Antiferromagnetism in the van der Waals layered spin-lozenge semiconductor CrTe3

1.2 MB·

by  Michael A. McGuire

Antiferromagnetism inthe vander Waalslayeredspin-lozenge semiconductor CrTe
3
MichaelA.McGuire,1,∗V.OvidiuGarlea,2SantoshKC,1ValentinoR.Cooper,1JiaqiangYan,1HuiboCao,2andBrianC.Sales1
1MaterialsScienceandTechnologyDivision,OakRidgeNationalLaboratory,OakRidge,Tennessee37831USA
2QuantumCondensed MatterDivision,OakRidgeNationalLaboratory, OakRidge, Tennessee37831USA
The crystallographic, magnetic, and transport properties of the van der Waals bonded, layered compound
CrTe3 have been investigated on single crystal and polycrystalline materials. The crystal structure contains
layersmadeup of lozenge shaped Cr4 tetramers. Electricalresistivitymeasurements show thecrystalstobe
semiconducting,withatemperaturedependenceconsistentwithabandgapof0.3eV.Themagneticsusceptibil-
7 ityexhibitsabroadmaximumnear300Kcharacteristicoflowdimensionalmagneticsystems.Weakanomalies
1 areobservedinthesusceptibilityandheatcapacitynear55K,andsinglecrystalneutrondiffractionrevealsthe
0 onsetoflongrangeantiferromagneticorderatthistemperature.Stronglydispersivespin-wavesareobservedin
2 theorderedstate. Significantmagneto-elasticcouplingisindicatedbytheanomaloustemperaturedependence

r ofthelatticeparametersandisevidentinstructuraloptimizationinvanderWaalsdensityfunctionaltheorycal-
a culationsfordifferentmagneticconfigurations. Thecleavabilityofthecompoundisapparentfromitshandling
M andisconfirmedbyfirstprinciplescalculations,whichpredictacleavageenergy0.5J/m2,similartographite.
Basedontheseresults,CrTe3isidentifiedasapromisingcompoundforstudiesoflowdimensionalmagnetism
2 inbulkcrystalsaswellasmagneticorderinmonolayermaterialsandvanderWaalsheterostructures.
2

] I. INTRODUCTION were identified as van der Waals layered antiferromagnets
l
e [23],andtheyhavebeenrevisitedrecentlyinlightoftheirpo-
-
r Electronic peculiarities and proposed applications of tential for studying monolayer materials [24–26]. Although
st graphene[1,2]ignitedintenseresearchintotwo-dimensional antiferromagnetic materials are in some ways less “func-
t. materialscomposedoflayersheldtogetherbyvanderWaals tional”thanferromagneticmaterials,interestinthemisgrow-
a bonding.Effortstoextendthisresearchtoothermaterialsled, ingasideasfortheiruseasrobustspintronicmaterialsdevelop
m
for example, to the discovery of interesting and potentially [27–29].Inthepresentmanuscriptwereporttheresultsofour
- useful optoelectronic behaviors in ultra-thin transition metal recentinvestigationofthelayeredantiferromagnetCrTe3.
d
n dichalcogenides [3–6], providing further demonstrations of ThecompoundCrTe3wasfirstreportedbyKleppandIpser
o newphysicsemergingasbulkmaterialsarereducedtomono- [30,31],andreceivedlittlesubsequentattention.Itadoptsthe
c layers. Interest has also risen in exploring van der Waals uniquelayeredcrystalstructureshowninFig.1athatcontains
[ heterostructures[7], which requires a library of layered ma- tetramersofCratomsarrangedinarhombusorlozengeshape.

2 terials that can be mechanically exfoliated and recombined This structure is described in detail in the literature [31–33]
v in customized stacks. The incorporation of materials with and in the discussion below. Canadell et al. [33] identified
1 complementary functionalities, including magnetism, holds CrTe3 asaMott-Hubbardinsulatorbasedonelectronicstruc-
2 promiseforthedevelopmentofnewphysicsanddevicesthat ture calculations and the observation of semiconducting be-
6 can be controlled by external fields. While the set of two- haviorinelectricalresistancemeasurements,butwereunable
8
dimensional materials beyond graphene and transition metal tocharacterizethemagneticpropertiesduetothepresenceof
0
dichalcogenidescontinuestoexpand[8–10],therearestillrel- stronglymagneticimpuritiesinpowdersamples.
