Sandra Julieta Gutiérrez-Ojeda1, Rodrigo Ponce-Pérez1, Daniel Maldonado-Lopez2, Do Minh Hoat3,4, Jonathan Guerrero-Sánchez1, Ma Guadalupe Moreno-Armenta1. 1. Centro de Nanociencias y Nanotecnología, Universidad Nacional Autónoma de México, Km. 107, Apdo. 14 Carretera Tijuana, Ensenada, Baja California 22800, México. 2. Department of Chemical Engineering & Materials Science, Michigan State University, East Lansing, Michigan 48823, United States. 3. Institute of Theoretical and Applied Research, Duy Tan University, Ha Noi 100000, Vietnam. 4. Faculty of Natural Sciences, Duy Tan University, Da Nang 550000, Vietnam.
Abstract
Structural, electronic, and magnetic properties of two-dimensional Cr2N MXene under strain were studied. The uniaxial and biaxial strain was considered from -5 to 5%. Phonon dispersion was calculated; imaginary frequency was not found for both kinds of strain. Phonon density of states displays an interesting relation between strain and optical phonon gaps (OPGs), that it implies tunable thermal conductivity. When we apply biaxial tensile strain, the OPG increases; however, this is not appreciable under uniaxial strain. The electronic properties of the dynamically stable systems were investigated by calculating the band structure and electron localization function (ELF) along the (110) plane. The band structure showed a metallic behavior under compressive strain; nevertheless, under tensile strain, the system has a little indirect band gap of 0.16 eV. By analyzing, the ELF interactions between Cr-N are determined to be a weaker covalent bonding Cr2N under tensile strain. On the other hand, if the Cr atoms reduce or increase their self-distance, the magnetization alignment changes, also the magnetic anisotropy energy displays out-of-plane spin alignment. These properties extend the potential applications of Cr2N in the spintronic area as long as they can be grown on substrates with high lattice mismatch, conserving their magnetic properties.
Structural, electronic, and magnetic properties of two-dimensional Cr2N MXene under strain were studied. The uniaxial and biaxial strain was considered from -5 to 5%. Phonon dispersion was calculated; imaginary frequency was not found for both kinds of strain. Phonon density of states displays an interesting relation between strain and optical phonon gaps (OPGs), that it implies tunable thermal conductivity. When we apply biaxial tensile strain, the OPG increases; however, this is not appreciable under uniaxial strain. The electronic properties of the dynamically stable systems were investigated by calculating the band structure and electron localization function (ELF) along the (110) plane. The band structure showed a metallic behavior under compressive strain; nevertheless, under tensile strain, the system has a little indirect band gap of 0.16 eV. By analyzing, the ELF interactions between Cr-N are determined to be a weaker covalent bonding Cr2N under tensile strain. On the other hand, if the Cr atoms reduce or increase their self-distance, the magnetization alignment changes, also the magnetic anisotropy energy displays out-of-plane spin alignment. These properties extend the potential applications of Cr2N in the spintronic area as long as they can be grown on substrates with high lattice mismatch, conserving their magnetic properties.
