
28
To consider the suitable k-points, we per-
formed a parameter test and observed that the system converges at
11 11 1 k-sampling (included in Fig. S1 of the supplementary
material). A large value of k-points will only be computationally
expensive beyond that. The maximum plane wave energy cutoff
was set to 600 eV, and a convergence test was performed as illus-
trated in Fig. S2 of the supplementary material. During the struc-
tural relaxation, numerical convergence was achieved with an
energy tolerance of 106eV/unit cell, and the force on all the
relaxed atoms is lesser than 0.01 eV Å1. For the V-3d orbitals, the
effective on-site Coulomb parameter U = 3.68 eV was used,
19,29
which was obtained through a convergence test using the linear
response theory (LRT) approach as illustrated in Fig. S10 of the
supplementary material. The lattice parameters of a = b = 12 Å were
considered, and to avoid the interaction along the non-periodic
direction between the neighboring layers and their replicas, an
additional vacuum padding of 20 Å was used along the c-direction.
We applied a biaxial strain on VClI2to tune the magnetic and
electronic properties, which can be defined as
19,30,31
η¼(a - a0)/a
0,
where a0(a) is the lattice constant in the unstrained (strained) con-
dition. The positive value of ηindicates a tensile strain, while a
negative value suggests a compressive strain. In addition to this, we
applied an electric field on monolayer VClI2perpendicular to the
plane of the layer at η¼0% and 5%.
III. RESULTS AND DISCUSSIONS
A. Material structure and stability
In monolayer VClI2, a honeycomb network is formed by the
vanadium atoms. These V atoms are sandwiched between two
halide atoms (Cl, I). Similar to the 2D CrI3structure,
32
one vana-
dium atom is surrounded by six nearest neighbor halogens, two
chlorine atoms, and four iodine atoms, forming a slightly distorted
octahedron. All the atoms are bonded together by the weak van der
Waals interaction. The optimized geometrical structure of VClI2is
shown in Figs. 1(a) and 1(b), in which V atoms are covalently
bonded to Cl and I atoms. The distance of I–I is 4 Å, the V–I bond
FIG. 1. Representation of the (a) top view and (b) the side view of monolayer VClI2. Variation of formation energy as a function of (c) strain and (d) electric field.
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length is 2.7 Å, the V–Cl bond length is 2.3 Å, the Cl–Cl bond dis-
tance is 3.5 Å and the V–V bond distance is 3.7 Å. The I–V–I
bond angle is 89:7, and the Cl–V–Cl angle is 92:2.
We calculated the formation energy to check the thermody-
namical stability using Eq. (1),
Eform ¼Etot pEVqECl rEI
pþqþr, (1)
where Etot is the total energy of the VClI2monolayer and EV,ECl,
and EIare the energies of the respective configurations of vanadium,
chlorine, and iodine atoms. Furthermore, p, q, and r indicates the
number of V, Cl, and I atoms in the system. The value of formation
energy in the unstrained (η¼0%) condition is 0:81 eV/atom.
Within the strain range of 5% η5%, Eform gradually decreases
[Fig. 1(c)]. The values of Eform at various values of strain,
η¼1%, 2%, 3%, 4%, and 5%, are, respectively, 0:7, 0:67, 0:64,
0:62, and 0:60 eV/atom, and these values are comparable to that
of NiI3(1:98 eV/atom),
22
FeCl3(0:24 eV/atom),
33
and CoBr3
(0:37 eV/atom)
34
monolayers. A similar scenario is present in the
case of compressive strain as well. On compression from
5% η1%, Eform decreases and the minimum value is found
at 0:23 eV/atom at η¼5%. However, with the application of an
electric field, from Ez¼2:5 to 10 V/nm, on both the unstrained
and strained (η¼5%) condition, the formation energy increases
[Fig. 1(d)]suchasEform ¼0:73 eV/atom at Ez¼7:5V/nm
(η¼0%) and 0:74 eV/atom at Ez¼10 V/nm (η¼5%).
Dynamical stability of VClI2is further assessed in terms of phonon
band structure calculation (included in Fig. S3 of the supplementary
material). The phonon band structure was calculated using Quantum
Espresso with a k-sampling of 2 21. Here, the unit cell of the
VClI2is used, consisting of two vanadium atoms, two chlorine
atoms, and four iodine atoms. We did not observe the presence of
any imaginary frequencies in the phonon band structure, which
further confirms the dynamical stability of the monolayer of VClI2.