.
1 atively few studies of easily cleavable magnetic compounds We have grown single crystals of CrTe and have stud-
3
0
andinterestinsuchmaterialsisgrowing. iedthestructural,thermal,magnetic,andtransportproperties
7
Recently, several investigations of van der Waals lay- of the material using x-ray and neutron diffraction, physical
1
: ered ferromagnets have been reported, including CrSiTe3, propertymeasurements,inelasticneutronscattering,andfirst
v
CrGeTe3, and CrSnTe3 [8, 11–14], Fe3GeTe2 [15–17], and principlescalculations. Wefindveryanisotropicandunusual
i
X chromium trihalides [18–22]. Decades ago the MPS3 and thermalexpansionbelowroomtemperature,withevidenceof
r MPSe3familiesofcompounds(M=divalenttransitionmetal) strong magneto-elastic coupling as in-plane magnetic corre-
a lationsdevelop. The compoundis easily cleavable, which is
clear from handlingthe crystals and from density functional
theorycalculationsincorporatingmagnetismandthe vander
∗[email protected] Waals interactions. These calculations predict a band gap
of 0.26eV for a magneticallyorderedstate, close to the val-
Notice: This manuscript has been authored by UT-Battelle, LLC un-
uesdeterminedfromelectricalresistivitymeasurementsnear
der Contract No. DE-AC05-00OR22725 with the U.S. Department of
Energy. The United States Government retains and the publisher, by roomtemperature. Themagneticsusceptibilityfollowsqual-
acceptingthearticleforpublication, acknowledgesthattheUnitedStates itativelythebehaviorexpectedforatwo-dimensionalantifer-
Government retains a non-exclusive, paid-up, irrevocable, world-wide romagnet.Alternatively,thedatacanbedescribedbyadapting
license to publish or reproduce the published form of this manuscript,
aspin-lozengemodelpreviouslydevelopedforothermaterials
or allow others to do so, for United States Government purposes. The
Department of Energy will provide public access to these results of containingspin-3/2tetramerslikethosefoundinCrTe3. Low
federally sponsoredresearchinaccordance withtheDOEPublicAccess dimensionalmagnetic correlationsdevelopaboveroom tem-
Plan(http://energy.gov/downloads/doe-public-access-plan). perature, and magnetic order is observed in neutron diffrac-
2
tion measurements below T =55K. Moments are arranged
N
inanup-down-up-downpatternaroundtheperimetersofeach
lozenge-shapedtetramers,andthelong-rangemagneticorder
consists of stripe-like antiferromagnetic arrangement of the
tetramerswithineachlayer,withlayersstackedantiferromag-
netically. Weak anomalies are observedin the heat capacity
and magnetic susceptibility at T . Inelastic neutron scatter-
N
ing reveals dispersive magnetic excitations at low tempera-
ture,supportingthepresenceofnon-negligibleinter-tetramer
interactions.Togethertheexperimentalandtheoreticalresults
presentedheresuggestCrTe3tobe(1)aninterestingmaterial J1 J1
in which to study low dimensional magnetism in bulk crys- J
2
tals,(2)aneasilycleavablematerialforinvestigatingmagnetic J J
1 1
monolayers or few layer systems, and (3) a candidate semi-
conductingmaterialforincorporatingmagnetismintovander
Waalsheterostructures.