Spintronics is one of the most active
research fields. Contrasting
conventional electronic devices which are performed by a charge carrier,
the switch of a spin-governed device uses spin waves as information
carriers or by the magnon–phonon effect, which can be much
faster and with less power dissipation.[1−3]Since the remarkable
physical and chemical properties of graphene
were explored,[4,5] other two-dimensional (2D) materials
have attracted interest and attention because of their intrinsic properties[6−9] that are being actively sought to fabricate high-performance electronic
devices. A great solution to reduce inefficiencies of graphene and
quasi-graphene structures is the creation of graphene-based van der
Waals (VdW) heterostructures by positioning graphene on top of other
2D materials.[10]In spite of the research
efforts in 2D semiconductors and optoelectronics
materials, 2D magnetic materials remain still unexplored, due to the
fact that most of the 2D materials already synthesized have been intrinsically
nonmagnetic. However, experimental and theoretical studies in recent
years reveal that magnetic properties can be controlled by introducing
edge structures, doping, surface functionalization, or creating defects.[11−13] In this sense, 2D hexagonal CrN displays half-metal behavior with
a possible ferromagnetic (FM) ordering when it is isolated[14] and preserves its properties as it happens in
MoSe2 and MoS2 heterostructure.[15] Besides, strain engineering[16] is an important strategy for tuning the lattice and electronic structure
of 2D materials, and there are different methods of inducing strain
from the lattice mismatch, for example, the use of different substrates,
such as flexible substrates, patterned substrates, and piezoelectric
substrates, to the action of atomic force microscope tips and bubbles.[17]MXenes are a new family of 2D transition-metal
carbide/nitrides,
discovered in 2011,[18] which are a family
of layered hexagonal transition-metal carbides/nitrides with theoretically
infinite lateral dimensions but atomically thin thickness.[19] The chemical formula is MXT2 (n = 1, 2, and 3), where M is an early transition-metal element, X
is carbon or nitrogen, and T (T = OH, O, and F) is a surface functional
group.[20] Since the first discovered Ti3C2T2 MXene, more than 70% of all MXene
research has been focused on it.[21] MXenes
had been predicted, and their physics and chemical properties were
described by theoretical studies,[22] principally
with intrinsic ferromagnetism.[23−25] The MXenes exhibit outstanding
electronic, optical-mechanical, and thermal properties with versatile
transition metal and surface chemistries.[26] Furthermore, they could be a promising candidate to be employed
in heterostructures as metal electrodes, photodetectors, and in solar
cell applications,[27−29] and due to the VdW interactions, they can be candidates
for anodes in batteries.[30] In addition,
when strain is applied on MXenes, for example WCrCO2, their
electronic properties change to a semi metallic character with a dual
narrow band gap.[31] The VdW heterostructure
Mn2CFCl/MoSSe has the potential applications in spintronic
devices due to its perpendicular magnetic anisotropy (PMA) that can
be regulated by the biaxial strain and an external electric field.[32]The nitride-based MXene possess an advantage
in comparison with
carbide MXenes due to a higher electronic conductivity[30,33] and magnetic moments,[34] so they could
be suitable candidates for electrodes in electrochemical capacitors
or metamaterials devices.[35,36] Moreover, a previous
theoretical study had considered possible magnetic configurations
where the most favorable for Cr2N pristine is the antiferromagnetic
(AFM) order where the different Cr layers are antiparallel to each
other and have metallic behavior.[37] Nevertheless,
this MXene displays a FM ground state that acts a half-metallic when
it is functionalized,[34,37] also the ground state above room
temperature is stable, robust, and can be maintained under tensile
strains up to 10%.[38] Subsequently, the
electronic and magnetic properties could be tunable by applying compressive
and tensile strain, such is the case for the MXene semiconductors[34] and in the MXenes that display magnetic anisotropy.[39]Electronic and magnetic properties of
Cr2N MXene could
be tunable as a result of lattice parameter mismatch to build heterostructure
or by deformation induction, as shown in 2D systems.[39,40] In this sense, we study the biaxial and uniaxial strain effect on
Cr2N MXene pristine. The MXene is dynamically stable under
compressive or tensile stress and keeps its metallic characteristics.
Even if it preserves the AFM behavior, the magnetic spin polarization
between Cr layers is different to pristine MXene unstrained, and the
magnetic moment magnitude depends if it is under compressive or tensile
strain, allowing it to be a good option for applications in 2D spintronics
as contacts.
Computational Methods
The structural, electronic, and
magnetic properties of the Cr2N MXene under tensile and
compressive strain are investigated
by spin-polarized first-principle calculations. Calculations were
performed in the periodic density functional theory (DFT) framework,
as implemented in the Vienna Ab initio Simulation Package,[41−73] that utilizes a plane wave basis set to represent electron states.