In addition to these, we performed ab initio molecular dynamics
(AIMD) simulations to confirm the thermodynamic stability further
at a finite temperature. To calculate this, we constructed a 2 2
supercell of VClI2, which contains a total of 32 atoms. The AIMD
simulation was performed under a constant-temperature and volume
(NVT) ensemble with a thermostat kept at 300 K by using the Nosé–
Hoover method, and the simulation was carried out over 3 105
steps with a total simulation time of 9 ns and a time step of 3ps. The
variations in the total potential energy and temperature with time
during the simulations show the absence of any sudden changes in
the profiles [included in Figs. S4(a) and S4(b) of the supplementary
material]. The mean temperature stayed around 300 K (bath temper-
ature of 300 K) with minimal fluctuations, and the total potential
energy stays around its mean value throughout the simulation time
during the course of the simulation, suggesting that the VClI2mono-
layer is thermally stable at room temperature. The combined tests
performed through formation energy calculation, phonon band
structure, and AIMD profile imply that the monolayer VClI2is ther-
modynamically and dynamically stable.
B. Electronic properties
Electronic properties play a crucial role in 2D magnetic
materials. Figures 2(a) and 2(b) are the representation of the band
structures and spin density of states (SDOS) at η¼0% and
under η¼4% strain. The band structure was calculated along the
Γ–A–L–B–Γsymmetry path of the Brillouin zone (included in
FIG. 2. Band structure and density of states at (a) η¼0% and (b) η¼4%. The blue color indicates spin-up bands, the red color indicates spin down bands, and the
dotted line implies the position of Fermi level.
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Fig. S5 of the supplementary material). In the unstrained (η¼0%)
condition, VClI2behaves as a half-metal with a wide half-metallic
gap of 0.4 eV, which is similar to that of 2D TiCl3.
21
The bulk con-
figuration of VClI2is also half-metallic in nature with an inter-layer
separation of 3.3 Å and a half-metallic gap of 1.173 eV for the
down spin-states (Fig. S9 of the supplementary material), while the
gap value is 1.142 eV for the monolayer.
Within the strain range of 1% η4%, it changes from
a half-metal !indirect bandgap semiconductor and then
again transforms to a half-metal at η¼5%. On compression at
5% η1%, it changes from a half-metal !metal phase.
Moreover, with the application of an electric field from
Ez¼2:5–10 V/nm at η¼0%, VClI2remains as a metal. In addi-
tion to this, we observed the combined effect of electric field and
strain. At Ez¼2:5 V/nm and η¼5%, the material is an indirect
bandgap semiconductor with a bandgap of 0.75 eV; however, under
the field range of 5 V/nm Ez10 V/nm at η¼5%, VClI2
becomes a half-metal.
At η¼0%, the 3d-orbitals of vanadium and 5p-orbitals of
iodine from the spin-up channel come closer and overlap at the
Fermi level [Fig. 3(a)]. Specifically, dxy,dz2,dx2y2,dyz ,dxz orbitals
of vanadium and py,pxorbitals of iodine from spin-up channel
contribute mostly at the Fermi level (included in Fig. S6 of the
supplementary material), while the contribution from the chlorine
px,pzorbitals are less at EF. The hybridization between these orbit-
als makes VClI2a half-metal, where spin-up states form a conduct-
ing channel around the Fermi level, while the spin down states
remain semiconducting. It is to be noted that the half-metallicity
we observe in unstrained VClI2is totally intrinsic, and no certain
external constraints are applied. The presence of such a spin-
polarized character allows the spin-up channel for the conduction
and blocks the spin down channel, which assures 100% of spin
FIG. 3. Projected density of states (PDOS) at different strain and electric fields: (a) η¼0%; (b) η¼2%; (c) Ez¼7:5 V/nm, η¼5%; and (d) Ez¼10 V/nm, η¼0%.
The blue line denotes the contribution from V-3d orbitals, the green line indicates contribution from Cl-3p orbitals, and the red line denotes contributes from I-5p orbitals.
The combined contributions of the orbitals is represented by the black line.