II. PROCEDURES
CrTe powderwasproducedbyreactingCrpowderandTe
3
shot in evacuated and sealed silica ampoules. The elements
weremixedina1:3molarratioandheatedto700◦Candheld
forseveralhours,thencooledquicklyto425◦Candannealed
for about 24 hours. The resulting sample was single phase
(d) 0.5
CrTe by powder x-ray diffraction, but some ferromagnetic
3
Cr Te was detected by magnetization measurements. This
5 8
0.4
impuritycouldbe reducedin concentrationby annealingthe
ppccaoorolmwldydpuesocersepidataitorbasnytiemleidkxilefcarerCosmtrseTmTtehe3pe.1ess.hraaomttuprinelest,hionertsbhayemspetaraertmsienpngocewulieothfbTuateTpevh-arypiscoihr- 2E - E (J / m)000..23
Singlecrystalsweregrownbytwomethods. Thefirstem-
ployedahalidefluxconsistingofamixtureofKClandAlCl 0.1
3
in a 45:55 molar ratio (m.p. 220◦C). Working in a helium
filled glovebox,about100mg of CrTe powderproducedas 0.0
3
0 1 2 3 4
describedabovewasaddedtothemixtureofdrysaltsinasil-
(d - d) / d
ica tube (9mm I.D., 1.5mm wall thickness) that was sealed 0 0
under vacuumwithoutexposureto air. The tube was heated
inahorizontalfurnacesothatoneendwasheldat450◦Cand FIG.1.(a)ThecrystalstructureofCrTe3,showingthelayersstacked
the other at 425◦C. After several days to one week the fur- along the a-axis that are formed by corner and edge sharing Cr-
centered octahedra (green) with Te atoms (yellow) at the vertices.
nacewasturnedoffandthetubecooledtoroomtemperature.
Thedark lines inthe plan view of thesingle layer represent Te-Te
Platelike crystals were recovered by washing the flux away
bondsformingdimersandtrimers.AlsoshownareasingleCr4Te16
withwater. Thismethodproducedmm-sizedthincrystalslike unit and the lozenge shaped Cr4 tetramer with magnetic exchange
thoseshowinFig.1b.Thesecondcrystalgrowthmethodused interactionslabeledbyJ1andJ2.(b)SinglecrystalsofCrTe3grown
excessTetogrowCrTe3 directlyfromthemelt. Mixturesof fromanAlCl3-KCleutecticmelt.(c)SinglecrystalsofCrTe3grown
CrandTecontaining1-3atomic%Crwereplacedinanalu- from excess Te. (d) DFT-calculated energy as a function of layer
minacruciblecoveredwithanaluminafrit[34],andheatedto separationinCrTe3 indicatingacleavageenergyof0.5J/m2.
1050◦Candheldfor16h,cooledto600◦Candheldfor24h,
thencooledatarateof1.5◦Cperhourto455◦C.Atthistem-
peraturetheexcessTewasremovedbycentrifugation.Crystal
producedbythismethodareshowninFig. 1candweretypi- using a PANalytical X’Pert Pro MPD powder diffractome-
callyseveralmmonasideandoftengrewinthick,blocklike ter (Cu-K radiation) with an Oxford PheniX cryostat and
α1
forms with thicknesses up to several mm, but are easily de- a Bruker SMART APEX CCD single crystal diffractometer
laminatedintothinsheets. IncreasingtheCrconcentrationin (MoK radiation). PowderdatawasanalyzedusingFullProf
α
themeltto4%producedsinglecrystalsofCr5Te8 insteadof [36]. Single crystal data were analyzed using SADABS for
CrTe3,consistentwiththepublishedphasediagram[35]. absorption corrections, XPREP for symmetry analysis, and
Powderandsinglecrystalx-raydiffractionwereperformed the ShelX suite for structuralsolutionand refinement. Mag-
3
netization measurements were conducted using a Magnetic
Property MeasurementSystem (Quantum Design). Heat ca-
0.0
pacityandelectricalresistivitymeasurementswereperformed
withaPhysicalPropertyMeasurementSystem(QuantumDe-
sign). Electrical contacts were made using silver paste and
-0.5
platinumwires. Heatcapacitywas measuredonsingle crys- K V
talsamples, withmeasurementsdownto 380mK carriedout 95 a
2 b
usingtheHelium-3Option. o -1.0 c
usiNngeutthroenPpOowWdGerEdNiffirnascttriuomnemnetaasutrtehmeeSntpsawllaetrieonpeNrfeourmtroend ative t layer sp.
