Table Of ContentManipulation of electronic and magnetic properties of M2C (M=Hf, Nb, Sc, Ta, Ti,
V, Zr) monolayer by applying mechanical strains
Shijun Zhao,1,2 Wei Kang,1,2,∗ and Jianming Xue1,3
1HEDPS, Center for Applied Physics and Technology,
Peking University, Beijing 100871, P. R. China
2College of Engineering, Peking University, Beijing 100871, P. R. China
3State Key Laboratory of Nuclear Physics and Technology,
School of Physics, Peking University, Beijing 100871, P. R. China
4
1
Tuningtheelectronicandmagneticpropertiesofamaterialthroughstrainengineeringisaneffec-
0
tivestrategytoenhancetheperformanceofelectronic andspintronicdevices. Recentlysynthesized
2
two-dimensional transition metal carbides M2C (M=Hf, Nb,Sc, Ta, Ti, V, Zr),known as MXenes,
r has aroused increasingly attentions in nanoelectronic technology due to their unusual properties.
a
In this paper, first-principles calculations based on density functional theory are carried out to in-
M
vestigatetheelectronicandmagneticpropertiesofM2Csubjectedtobiaxialsymmetricmechanical
strains. At the strain-free state, all these MXenes exhibit no spontaneous magnetism except for
1 Ti2C and Zr2C which show a magnetic moment of 1.92 and 1.25 µB/unit, respectively. As the
tensile strain increases, the magnetic moments of MXenes are greatly enhanced and a transition
]
l from nonmagnetism to ferromagnetism is observed for those nonmagnetic MXenes at zero strains.
al The most distinct transition is found in Hf2C, in which the magnetic moment is elevated to 1.5
h µB/unitatastrain of1.80%. WefurthershowthatthemagneticpropertiesofHf2Careattributed
- totheband shift mainly composed of Hf(5d) states. Thisstrain-tunablemagnetism can beutilized
s todesign futurespintronics based on MXenes.
e
m
. Two-dimensional(2D)materialshaveattractedagreat Intheapplicationsbasedonnanoelectronicdevices,an
t
a dealofattentionduetotheiruniquemechanicalandelec- essential requirement is the versatile ability to modulate
m tronic properties and numerous potential applications.1 the electronic and magnetic properties via external con-
- Very recently, a family of 2D materials was synthesized trols. Ithasbeenwellestablishedthattheelectronicand
d
by the exfoliationof the layeredternarytransitionmetal magnetic properties of materials can be tuned by apply-
n
carbides, which are known as MAX phase.2,3 The MAX ing mechanical strains.17,18 In particular, the effects of
o
c phases represent a large (more than 60 members) family strain will be more significant in 2D systems as demon-
[ of ternary layered machinable transition metal carbides, strated in graphene and other transition metal chalco-
nitrides,andcarbonitrides,whichpossessuniqueproper- genides such as MoS , NbS , NbSe and VSe .17,19 For
2 2 2 2 2
ties such as remarkable machinability, high damage tol- example, a uniaxial strain larger than 20% applied in
v
9 erance, excellent oxidation resistance, and high electri- graphene along the zigzag direction is predicted to open
5 cal as well as thermal conductivity.4,5 The MAX phases abandgapduetolevelcrossing.20Differentfrombulkma-
2 are layered hexagonal (space group P63/mmc) with the terialsinwhichstrainscanberelaxedbydislocationplas-
6 formula of M AX (n=1,2,3), where M represents an ticity or fracture, 2D materials are well suited for strain
n+1 n
.
1 early transition metal, A is an A-group element (mostly engineering. Fromexperimentalview point, strainin 2D
0 groups IIIA and IVA) and X denotes carbon or nitro- sheet can be achieved rather easily by manipulating its
4 gen. ThelayeredstructuremakestheexfoliationofMAX substrate.