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polarization. This characteristic has major implications in the effi-
ciency of the spintronic devices and further increases their potential
magnetoresistance by a huge factor. Moreover, we get a phase transi-
tion from a half-metal !semiconductor (included in Fig. S7 of the
supplementary material) under the strain range of 1% η4% on
monolayer VClI2[Fig. 3(b)]. We know that, on the application of
biaxial strain to any material, it changes the lattice parameter of that
material, which, further, according to the Kroning–Penney model,
effects the band structure of the material due to the dependency of
the ground state energy on the lattice constant. Now, when we are
applying strain on the system, the lattice parameter gets tuned and
accordingly, the hybridization between the respective orbitals
enhances, and as a result, the bandgap changes. Under the applica-
tion of tensile strain, the valence band is mainly dominated by px,
py,andpzorbitals of I, pxand pyorbitals of Cl, while the conduction
band is contributed by the dxy ,dx2y2,dyz,dxz ,dz2orbitals of V and
px,pzorbitals of I. Overlapping between these orbitals around the
Fermi level makes VClI2a semiconductor. However, with increasing
strain from η¼1% !4%, the degree of hybridization is more,
which leads to a decrease in the bandgap from 0.86 to 0.69eV.
Again, at η¼5%, p orbitals of I and Cl and dx2y2,dxz ,dz2orbitals
of V overlap at EFand transform in a half-metal from a semiconduc-
tor. Similarly, on compression of 5% η1%, the hybridiza-
tion between the px,py,pzorbitals of I, pxand pyorbitals of Cl, and
dx2y2,dxz,dz2orbitals of V from both the spin-up and -down chan-
nels contribute mostly and makes monolayer VClI2ametal.
Apart from the strain, we observe metallic nature under the
application of an electric field from Ez¼2:5 to 10 V/nm at
η¼0%. Such a transition from a half-metal !metal is due to the
contribution from dorbitals of vanadium, pxorbital of iodine, and
px,pzorbitals of chlorine at the Fermi level. However, at
Ez¼2:5 V/nm, in the presence of η¼5%, VClI2is a semiconduc-
tor with a bandgap of 0.75 eV. Here, the valence band is mainly
contributed by the px,py, and pzorbitals of iodine, px,pyorbitals
of chlorine, while the conduction band is mainly dominated by the
dx2y2,dxy,dxz , and dz2orbitals of V and a little contribution from
the pxand pyorbitals of I. With increasing electric field (η¼5%),
these orbitals from the spin-up channel come closer to the lower
energy range and finally overlap at the Fermi level, which makes
VClI2a half-metal from a semiconductor with a half-metallic gap
of 0:11 eV.
C. Magnetic properties
To explore the preferred magnetic interaction, we considered
four different configurations: one ferromagnetic (FM) and three anti-
ferromagnetic (AFM) arrangements as shown in Figs. 4(a)–4(d).The
exchange energy is given by
35
ΔE¼EFM EAFM, where EFM (EAFM)
FIG. 4. Representation of the various possible magnetic configurations in the monolayer VClI2: (a) FM, (b) AFM-zigzag, (c) AFM-Néel, and (d) AFM-stripe.
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is the energy corresponding to the FM (AFM) configuration of
VClI2. Note that ΔE,0 implies FM ordering and ΔE.0 signifies
AFM ordering. In the unstrained condition, the FM ground state is
more stable than the AFM states. In the presence of tensile strain
from η¼1% !4%, a FM !AFM transition is observed, and at
η¼5%, it transforms to a ferromagnet. Under the compressive
strain range of 5% η1%, a FM !AFM transition is
observed. A similar result was reported for CrI3, CrCl3, and CrBr3
on compression.
36,37
On the entire range of electric field, 2.5 V/nm
Ez10 V/nm at η¼0%, VClI2remains an antiferromagnet.
However, in the presence of both electric field and η¼5% of strain,
it reaches an AFM ground state at Ez¼2:5 V/nm, while the FM
ground state emerges from Ez¼5 to 10 V/nm. We observed that,
whenever the material is a ferromagnet, it is a half metal as well, and
therefore, the presence of both ferromagnetism with half-metallicity
makes VClI2a useful candidate for future spintronic applications.
For the practical use in spintronics, the Curie temperature
plays a key role, and to estimate this accurately, we considered the
statistical Monte Carlo simulations based on the 2D Ising model,
which has been used in previous studies on similar systems.
38–41
For this, we constructed a 100 100 supercell of VClI2with each
calculation running for 105iterations. The interaction between
neighboring spins of a VClI2magnetic lattice can be defined by the
Hamiltonian in Eq. (2),
42
H¼X
i.j
JijSiSj, (2)
where Siand Sjare the spins located at the ith and jth sites and Jij is
the exchange integral between the spins Siand Sj, which can be
further defined as
43
J¼ ΔE
2NS2, where ΔE is the exchange energy, N
is the number of nearest neighbors, and S is the spin. Magnetic
ordering can also be deduced from the J values, and a positive
(negative) value of J indicates FM (AFM) ordering.