el -1.5
Source (SNS) at Oak Ridge National Laboratory. For these e r
measurements, the powder sample was loaded into 8mm g
n
a
diameter vanadium can, and cooled down to 10K using a h
c
closed-cycle-refrigerator. Two frames with center neutron- nt 0.0
wavelengthsof1.333A˚ and2.665A˚ wereusedforcollecting ce
dataovera sufficientlylarged-spacingrange(0.5A˚ to 10A˚) per

attwodifferenttemperatures:10Kand300K.Atemperature
-0.1
dependence study was carried out by collecting data contin-
uouslyusingthe2.665A˚ framewhilecoolingthesamplebe-
tween300Kand10Katanominalrateof0.5K/min.Thedata
-0.2
wererebinnedintodatasetsevery10Kwithanominalcount-
ingtimeof20minutes. Thestructuraldatawasrefinedusing
FullProf [36]. Neutron diffraction study of a single crystal 0 50 100 150 200 250 300
specimen(identicaltothatusedforthemagnetizationstudy) T (K)
wasperformedusingtheHB3A4-circlediffractometeratthe FIG.2. PercentchangeinlatticeparametersofCrTe3uponcooling
High Flux Isotope Reactor. Data were collected using the from295Kdeterminedfrompowderneutrondiffractiondata.
neutron wavelength of 1.546 A˚. Inelastic neutron scattering
(INS) measurements were performed using the hybrid spec-
trometer HYSPEC at the SNS. HYSPEC is a highly versa-
approximated with the generalized gradient approximation
tiledirectgeometryspectrometerthatcombinestime-of-flight
(GGA)ofPerdew-Burke-Ernzerhof(PBE)functionals[45]as
spectroscopy with the focusingBragg optics [37]. The inci-
wellasthevdW-DF-optB86bfunctional[38–40,46]inorder
dentneutronbeamismonochromatedusingaFermichopper
toincorporatevanderWaalsinteractionduringstructuralopti-
and is then vertically focused by Bragg scattering onto the
mization.TheMonkhorst-Pack[47]k-pointsamplingmethod
samplepositionbyhighlyorientedpyrolyticgraphite.Forthe
in the Brillouin zone with a 4x4x4 and a 8x8x8 meshes for
INS measurements, approximately5g of CrTe powder was
3
ionic and electronic optimization, respectively. The energy
loaded in an aluminum can and placed in an Orange cryo-
cutoff was 500eV and the criteria for energyand force con-
stat capable of reaching1.5K. Data was collected with inci-
vergencearesettobe1×10−4eVand0.01eV/A˚,respectively.
dent energies E =50meV and 35meV, and Fermi chopper
i
frequencyof300Hz.
Density functional theory calculations were performed in
III. RESULTSANDDISCUSSION
ordertounderstandtheatomic,magnetic,andelectronicprop-
erties of CrTe . The cleavage energyis calculated using the
3
spin polarized vdW-DF-C09 functional [38–41] with norm A. Crystalstructureandthermalexpansion
conservingpsedopotentialusingtheQuantumEspressopack-
agev5.4.0[42],inwhichthespinisincludedinthenon-local Diffractiondata collected in this study are consistent with
partof the exchange-correlationfunctional. For these calcu- the published crystal structure of CrTe [31], and crystallo-
3
lations a model containing six layers per unit cell was con- graphicparametersdeterminedatseveraltemperaturescanbe
structed that included 192 atoms. The plane wave cut off foundintheSupplementalMaterial[48]. Thelayerednature
was set to 80Ry and the Brillouin zone sampling used for of the compound is apparent in Fig. 1a, where the van der
the supercell was 1×3×3. This approach does not, how- Waals gapseparatinglayersof compositionCrTe3 is visible.
ever,allowautomatedrelaxationandenergyminimization,so A plan view of a layer is also shown. The layers are made
forthestructuraloptimizationstheViennaAb-initioSimula- up of Cr Te units (Fig. 1a) comprising four edge-sharing
4 16
tion Package (VASP version 5.3.5) [43] with the projector- CrTe octahedra. The octahedra share corners with those in
8
augmented wave (PAW) [44] potentials was used. In both neighboringCr Te unitstoformthetwodimensionallayers.