1
phase feasible and by removal of the A group layer from In the present work, therefore, we study the effect of
:
v theMAXphase,2DMXenescanbeobtainedwhichshare mechanicalstrainsontheelectronicpropertiesofMXenes
Xi the structural similarities with graphene.6,7 of the form M2C (M=Hf, Nb, Sc, Ta, Ti, V, Zr). The
r Theextraordinarypropertiesof2DMXeneshavebeen influence of homogeneous biaxial tensile strain on these
a intenselyinvestigatedsinceitssuccessfullysynthesization MXenesaresystematicallyinvestigatedbasedondensity
experimentally.6–14 High conductivities and high elastic functional theory calculations. Our results demonstrate
moduliarefoundinMXenes.6–8Besides,theapplications that the Hf2C structure can be efficiently magnetizedby
of MXenes in Li-ion battery anodes and hybrid electro- simply applying a tensile strain, during which the struc-
chemical capacitors are also demonstrated.9,10 Most of tures of MXenes are still maintained. The effect of com-
thesynthesizedM X layersaremetallicwithnoband pressive strain is not considered in the present work be-
n+1 n
gap,althoughitisshownthattheelectronicstructurecan cause it is impractical for experimental implementation.
be modulated by appropriate surface terminations such Electronicstructurecalculationshavebeencarriedout
asoxygenandfluoride.6,15 However,previoustheoretical using the density functional theory as implemented in
studies indicate that the majority of the functionalized the Vienna ab initio simulation (VASP) code.21 The
MXene systems are nonmagnetic. For the “pure” MX- electron-ion interactions are described by Projector-
enes, only the Ti X (X=C,N) monolayers are mag- augmented-wave (PAW) pseudopotentials with semi-
n+1 n
netic due to the 3d electrons of surface Ti atoms.16 core states treated as valence states.22 The exchange
2
and correlation energies are treated within the general- To study the effect of strain on the electronic prop-
ized gradient approximation (GGA) according to PW91 erties of MXenes, we first relaxed the atomic positions
parametrization.23 To obtain the unstrained configura- as well as lattice vectors and obtained their optimized
tion of M X monolayer, both the atomic positions and structures. The calculated lattice parameters of M X
2 2
latticevectorsarefullyrelaxedwiththeconjugategradi- monolayer is summarized in Table I with available data
ent algorithm to obtain the equilibrium lattice constant. from literatures shown for a comparison.
Thelatticeconstantisthenincreasedgraduallytomodel
the biaxial strain, in which all atoms are optimized to
calculate the electronic structure. The convergence for TABLEI.Latticeparameters(in˚A)ofM2Xmonolayerdeter-
energyischosenas10−4eVbetweentwoconsecutiveself- mined with PW91 functional in this work. Available results
consistent steps and the atomic relaxation is performed from literatures computed from different functionals are also
until the interatomic forces are less than 0.01 eV/˚A. A included for a comparison.
plane wave cutoff of 520 eV is used for all the calcula- MXenes Hf2C Nb2C Sc2C Ta2C Ti2C V2C Zr2C
tions.
present 3.212 3.135 3.332 3.087 3.078 2.897 3.293
In our calculations, the M2X is represented by a 4×4 PBE24 3.076
supercellwithavacuumspaceof18˚Abetweentwoadja-
PBE25 3.0395
centlayerstoavoidinteractionsbetweenperiodicimages
DFTB26 3.33
ofslabsinthe z-direction. TheBrillouinzoneissampled
using a6×6×1Monkhorst-Packgridin relaxationcalcu- Wu-Cohen27 3.239 3.138 3.007 2.869 3.238
lations,while adensermeshof12×12×1isconsideredto
generate density of states and charge densities.
It can be seen that our results are in good agreement
ThesideandtopviewsofgeneralizedstructureofM2X with available theoretical calculations, which also vali-
MAxenes with hexagonal symmetry are illustrated in datesourapproachinpredictingthestructuralproperties
Fig. 1, which are constructed by removing “A” atoms oftheseMXenes. Notethatthereisstillnoexperimental
from corresponding bulk MAX phases. In Fig. 1(b), the values about the lattice parameters. Here it is helpful to
schematic illustration of the biaxial tensile strain are in- make a comparison of these lattice constants with their
dicated. Here, the strain is defined as ǫ=(a−a0)/a0 = correspondingMAXphases. TakingTi2AlC asanexam-
∆a/a0, where a0 and a is the lattice parameter of the ple, the lattice constanta of bulk Ti2AlC is 3.065˚A de-
unstrained and strained supercell, respectively. As de- termined from experiment,5, which is comparable to the
scribed previously, the structure of M2X suggest that calculated constant of Ti2C as shown above. Therefore,
it can bear a relatively large range of in-plane elastic it can be concluded that the structures of MXenes are
strains compared to the perfectly flat graphene and BN almost the same as those in MAX phases.