The exchange–correlation energies were treated using the generalized
gradient approximation with Perdew–Burke–Ernzerhof parametrization.[42] Because Cr is a transition metal with 3d orbitals,
it exhibits high correlation electrons. Therefore, to treat the high
correlated electrons, we use the Hubbard Correction (DFT + U) method,[44] employing the methodology proposed by Dudarev
et al.[43] We employed a value of U = 3 eV to treat the Cr-3d orbitals as
in previous reports.[46] The electronic states
were expanded using the projector-augmented wave basis[45,74] with an energy cutoff of 460 eV. The Cr2N MXenes were
simulated with the supercell method with a vacuum space of 15 Å.
To study the electronic and magnetic properties, a monolayer of the
Cr2N supercell with 2 × 2 periodicity was constructed,
and we consider different magnetic configurations without any constraints.
To achieve convergence, all the force components must be less than
0.01 eV/Å and total energy differences less than 1 × 10–9 eV. The Brillouin zone was sampled using a Monkhorst–Pack
mesh[47] of 15 × 15 × 1 k points.
Phonon dispersions were obtained using the finite-differences method[48] combined with the Phonopy code.[49] By using 2 × 2 periodicity with integration of 7 ×
7 × 1, the dynamical stability of the system has been achieved.
Furthermore, the molecular dynamics simulations were performed by
the CASTEP package[50] at 300 K, and a time
step of 5 fs is set with 500 simulation steps.
Results and Discussion
The structure of MXene was built
by removing the A-element group
element atomic layer from their corresponding Cr2GaN MAX
phase (mostly IIIA and IVA).[46,51] The unit cell includes
three atoms, two chromium (Cr) and one nitrogen (N), which resides
in the P3̅m1 space group. The Cr atoms are
located at (1/3, 2/3, z) and (2/3, 1/3, −z)
on the 2d Wyckoff sites; meanwhile, the N atom is
located at (0, 0, 0) on the 1a Wyckoff site.[52][53] Then, the MXene
Cr2N has a centered honeycomb (T) structure where the N
atoms are in-between two layers of the hexagonal lattice of Cr atoms.[54] The interplanar distance is 1.14 Å, and
the Cr–N bonds have a distance of 2.12 and 2.06 Å, for
more details see Figure S1 in Supporting
Information. Figure displays a top and side view of the crystal structure of the unstrained
Cr2N MXene.
Figure 1
Top and side view of Cr2N MXene with (2 × 2) periodicity.
Top and side view of Cr2N MXene with (2 × 2) periodicity.To study the strain effect on this MXene, biaxial
(x–y) and uniaxial (y) strain
(ε) was applied, see Figure . The strain is defined aswhere a0 and a are the lattice parameters of the unstrained and strained
structures, respectively. The positive and negative values correspond
to tensile and compressive strains, respectively, for a range from
−5% ≤ ε ≤ 5% for each deformation.
Figure 2
Top and side
view of Cr2N under biaxial and uniaxial
strain.
Top and side
view of Cr2N under biaxial and uniaxial
strain.To determine the dynamical stability, we calculate
the phonon bands;
results are shown in Figure . These phonon dispersions are plotted along the path Γ-M-K-Γ.
It is worth to notice that non-negative frequencies are present for
any deformation, meaning that the system is stable under biaxial and
uniaxial strain in all the range applied. As reported for a similar
crystal structure and chemical bonding M2C MXene,[55] the phonon dispersions have three acoustic modes;
two of them exhibit a linear dispersion near Γ and correspond
to in-plane rigid body motions. In contrast, the third acoustic mode
corresponds to out-of-plane vibrations, and it has a quadratic dispersion
close to Γ and lower energy in the rest of the spectrum, which
is a common feature in covalent, VdW monolayer and multilayer 2D lattices[52,56,57] due to accuracy of the harmonic
interatomic force constants.[58−60] Taking into account the crystal
structure of the MXene, the optical modes at the zone center of the
Brillouin zone can be classified with the following irreducible formula[61]where the E-symmetry modes (Eg and Eu) are doubly degenerate.