4 16
codes, 3p6 4s1 3d5 forCr and5s2 5p4 forTe wereexplicitly ThefourCratomsin eachunitarearrangedin arhombusor
included as valence electrons in the pseudopotentials. Bulk lozengeshape.Theintra-lozengeCr−Crdistanceslabeledby
CrTe with various magnetic configurations were relaxed to J andJ inFig. 1aare3.62−3.64A˚ and3.89A˚,respectively,
3 1 2
get the optimized geometry. The exchange-correlation was so no Cr-Cr chemical bonding is expected (the Cr−Cr dis-
4
tanceinCrmetalis2.5A˚).Thereare,however,shortdistances
betweenTeatomsonneighboringCr4Te16units,shownbythe 105
darklinesintheplanviewinFig. 1a,formingTe dimersand
2
Te trimers [31]. Such bondingbetween anions is relatively CrTe3
3
commonintelluridecompounds[32]. Simpleelectroncount- 104 crystal 1, H = 0
crystal 2, H = 0
ing gives oxidation states of zero for the Te atoms with two
crystal 2, H = 50 kOe
bonds (centers of the trimers), 1- for the Te atoms with one 3
bond (dimers and ends of trimers), and 2- for the Te atoms m) 10
c
bondedonlytoCr. Thisresultsintheexpectedoxidationstate m-
of3+forCr. Firstprinciplescalculationsindicatestrongco- Oh 102
valencyin this material, with nearly equalcontributionfrom (
CrandTeinstatesneartheFermilevel,asshownintheSup-
1
plementalMaterial[48]. 10
Asnotedabove,crystalsofCrTe areeasilyseparatedinto
3
0
thin sheets due to the van der Waals bonding between the 10
layers, suggesting these materials could be of some interest
in forming van der Waals heterostructures. To further sup- 0.002 0.004 0.006 0.008
-1
portandquantifythisobservation,firstprinciplescalculations 1/T (K )
were performed to estimate the cleavage energy, defined as
FIG.3. ElectricalresistivityofaCrTe3 crystalmeasuredinthebc-
the energy per unit area required to separate a crystal at the plane in zero magnetic field and in a magnetic field of 50 kOe di-
van der Waals gap into two. For the purposeof these calcu- rectedoutoftheplane.
lations,astructuralmodelwasbuiltthatcontainedsixCrTe
3
layers per unit cell and the distance (d) between two of the
layerswasgraduallyincreasedfromtheequilibriumvalue(d0
= 3.5 A˚), as shown in Fig. 1d. The figure shows the calcu-
lated energy relative to the equilibrium energy as a function
of (d − d0)/d0. The curve approaches a saturation value,
the cleavage energy, of about 0.5J/m2. This is comparable TeplanesoneachsideofaCrplane(Fig.1a).Thelayerspac-
to well knowncleavablematerialsused forstudies of mono- ingas definedaboveis the sum of these two distances. This
layermaterialsandconstructionofvanderWaalsheterostruc- analysis shows that the van der Waals gap distance does in-
tures,includinggraphite0.43J/m2[49],MoS 0.27J/m2[49], deed decrease upon cooling, by 0.2% between 250 and 100
2
CrSiTe and CrGeTe 0.35−0.38J/m2 [11], transition metal K,butthisiscompensatedbyanincreaseofnearlythesame
3 3
thio-andseleno-phosphates(MPS ,MPSe )0.35−0.55J/m2 amountinthelayerthickness,resultinginlittlechangeinthe
3 3
[50],andchromiumtrihalides0.3J/m2[19,51]. layerspacing. Itis expectedthattheincreaseinthicknessof
the layersuponcoolingis drivenbythe verystrongcontrac-
The temperature dependenceof the monocliniclattice pa-
tionofthein-planeblatticeparameterseeninFig.2a. Within
rameters,unitcellvolume,andlayerspacingdeterminedfrom
theCrsublattice,thein-planecontractionarisesmostlyfrom
neutron powder diffraction measurements are shown in Fig.
thecontractionofthetetramersthemselves,whichactuallybe-
2 with more details in the Supplemental Material [48]. The
comefurtherseparatedfromneighboringtetramersuponcool-
layer spacing is defined as the distance between neighbor-
ing. The Te-Te dimers and Te-Te-Te trimers are quite rigid,
ing layers measured perpendicular to the planes of the lay-
withintra-dimerandintra-trimerdistanceschangingbyabout
ers (along the a* reciprocallattice direction) and is equal to
a·sin(β). Very anisotropicthermalexpansionis observed,as 0.1% between 250 and 100 K, while distances between Te
atomsnotboundintothesepolymericunitsdecreasebyabout
isoftenthecaseforlayered,vanderWaalsbondedmaterials,
1%.