layer due to the possible deformation in the perpendicu-
After the stable structures of MXenes are obtained,
lar direction.19
we startto apply biaxialsymmetric strains to the lattice
to investigate the influence of strain on their electronic
and magnetic properties. Previous theoretical calcula-
tions based on density functional theory have revealed
that most of the MXenes are metallic. Indeed, our re-
sults demonstrate that all the investigated MXenes in
this study are metallic system with no energy gap. This
is still the case when strain is applied and the metallic
properties of these MXenes are not changed. However,
the magnetic properties are much affected. Here the to-
talmagneticmomentofMXenesas afunctionofapplied
strains are presented in Fig. 2.
As we can see, the magnetic properties of these MX-
enes can be effectively tuned by external strains. At the
strain-free state, only the Ti C and Zr C has magnetic
2 2
moment, which is 1.92 and 1.25 µ /unit respectively.
B
The results for Ti C is in good agreement with previ-
2
ouscalculationsof1.85µ /unit.16 Anoteworthyfeature
B
is that the Hf C display no magnetism although it is in
2
the same group as Ti and Zr in the periodic table. In
fact,ithasbeenreportedthatintheMAXphaseM AC,
2
this group elements (M=Ti, Zr and Hf) exhibit the low-
est bulk moduli than other MAX phases. The reason
FIG.1. (a)Sideand(b)topviewofM2C,wheretheMandX is interpreted as the weak M d-orbital and C p-orbital
atomsaredenotedbyorangeandyellowspheres,respectively. bonding in these materials.28 As the atomic number in-
3
creases, more carbon p electrons are participated in the )B
0.6
M-C bonding. In the case of MXenes, the same trend mnt ( 0.5 (a)
is observed. The p orbital of carbon atom hybridizes e 0.4
m
weakly with d orbitalof Ti, while a strong hybridization o 0.3 Hf
m
is observed between Hf(5d) and C(2p) orbitals. There- c 0.2 C
fore, the unsaturated Ti(3d) dangling bonds lead to the eti 0.1
n 0.0
magnetism in the Ti2C monolayer. On the contrary,the ag −0.1
M 0 0.02 0.04 0.06 0.08
strongbondinginteractionbetweenHfandCgivesriseto
no magnetism in Hf C, which will be discussed in more
2 −456 (b)
details below. V)
e
AllthemagneticmomentoftheseMXenesareelevated y ( −459
by applied strains, although they show different behav- g
iors. The most distinct variation is observed for Hf C, ner −462
2 E Total Energy
which turns from nomagnetism to ferromagnetism with
−465
a high magnetic moment of 1.70 µB/unit at a strain of 0 0.02 0.04 0.06 0.08
2%. In fact, the system becomes magnetic as long as 6
the strainis applied, with a linearlyincreaseof the mag- a) (c)
netic moment. At about 6% strain, the spin moment GP 4 s
isntrcareinass.esTshlioswinlydiacnadtesretmhaatinasslailgmhtosvtarcioantisotnanotftfohreslatrragienr ess ( 2 ss yxyx
applied on the Hf2C layer can induce a large change of Str 0 zz
the spin moment.
0 0.02 0.04 0.06 0.08
Strain
)
t
ni
u 2.0
/B FIG. 3. Per atom magnetic moment, total energy and stress
( Hf2C of Hf2C as a function of applied strain.
t 1.5 Nb2C
n Sc2C
e
m Ta2C
mo 1.0 TVi22CC InFig.3(b)and(c),wehaveshownthedependenceof
Zr2C the total energy and stress of Hf2C sheet on the applied
c
ti 0.5 strain. The total energy is monotonically increased with
e strain, indicating the structure is still stable when it is
n
g subjectedtothesestrainssincenophasetransitionisob-
a
M 0.0 served. This implies that the Hf2C monolayer can bear
a large elastic strain range. The smoothly increase also
0.00 0.02 0.04 0.06 0.08 suggests that the magnetic modulation is in the elastic
range and reversible. This feature is significant for prac-
Strain
ticalnanomechanicalcontrolofthepropertiesoftheMX-
enes systemin device applications. The in-plane stresses
FIG.2. DependenceofmagneticmomentsofvariousMXenes
on theapplied strain. of σxx and σyy are almost the same, which is the result
of biaxial symmetric strains.