The result of Monte Carlo simulations is shown in Figs. 5(a)
and 5(b). The sharp fall of magnetization in Fig. 5(a) clearly conveys
the phase transition from the ferromagnet (FM) !paramagnet (PM)
state at a certain value of temperature, which is denoted as the Curie
temperature (Tc) of the system. Furthermore, to confirm the values of
Tcunder various constraints, we observe the variation of specific heat
with temperature and a sharp peak is noticed at the respective critical
temperatures. In Fig. 5(b),wegetTc¼21 K at η¼0%, Tc¼13 K at
η¼5%, and Tc¼35 K at η¼5% and Ez¼7:5V/nm. The transi-
tion from FM !PM state is a second order phase transition because
we get a divergence in the susceptibility curve (included in Fig. S7 of
the supplementary material), which breaks the spontaneous spin
symmetry.
Unstrained VClI2has a Tcof 21 K, which reaches a value of
13 K at η¼5%. However, under the application of strain (η¼5%)
with field (5 V/nm Ez10 V/nm), Tchas increased. From
Fig. 6(a), we observe that at Ez¼5 V/nm and η¼5%, Tcincreases
to 28 K and then gets a value of 35 K at Ez¼7:5 V/nm, but at
Ez¼10 V/nm, it decreases to 29 K. Therefore, 67% of enhance-
ment is noticed than the unstrained situation.
The reason behind the existence of long range magnetic order-
ing in VClI2is due to the presence of anisotropy energy. Magnetic
anisotropy is basically the dependency of magnetic properties on a
preferred crystallographic direction. However, the Mermin–Wagner
theorem
44,45
suggested that, in low-dimensional materials, the long
range spontaneous magnetization is not possible due to the pres-
ence of thermally induced magnon excitations at finite temperature.
Magnetic anisotropic energy (MAE)
46
is an important parameter,
which prevents thermal fluctuations in the 2D magnets to create
long-range magnetic ordering. MAE is defined as the energy differ-
ence between in-plane and out-of-plane component of magnetiza-
tion; i.e., MAE = EkE?. In another word, it is the required
energy to flip the magnetic moment from the easy axis of magneti-
zation to the hard axis of magnetization of a crystal. The positive
value signifies the off-plane easy axis; however, a negative value
indicates an in-plane easy axis of magnetization. In the unstrained
condition, the value of MAE is 8 meV, but it decreases to 2.74 meV
at η¼5%. Thus, here, the positive value of MAE shows the off-
FIG. 5. Results of the Monte Carlo simulations: (a) variation of magnetization with temperature and (b) variation of specific heat with temperature at various values of
strain and electric field.
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plane easy axis of magnetization. Figure 6(b) shows the variation of
MAE with electric field at η¼5% of biaxial strain. The preferred
direction for this calculation is along {100} and {010} with respect
to {001} direction. Because of the presence of hexagonal symmetry,
the energy difference values are indistinguishable. The similarity
between Figs. 6(a) and 6(b) clearly shows the connection between
MAE and Tc. When the value of MAE is increasing, the spin align-
ment of the vanadium-3d electrons is more ferromagnetic in
nature, which requires high energy to divert the magnetization
direction from easy to the hard axis, that enhances the exchange
integral, and as a result, the Curie temperature increases. Due to
this reason, the maximum value of both Tcand MAE is seen at
Ez¼7:5 V/nm of electric field (η¼5%).