inwhichthebondingbetweenthelayersisweakcomparedto
theintralayerbonding.However,inCrTe ,thethermalexpan-
3
sion is largest along the b-axis, which lies within the layers, Inadditiontotheunusualrelativethermalexpansionamong
andthea-axisandlayerseparationhaveonlyaweaktempera- thedifferentcrystallographicdirections,anomalousbehavior
turedependence.Thisisseenmoreclearlyinthelowerpanel inthetemperaturedependenceofindividuallatticeparameters
ofFig. 2. isalsoseen(Fig. 2). Thisismostapparentinthelayerspac-
Toinvestigatetheoriginofthisunusualthermalexpansion ing,butthein-planelatticeparameterbandunitcellvolumeV
behavior,fullsinglecrystaldiffractiondatasetswerecollected alsobehaveinanunusualway. Inparticular,negativecurva-
at 250, 173, and 100K, and refined to determine accurately tureisobservedinthesedatafromroomtemperaturedownto
theatomicpositionsandinteratomicdistances. Resultsofthe about150K.Thesebehaviorsareexpectedtoberelatedtothe
refinements are included in the Supplemental Material [48]. onset of magnetic correlations, since first principlescalcula-
Knowledge of the coordinates of each Te atom allows mea- tionsdiscussedbelowshownotablevariationintheoptimized
surementofthevanderWaalsgap,definedastheperpendicu- latticeparameterswhendifferentmagneticconfigurationsare
lardistancebetweenTeplanesoneachsideofthegap,andthe used.Thusthepresentresultsindicatestrongmagneto-elastic
layerthickness,definedastheperpendiculardistancebetween couplingispresentinCrTe .
3
5
B. Electricalresistivity
The semiconducting nature of CrTe is illustrated by the
3
electrical resistivity (ρ), which was measured with the cur-
rent in the bc-plane of two crystals grown using a tellurium
flux (Fig. 3). The same qualitative behavior is seen in both
samples, buttheabsolutevaluesdifferbyabouta factorof2
over the entire temperature range. This is likely attributable
to uncertaintyin the actual thicknessthroughwhich the cur-
rentflowsinthiseasilydelaminatedmaterial. Comparisonof
datacollectedinzerofieldandina 50kOeappliedmagnetic
fieldindicatesnegligiblemagnetoresistance. Thetransportin
CrTe isclearlyactivated,withachangeinactivationenergy
3
occurringnearroomtemperature. Linearfitstolog(ρ)vs1/T
at high and low temperaturesare shown for both samples in
Fig. 3. From these fits, activation energiesof 0.07−0.08eV
and 0.14−0.15eV are determined at low and high tempera-
tures,respectively.Thelowtemperaturebehaviorlikelyarises
from activation of defects or impurities acting as donors or
acceptors. Intrinsicsemiconductingbehaviormayberespon-
sible forthe behavioraboveroomtemperature. If that is the
case,abandgapof0.28−0.30eVcanbeestimated. Anacti-
vationenergyof0.35eVhasbeenreportedbasedonresistiv-
itymeasurementsonacold-pressedpolycrystallinesampleof
CrTe , but that determination was made using data only be-
3
low300K[33].Interestingly,firstprinciplescalculations(see
[48])giveasimilargapof0.26eVinthemagneticallyordered
state.
C. Heatcapacity
The specific heat capacity (c ) of a CrTe single crystal
P 3
is shown in Fig. 4. The data reach 24.4J/mol-at./K at 200
K (Fig. 4a), close to the Dulong-Petit limit of 24.9J/mol-
at./K.Nolargeanomaliestypicallyassociatedwithlongrange FIG. 4. (a) Heat capacity of a CrTe3 single crystal. The weak
magneticorder are seen; however, close inspection revealsa anomalyobservednear53Kisshownintheinset.(b)Heatcapacity
weakanomalythatlikelyindicatesabroadlambda-likepeak between0.38and2Kcollectedinzeroand5Tmagneticfieldsshow-
centered at about53K (Fig. 4a, inset). Data were collected ingcP ∝T3behavior.Alinearfittothezerofielddataisshownand
throughthistransitioninzerofieldandinanappliedfieldof theresultingparametersarelistedontheplot.