Asaprototypeofstrain-engineeredmodulationonthe It is well established that the partially filled d charac-
magneticpropertiesofMXenes,wehavemadeadetailed ter of the transition metal atoms can induce significant
analysis on the interplay between the mechanical strain magnetism in materials. In our case, the magnetism is
andthe magnetic behaviorsfor Hf C. The magnetic mo- indeedinducedbytheHfatomasdemonstratedinFig.3.
2
ments of Hf and C atoms as a function of the applied TheHfatompossessestwo5delectrons. However,dueto
strain is represented in Fig. 3(a). It is shown that the the strongcovalentinteractionsbetweenHf andC inthe
magnetic moment of Hf starts to increase sharply when sandwiched structures, the monolayer MXene of Hf C
2
the strain is applied and saturates to a value of 0.5 exhibits no magnetism. This phenomena have been ob-
µ /atom at a strain of 5%. The increase of magnetic served in other monolayer structures such as NbS and
B 2
moment in the strain range up to 2% is nearly linear NbSe . In these materials, the strong ligand field owing
2
with respect to the strain, which means that the mag- to the covalent bonds tend to quench the magnetism of
netic property of Hf C is rather sensitive to the strain. the transition metal. When external strain is applied,
2
Ontheotherhand,thenonmagneticpropertyofCisnot the covalent bonding interactions inside Hf C is reduced
2
muchinfluencedbythestrain. Theseresultssuggestthat and result in the release of the feature of d electrons of
themagnetismofHf Cunderstrainsismainlyoriginated Hf and finally give rise to magnetism in the system. In
2
from Hf atoms. order to analyze the origin of the magnetism observed
4
above, we show in Fig. 4 the projected density of states ferromagnetismismainlyattributedtheHfsincethe un-
(PDOS) of Hf C monolayer under different strains. paired spin electrons are mostly concentrated on the Hf
2
atoms. Only a small fraction of spin density is located
at C atoms. This is consistent with the results shown in
30 (a)
unit) 15 HHff((55pd)) the PDOS in Fig. 4.
arb. 0 C(2p)
S ( −15
O
D
−30
30 (b)
unit) 15 HHff((55pd))
b. C(2p)
ar 0
S ( −15
O
D
−30
30 (c)
unit) 15 HHff((55pd))
arb. 0 C(2p)
S ( −15
O
D
−30
30 (d)
unit) 15 HHff((55pd))
b. C(2p)
ar 0
S ( −15
O
D −30 FIG. 5. The spin density distribution (ρ ↑ - ρ ↓) with the
−12 −9 −6 −3 0 3 positive portion denoted by yellow and negative denoted by
blue. The isovalue is set to be 1 × 10−4 e/˚A3.
Energy (eV)
The spin-resolved band structure of Hf C under dif-
2
FIG. 4. Evolution of PDOS of Hf2 along with biaxial sym- ferent biaxial strains is shown in Fig. 6, which clearly
metric strain: (a) 0.00%, (b)1.56%, (c)4.67% and (d)7.78%. displays the opposite shift of Fermi level in the majority
and minority spin bands when the strain is applied. As
It can be seen from Fig. 4(a) that the pristine Hf C is a consequence, the symmetric band structure becomes
2
ametallicsystemwheretheenergystatesneartheFermi asymmetrical due to the shift of conduction and valence
energy are mainly composed of Hf(5d) orbitals. In the bands, in accordance with the DOS plot. The energy
energy range from -5 to -2 eV, the states of C(3p) and bands in the vicinity of Fermi level determines the mag-
Hf(5d) hybridize, forming bands separated by a gap of netic behaviors as demonstrated above. The band split-
around 1eV from the Hf(d) bands. The metallic nature ting in this region changes Hf C to a magnetic metal.