In VClI2, the vanadium atoms are surrounded by six nearest
neighbor halogens. In such a compound, the oxidation state of V is
þ3. The electronic configuration for the Vþ3ion is [Ar] 4s03d2.In
an octahedral crystal field, d-orbitals split into two manifolds: one
is a higher energy egstate, which is a doublet, and another one is a
lower energy t2gtriplet. Unlike CrI3, VClI2has a partially half-filled
t2gopen shell and an empty egshell. The total spin is S = 1 for
Vþ3, and furthermore, it has a non-zero orbital moment, which
consequently gives rise to the spin–orbit coupling (SOC), and
hence, due to the presence of both SOC and crystal field, strong
single ion magnetic anisotropy is originated, which makes the
material an intrinsic 2D Ising ferromagnet. The FM and AFM cou-
pling result from different superexchange phenomena. According
to the Goodenough–Kanamori rule,
47,48
the FM coupling is favor-
able when the bond angle is 90during the superexchange
process, while AFM ordering is favored when that angle is tending
to 180. The superexchange takes place between the vanadium ions
via 5p-orbitals of iodine and 3p-orbitals of chlorine by the virtual
hopping between t2gorbitals, which as a result gives rise to FM and
AFM ground states [Fig. 6(c)]. The path of a superexchange inter-
action is along V–I–V and V–Cl–V paths. Around the Fermi level,
the 3d-orbitals of V, 5p-orbitals of I, and 3p-orbitals of Cl contrib-
ute the most. The degree of overlappings between the different
orbitals causes the variation in the Curie temperature. The more
the hybridization happens, the higher is the Tc, and the material
becomes a strong ferromagnet. Moreover, in the unstrained condi-
tion, the magnetic moment is 2.41 μB/V atom, which reaches a
value of 2.48 μB/V atom at 5% of strain and further under the elec-
tric field range of 5 V/nm Ez10 V/nm at η¼5%, the mag-
netic moment is 2.47 μB/V atom. Thus, there is an 10% of
enhancement present than the unstrained condition, which con-
firms the dominant ferromagnetic nature in VClI2.
D. Conclusion
In summary, we report a new two-dimensional ferromagnet
VClI2using first-principles based density functional theory calcula-
tions. It is an intrinsic half-metal with a half-metallic gap of 0.4 eV.
The half-metallic character is further induced by applying η¼5%
strain and an electric field from Ez¼5 to 10 V/nm at η¼5% with
ferromagnetic coupling. We also noticed a phase transition from a
half-metal !semiconductor !metal with an AFM ground state
under various strains and electric fields. The overlapping between
different orbitals of V, I, and Cl is responsible for such transitions.
We observed a Curie temperature of 21 K for the unstrained VClI2
by a statistical Monte Carlo simulation technique based on 2D
Ising Model. The Tcis further enhanced to 35 K at Ez¼7:5 V/nm
(η¼5%), which corresponds to 67% of increment. Enhancement
of Tcand ferromagnetic coupling is due to the inherent magnetic
anisotropy that can be explained via the superexchange mechanism
between V–I–V and V–Cl–V paths. Therefore, based on these anal-
yses, the intrinsic half-metallicity with a wide half-metallic gap, fer-
romagnetic/antiferromagnetic couplings, and a high magnetic
moment with enhanced Curie temperature make VClI2a potential
candidate for use in future spintronics.
SUPPLEMENTARY MATERIAL
See the supplementary material that contains additional infor-
mation and data on the observations made in the paper.
FIG. 6. (a) Variation of Curie temperature with electric field at η¼5%, (b) variation of MAE with electric field at η¼5%, and (c) a schematic representation of a spin
electron density isosurface of monolayer VClI2with a isosurface value of 0.002 307 28 Å3.
Journal of
Applied Physics ARTICLE scitation.org/journal/jap
J. Appl. Phys. 133, 084303 (2023); doi: 10.1063/5.0139843 133, 084303-7
Published under an exclusive license by AIP Publishing

ACKNOWLEDGMENTS
This work was financially supported by the Department of
Science and Technology, India through the INSPIRE scheme (Ref.
No. DST/INSPIRE/04/2015/003087), the ECR grant (Ref. No.
ECR/2017/002223), and the CRG grant (Ref. CRG/2019/003289).
S.J.R. sincerely acknowledges the support provided by the
UGC-DAE Consortium for Scientific Research (Ref. Nos.
CSR-IC-263 and CRS-M-321). The authors gratefully acknowledge
the support and resources provided by the PARAM SHIVAY
Facility at the IIT BHU and PARAM YUVA Facility at CDAC,
Pune under the National Supercomputing Mission of Government
of India.
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
T.M., P.K., and S.K. contributed equally to this paper.
T. Mukherjee: Formal analysis (equal); Investigation (equal);
Methodology (equal); Validation (equal); Visualization (equal);
Writing –original draft (lead). P. Kumari: Investigation (equal);
Validation (equal); Writing –review & editing (equal). S. Kar:
Data curation (equal); Formal analysis (equal); Project administra-
tion (equal); Visualization (equal); Writing –review & editing
(equal). C. Datta: Validation (equal); Writing –review & editing
(equal). S. J. Ray: Conceptualization (lead); Project administration
(lead); Writing –review & editing (equal).
DATA AVAILABILITY
The raw/processed data required to reproduce these findings
cannot be shared at this time due to technical or time limitations.
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Published under an exclusive license by AIP Publishing