The two Raman-(Eg + A1g) and IR (A2u + Eu) optical mode frequencies of MXene free and
under stress or strained are listed in Table . Note that for uniaxial compressive and
tensile strain, the Eg and A2u phonon bands unfold, 196.66 and 187.79 cm–1 for Eg while for Au2 are 442.84 and 438.78 cm–1, see Figure . This is due to
the symmetry breaking, although the system is dynamically stable,
as reported in similar MXenes.[61] The correspondence
between the vibrational modes of Cr2N free and under compressive
and tensile strain is determined by the direction of the vibrations
and the nature of the contributing atoms, then for Cr atoms, the Raman-active
modes are associated with in-plane and out-plane vibrations for Eg and A1g, respectively,
as reported by Champagne.[52] The schematic
displaced representations of the atoms are illustrated in Figure , where the atoms
are displaced along x–y for Cr2N free-strain due to Eg intensity being
higher than A1g, while under biaxial and
uniaxial strain, the atoms change their out-plane z displacement because the phonon band intensity of A1g is comparable with Eg.
Figure 3
Phonon
band structure and densities of states of unstrained Cr2N (upper part), under biaxial compressive and tensile strain
(middle part), and under uniaxial compressive and tensile strain (bottom
part).
Table 1
Vibrational Mode Frequencies of the
Stable Cr2N MXenea
Raman
modes
IR modes
P3̅m1 (164)
Eg
A1g
A2u
Eu
Cr2N unstrained
179.28
305.14
416.17
651.67
–5% biaxial
strain
198.49
239.75
416.36
661.91
5% biaxial strain
203.61
275.72
594.77
502.81
–5% uniaxial
strain
171.65
196.66
299.23
388.51
442.84
656.68
5% uniaxial strain
144.36
187.79
260.26
389.65
438.78
631.05
E modes are degenerate.
Figure 4
Atomic displacements of the vibration modes for Cr2N
MXene unstrained and under biaxial or uniaxial compressive and tensile
strain. The dot on the atom corresponds to vibration direction pointing
into the plane, and the arrow corresponds to the in-plane vibration.
Phonon
band structure and densities of states of unstrained Cr2N (upper part), under biaxial compressive and tensile strain
(middle part), and under uniaxial compressive and tensile strain (bottom
part).Atomic displacements of the vibration modes for Cr2N
MXene unstrained and under biaxial or uniaxial compressive and tensile
strain. The dot on the atom corresponds to vibration direction pointing
into the plane, and the arrow corresponds to the in-plane vibration.E modes are degenerate.The highest peaks in energy in the phonon density
of states (phonon
DOS) correspond to N atom vibrations. Moreover, the first three optical
branches in the phonon spectrum demonstrate lower frequencies close
to the three acoustic phonon branches where it corresponds to the
vibration of Cr atoms. Furthermore, the optical phonon gap (OPG) induced
is summarized in Table . It is noteworthy that under uniaxial strain, the OPG decreases
while under biaxial strain decreases and increases when applying compressive
and tensile strain, respectively (for details, see Figures S2 and S3 in the Supporting Information). The existence
of a phonon gap between optical phonons implies larger thermal conductivity[56] that could be engineered by strain.
Table 2
Optical Phonon Gap and Upper Limit
Optical Branch for Cr2N Unstrained and under Strain
biaxial strain
uniaxial strain
Cr2N unstrained
–5%
5%
–5%
5%
optical phonon gap [cm–1]
109.08
59.38
167.79
48.20
91.23
upper limit optical branches
[cm–1]
715.86
744.88
683.67
745.88
656.31
In addition, Table exhibits the maximum frequencies of the phonon spectrum
that could
be associated with the Debye temperature and describe the Debye stiffness
of the system[56] due to the fact that it
includes the optical phonon excitation resistance.[62] In this sense, Debye stiffness (being an important parameter
to represent the resistance to overall phonon excitation[62]) of the Cr2N under strain is much
lower than that of graphene, where the maximum optical frequency is
around 1500 cm–1,[56] two
times higher than the strained Cr2N MXene.To analyze
the thermal stability of unstrained and strained Cr2N monolayer, Figure displays the ab
initio molecular dynamics (AIMD) simulation
results that have been carried out at 300 K. Herein, a time step of
5 fs is set with 500 simulation steps (total simulation time of 2.5
ps). Note that no structural destruction occurs despite its constituent
atoms vibrate around their equilibrium positions, suggesting good
thermal stability of the studied 2D materials in both unstrained and
strained states.