2
ofHf Cisnotalteredbyappliedstrainsincethereareal- The effects of spin-orbit coupling (SOC) on the cal-
2
waysbandscrossingtheFermilevel. However,thesplitof culated magnetism are also evaluated. With the unit
bandisinduced. Thespin-upstatesofHf(5d)andHf(5p) cellofHf C, weperformedSOC calculationswhich treat
2
starttoshifttowardslowerenergies,whilethespin-down magnetism noncollinearly using quantization axis (0, 0,
statesshifttowardshigherenergies. Asaresult,themag- 1) (i.e., z axis) based on the charge density from no
netism is observed which is mainly contributed by the SOC. Although the inclusion of SOC lowers the total
Hf(5d) states. This magnetism is ascribed to the redis- energy about 1.42 eV, the calculated magnetic moment
tribution of atomic charges under external strain. is not influenced. This result is in line with previous
Closer examination of the PDOS reveals that the d calculations regarding the effects of SOC on magnetic
yz
and dxz states as well as dxy and dx2−y2 states of Hf are moment.29 Therefore, our conclusion still holds irrespec-
degenerated. Thelargestcontributionforthemagnetism tive of SOC.
is from the shift of d and d bands. This is in accor- We also checked the dependence of our results on the
yz xz
dancewiththebiaxialstrainweapplied. Sincethestrain functional we have used so as to give more reliability of
is symmetric, the degeneracy is not destroyed. our results. In this case, we have performed a set of cal-
The spin density plot at a strain of 1.56% is provided culationsaboutHf CwithPBEfunctionalwhichhasfre-
2
in Fig. 5. At strain free state, there is no spin density quentlyusedforthestudyofMXenes.24,25Theresultsin-
in the Hf C monolayer,which is the refection of its non- dicatethatthedependenceofmagneticmomentsofHf C
2 2
magnetic property. It is shown that the strain induced on applied strain is more sensitive for PW91 than PBE
5
2 als predict a non-magnetic to magnetic transition when
(a)
the strain is larger than 2%. Therefore, the main results
1 discussed in this paper are not influenced.
eV) Since the experimental synthesized MXenes are usu-
gy ( 0 ally terminated with oxygen-containing and/or fluoride
ner groups,wealsoexaminethe effectofstrainontheir elec-
E
-1 tronic structures. The results show that all the MX-
enes considered exhibit no magnetism upon fictionaliza-
-2
G K M G G K M G tion. This conclusion is also found in Ti2C in previ-
ous calculations.16 Our further simulation indicates that
2
(b) the nonmagnetic properties of H-, O- and F- functional-
ized Ti C monolayer is not changed along with applied
1 2
V) strains.
e
y ( 0 In2Dmaterials,aconventionalmethodtoinducemag-
g
er netism is to introduce vacancy or foreign atoms.30,31
n
E -1 However, the precise control of these structure is rather
difficult experimentally. Besides, the generated mag-
-2 netism in this way is often localized. Our results indi-
G K M G G K M G
cates that the magnetismof MXenes canbe switchedon
2 (c) and off facilely by applied strains. In experiment, these
strainscanbeachievedinacontrolledmanner,asdemon-
V) 1 strated recently in 2D materials such as graphene.32 At
y (e 0 strain-freestate,onlytheCr2Carefoundtobemagnetic
erg amongvariousMXenes,ourresultsthus broadenthe ap-
n
E plicability of MXenes in future spintronics.
-1
Insummary, the electronicand magnetic propertiesof
-2 recently synthesized MXenes subjected to external biax-
G K M G G K M G ial symmetric strain are investigated by virtue of first-
2 principles calculations based on density functional the-
(d)
ory. AlltheconsideredMXenesaremetallicinthestrain-
1 free state and the metallic characteristics are not influ-
V)
e encedevenwithalargeappliedstrains. Nevertheless,the
gy ( 0 magneticmoments ofthese MXenes areverysensitiveto
er
n strains. Among the studied MXenes, the magnetic mo-
E
-1
ment of Hf C exhibits a large variation which renders it
2
magnetic with a magnetic moment of 1.5 µ /unit at a
-2 B
G K M G G K M G strainof1.80%. Ouranalysisrevealsthatthemagnetism
isoriginatedfromthe shift ofHf(5d)bands. The present
workprovidesaroutetoharnessthemagneticproperties
of two-dimensional MXenes for spintronic applications.
FIG. 6. Spin-resolved band structure of Hf2 under different
biaxial strains: (a) 0.00%, (b)1.56%, (c)4.67% and (d)7.78%.
ACKNOWLEDGMENTS
ThisworkisfinanciallysupportedbytheNSFC(Grant
functional at small strains. Nevertheless, both function- No. 11274019).
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