Figure 5
Fluctuation of temperature as a function of molecular
dynamics
simulation steps at 300 K of Cr2N monolayer at (a) biaxial
compression of −5%, (b) biaxial tension of +5%, (c) unstrained
state, (d) uniaxial compression of −5%, and (e) uniaxial compression
of +5%.
Fluctuation of temperature as a function of molecular
dynamics
simulation steps at 300 K of Cr2N monolayer at (a) biaxial
compression of −5%, (b) biaxial tension of +5%, (c) unstrained
state, (d) uniaxial compression of −5%, and (e) uniaxial compression
of +5%.Regarding the magnetic properties, Figure a,b shows the different magnetic
configuration
of the 2D unstrained Cr2N MXene and the magnetic anisotropy
at the high symmetry hexagonal lattice, respectively. The Cr atoms
at different polarizations are marked with yellow and red balls for
spin up and spin down, respectively. The FM and different AFM configurations
were considered in the calculations. Since the Cr2N has
two Cr monolayers on top and bottom, the spin in the different Cr
layers was polarized parallel to each other (FM, AFM2, and AFM4),
or the Cr layers are antiparallel (AFM1, AFM3, and AFM5).[37] The magnetic anisotropy is calculated by the
spin–orbit coupling for magnetic alignments along the x- and
z-axes, as shown in Figure b. Magnetic alignments are set without any constraint.
Figure 6
(a) Possible
magnetic polarization in Cr2N MXene; yellow
and red balls correspond to spin up and spin down, respectively, and
(b) schematic of the Cr2N MXene structure highlighting
high-symmetry axes, in-plane are (100), (110), and (010), and out-of-plane
are (001) and (111) directions.
(a) Possible
magnetic polarization in Cr2N MXene; yellow
and red balls correspond to spin up and spin down, respectively, and
(b) schematic of the Cr2N MXene structure highlighting
high-symmetry axes, in-plane are (100), (110), and (010), and out-of-plane
are (001) and (111) directions.The relative energies per primitive cell of the
FM, AFM1, AFM2,
AFM3, AFM4, and AFM5 unstrained MXenes are 1.42, 0.93, 0.43, 0, 5.76
× 10–5, and 0.43 eV, respectively. Note that
Cr2N unstrained has an AFM3 ground state, as described
in previous reports,[37] also we consider
different values of U to treat the highly correlated electrons from
Cr, and our results show that U = 3 eV reproduces
the results previously published (for more details, see Table S1 of Supporting Information). Table summarizes the relative
energies for the six magnetic configurations when applying compressive
and tensile strain. For biaxial strain, the AFM4 is the most favorable
configuration under compressive deformation; nevertheless, under tensile
strain in the interval 1% < ε ≤ 3%, the AFM3 is the
most favorable, and for larger values of strain, the system switches
to AFM4 as the most favorable configuration. Meanwhile for uniaxial
strain, the AFM4 is the most favorable configuration under compressive
deformation in the interval −5% < ε ≤ −3%
and preserve the AFM3 configuration only from −2% < ε
≤ 0%, although for a tensile strain, the AFM4 is the most favorable
characteristic.
Table 3
Relative Energies (meV) of Magnetic
Configurations of the Cr2N MXene Unstrained and Biaxial
and Uniaxial Strained
biaxial
strain
uniaxial strain
% strain
FM
AFM 1
AFM 2
AFM3
AFM4
AFM 5
FM
AFM 1
AFM 2
AFM 3
AFM 4
AFM 5
–5
1783.77
1483.09
261.27
0.22
0.00
261.16
1598.39
1120.01
401.61
56.42
0.00
324.68
–4
1677.83
1332.92
288.59
0.34
0.00
288.24
1541.35
889.68
384.35
27.04
0.00
340.87
–3
1583.58
1199.23
317.49
0.03
0.00
317.19
1496.07
954.01
379.40
6.32
0.00
361.24
–2
1511.61
1089.76
349.68
0.02
0.00
349.52
1465.12
866.50
391.28
0.00
6.23
388.16
–1
1455.77
999.86
386.98
0.01
0.00
387.16
1441.17
799.23
411.30
0.00
10.91
414.51
0
1415.83
930.76
430.00
0.00
0.06
429.98
1415.83
930.76
430.00
0.00
0.06
429.98
1
1386.60
880.19
477.17
0.00
0.07
477.14
1395.83
896.76
455.05
2.71
0.00
447.24
2
1345.71
848.34
527.03
0.00
0.18
527.14
1385.53
872.73
490.91
20.52
0.00
468.43
3
1291.70
836.33
584.41
0.00
0.01
584.55
1375.33
847.45
531.54
45.00
0.00
490.50
4
1240.79
834.80
642.87
0.03
0.00
642.88
1359.91
819.48
575.53
76.33
0.00
514.32
5
1201.22
834.84
704.04
0.04
0.00
704.03
1339.38
787.40
621.93
113.01
0.00
538.98
Moreover, from the magnetic anisotropy energy (MAE)
performed for
the upper and lower strain limits, the results exhibit an out-of-plane
spin alignment for unstrained and under uniaxial strain. Regarding
MXene under biaxial tensile strain, it preserves the same spin alignment
as unstrained Cr2N; nevertheless, under compressive strain,
the in-plane alignment is the most stable. The out-of-plane alignment
is 0.05 meV less stable. Table S2 of Supporting
Information displays the MAE for all deformation percentages. Note
that the spin orientation changes due to the increment or decrement
distance between the Cr layer (see Figure S4). This effect gains importance when applying biaxial compressive
strain.With this in mind, it can be seen that the magnetic
configuration
depends on the Cr–N bond length. Figure a,b exhibits the bond distance of Cr2N under biaxial and uniaxial strain, respectively. Three kinds
of bond lengths named as Cr–N1, Cr–N4, and Cr–N2
(black, red, and green dots-lines, respectively) have been plotted
that correspond with the [−210], [−120], and [110] directions,
respectively. Unstrained Cr2N MXene displays AFM3 configuration
with Cr–N4 > Cr–N1 and Cr–N1, and the Cr–N1
is equal to Cr–N2. After applying compressive or tensile strain,
the bond lengths display a linear decrement or increment, respectively.
Figure 7
Bond length
and the most stable magnetic configuration of the Cr2N
MXene unstrained, (a) under biaxial and (b) under uniaxial
strained.
Bond length
and the most stable magnetic configuration of the Cr2N
MXene unstrained, (a) under biaxial and (b) under uniaxial
strained.Concerning with Figure a, when the Cr2N is under biaxial
−5% strain,
the AFM4 configuration is favorable because of keeping the relation
Cr–N2 > Cr–N1 > Cr–N4 where the Cr–N2
has a slope of 0.122 (green dots) and 0.105 for Cr–N1 and Cr–N4
(black and red dots, respectively). The magnetic configuration switch
to AFM3 in the range from 1 to 3% strain with a relation Cr–N4
> Cr–N1 and Cr–N2; the Cr–N4 bond slope is
0.098
(red dots) and 0.107 for Cr–N2 and Cr–N1 (green and
black dots, respectively), persevering the relation of Cr2N unstrained. Although for 4 and 5% strain, the system prefers the
AFM4 behavior, where Cr–N2 > Cr–N4 > Cr–N1
and
the slope for Cr–N2, Cr–N1, and Cr–N4 bonds are
of 0.10, 0.134, and 0.119, respectively.In the meantime, under
larger values of uniaxial compressive strain
shows AFM4 due to Cr–N2 > Cr–N4 > Cr–N1
where
the Cr–N2, Cr–N4, and Cr–N1 have a slope of 0.060,
0.022, and 0.071 (green, red, and black dots, respectively), see Figure b. Nevertheless,
under −2 and −3% of compressive strain, the system switches
to AFM3 configurations because the bond relations are Cr–N4
> Cr–N2 > Cr–N1 with a slope of 0.022, 0.060,
and 0.071
for Cr–N4, Cr–N2, and Cr–N1, respectively (red,
green, and black dots, respectively). Under tensile strain, the system
has AFM4 characteristics due to Cr–N2 > Cr–N1 >
Cr–N4,
where Cr–N2 and Cr–N1 have a slope of 0.045 and 0.122,
respectively (green and black dots, respectively) but for Cr–N4
displays a slope of 0.006 (red dots).Regarding variation of
the Cr magnetic moment magnitude, it maintains
a dependence with the Cr layer distance, see Figure . In the other words, under biaxial and uniaxial
compressive strain, the Cr magnetic moment magnitude decreases to
±3.12 μβ and ±3.18 μβ, respectively, in comparison with unstrained MXene ±3.23 μβ. However, under biaxial and uniaxial tensile strain,
the magnitude increases to ±3.30 μβ and
±3.27 μβ, respectively. It could be associated
with the inverse magnetostriction effect, where the magnetic properties
change after applying mechanical deformation, as shown in some 2D
systems.[63−65] This could be further used to combine MXene with
other 2D materials and produce VdW heterostructures.[55]
Figure 8
Cr and N magnetic moment of the Cr2N unstrained and
biaxial and uniaxial compressive/tensile strain.
Cr and N magnetic moment of the Cr2N unstrained and
biaxial and uniaxial compressive/tensile strain.Note that the magnetic moment magnitude displays
a major increment
or decrement when the Cr2N is under compressive and tensile
biaxial strain because the distance between Cr layer tends to be larger
than that under uniaxial strain, as shown in Figure S4 of Supporting Information. Therefore, as the system is strained,
the magnetic moment of Cr enhances, as shown in Cr2NO2.[38] Furthermore, the N atoms have
induced magnetic moment either under uniaxial or biaxial strain of
the order of ±0.12 μβ.Based on
the stable magnetic configurations after applying compressive
or tensile strain, the charge transfer was studied by the electron
localization function (ELF) along the (001) plane. Figure shows a Cr2N MXene
top view of the ELF, where the first, second, and third columns from
left to right correspond to compressive strain, strain-free, and tensile
strain, respectively.
Figure 9
ELF results of the Cr2N MXene under biaxial/uniaxial
compressive strain, unstrained, and under biaxial/uniaxial tensile
strain.
ELF results of the Cr2N MXene under biaxial/uniaxial
compressive strain, unstrained, and under biaxial/uniaxial tensile
strain.ELF analysis allows a direct observation of the
change of chemical
bonding, the regions close to the unity (red areas) contain many localized
electrons, which indicates a region around a nucleus or in a very
strong covalent bonding condition. Values close to zero (blue areas)
represent the regions with low electron density, and the values close
to 0.5 (green areas) correspond to a uniform electron gas where the
bonding might have a metallic character.[66,67]It can be noted that for unstrained Cr2N, the Cr
atom
electrons are transferred to N atoms, then the electron concentration
is located around N atoms, characteristics of ionic bonds.[68−70] Besides, after applying biaxial compressive strain, N atoms preserve
the electron distribution. Nevertheless, under uniaxial compressive
strain, the electron dispersion of N atoms is not uniform, the higher
electron concentration is oriented in the direction to Cr atoms that
the total electron transferred; meanwhile, the region with values
close to 0.5 is oriented toward Cr atoms with a low electron density.
Instead, electron clouds rise around Cr atoms that could propitiate
a covalent bond with N atoms when the MXene is under biaxial and uniaxial
tensile strain; this behavior is discussed with the band structure
hereinafter.To explore electronic properties, the band structure
was calculated
based on the stable magnetic configurations after applying compressive
or tensile strain. The top and bottom graphs, as shown in Figure , correspond for
upper and lower limits of biaxial and uniaxial strain, respectively.
The compressive and tensile strain upper limits where the Cr2N is dynamically stable in the interval from −5% < ε
< 5%, strains were plotted. In all plots, the Fermi level is the
energy reference. The Cr2N MXene free-strain has a metallic
behavior, which is preserved under compressive strain. Nevertheless,
under tensile strain, it presents an indirect band gap, in which the
valence band maximum coincides along the G-M direction and conduction
band minimum locates at K-point. The band gap is of 0.16 and 0.05
eV for biaxial and uniaxial tensile strain, respectively. As shown
under tensile strain ELF, the increment of electron density around
Cr atoms could cause a covalent bonding. Band structures for all compressive
and tensile strain percentages can be found in Figures S5 and S6 in Supporting Information.
Figure 10
Band structure of MXene
Cr2N under biaxial strain, (a)
compressive, (b) without strain, and (c) tensile strain. The Cr2N with uniaxial strain, (d) compressive strain, (e) without
strain, and (f) tensile strain.
Band structure of MXene
Cr2N under biaxial strain, (a)
compressive, (b) without strain, and (c) tensile strain. The Cr2N with uniaxial strain, (d) compressive strain, (e) without
strain, and (f) tensile strain.As semiconductor MXenes, where the band gap is
controllable with
respect to various biaxial strains,[71] the
Cr2N MXene displays a similar behavior where it preserves
AFM characteristics. Note that in this case, we do not consider another
band gap correction due to this behavior, which is not experimentally
reported yet, we only consider the appropriate Hubbard parameter,[37].[38]
Conclusions
We have performed a comprehensive study
of the effect of biaxial
and uniaxial stress on the structural, electronic, and magnetic properties
of Cr2N MXene through first-principles simulation. The
OPG of the MXene can be continuously tuned via external compressive
or tensile strain, preserving the structural stability. After applying
an appropriate strain, the MXene experiments a magnetic transition
from AFM3 to AFM4 configurations. The MAE displays that the unstrained
MXene has an out-of-plane spin alignment and in-plane under biaxial
compressive strain where the magnetic moment magnitude of the Cr atoms
decreases or increases if the MXene is under compressive or tensile
strain. Furthermore, the band structure graphs indicate that the MXenes
under compressive strain preserve the metallic property; nevertheless,
under tensile strain, it has a little indirect band gap. These properties
extend the potential applications in the spintronics area as long
as they can be grown on substrates with high lattice mismatch or employed
with other 2D materials and produce VdW heterostructures, owing to
the tunable electronic and the Cr spin orientation by the compressive
or tensile strain applied.
Authors: K S Novoselov; A K Geim; S V Morozov; D Jiang; Y Zhang; S V Dubonos; I V Grigorieva; A A Firsov Journal: Science Date: 2004-10-22 Impact factor: 47.728
Authors: Michael Naguib; Murat Kurtoglu; Volker Presser; Jun Lu; Junjie Niu; Min Heon; Lars Hultman; Yury Gogotsi; Michel W Barsoum Journal: Adv Mater Date: 2011-08-22 Impact factor: 30.849
Authors: Artem V Kuklin; Alexander A Kuzubov; Evgenia A Kovaleva; Natalya S Mikhaleva; Felix N Tomilin; Hyosun Lee; Pavel V Avramov Journal: Nanoscale Date: 2017-01-05 Impact factor: 7.790