50kOe,andnofieldeffectisobserved.
Lower temperature data on a single crystal was also col-
lectedtolookforadditionalanomalies.Theresultsareshown
D. MagneticProperties
in Fig. 4b. Debye-like behavior is seen to persist down to
380mK. A linear fit to c /T vs T2 for the data collected in
P
zero field is shown. The y-axis intercept of the fit is nearly Figure 5a shows the magnetic susceptibility (χ) measured
zero, as expectedfor a semiconductorwith no T-linear elec- on a single crystalbetween 2 and 380K with the field along
tronic contribution to the heat capacity. Assuming the heat the layer stacking direction (out of plane) and with the field
capacityinthistemperaturerangeisentirelyduetophonons, in the plane of the CrTe layers (in plane). Higher temper-
3
a Debye temperature of θ =170K can be determined (al- aturemeasurementswereperformedonasamplecomprising
D
though antiferromagnetic magnons would also contribute to foursinglecrystals. Figure5bisacompositeofthathightem-
the T3 term). This is consistent with the high temperature peraturedata (300−720K) andthe powderaveragefromthe
behaviorofc ,whichreaches95%ofthe3Ratthistemper- single crystal measurements shown in Fig. 5a. (2−380K).
P
ature. Data collected with a 50kOe magnetic field applied At higher temperature χ shows an unusual temperature de-
perpendiculartothebc-planeisshowninFig. 4aswell. The pendence,withabroadhumpatroomtemperature. ACurie-
magneticfieldisseentohaveanegligibleeffect. Weissmodelcanonlydescribethedataatthehighesttemper-
6
abovethelongrangeorderingtemperatureareresponsiblefor
(a) theweaknessoftheheatcapacityandmagneticsusceptibility
3.0 CrTe3 anomaliesnear55K.
H in plane Thebroadhumpinχissuggestiveoflowdimensionalmag-
H out of plane
2.5 neticcorrelations. Forexamplethesusceptibilitydatashown
in Fig. 5a are reminiscent of the quasi-2D antiferromagnet
ol) 2.0 K2V3O8,whichshowsabroadmaximumnear10Kandlong
m range magnetic order below 4K [55, 56], and layered thio-
3 cm / 1.5 ol) 0.8 phosphateslikeMnPS3,whichshowsabroadmaximumnear
-3 10 3 m /m 55 K 1p2re0taKtioanndolfotnhgermanaggeneotridcerdabtealoaws 7ar8isKin[g57fr,o5m8].2DThceorinretelar--
( 1.0 -3 0 c 0.6 tionsisconsistentwiththelayerednatureofthecrystalstruc-
1
( ture of CrTe3; however, since the CrTe3 layers themselves
0.5 0.4 are made up of Cr4Te16 units containing tetramers of Cr, a
40 50 60 70 80
zero-dimensionalormolecularmagnetismviewpointcanalso
T (K)
be considered. Magnetism associated with lozenge shaped
0.0 tetramers formed by spin-3 magnetic ions like those found
0 50 100 150 200 250 300 350 2
inCrTe hasbeenstudiedinseveralsystems[59–62], byas-
T (K) 3
sumingmagneticallyisolatedtetramerswithintra-tetramerin-
(b)
3.0 teractionsdescribedbyJ1 andJ2 definedin Fig. 1a. Results
of fitting the the magnetic susceptibility of CrTe using the
3
2.5 model of Drillon et al. [61], assuming g=2 and a spin of
mol) 3/2 per Cr, are shown in Fig. 5b. The model works reason-
3 m / 2.0 ably well down to 350K, and gives J1/kB=-39.9(1)K and
J /k =35(2)K.Themodeldoesnotworkwellatlowertem-
c 1.5 2 B
-3 0 Curie-Weiss model peratures, likely due to the other magnetic interactions that
(1 1.0 spin-lozenge model are not taken into account. Since long rangemagnetic order
is observed, it is assumed that non-negligible inter-tetramer
0.5 interactions are present in CrTe . The same was noted for
3
Na RuO by the authors of Ref. 63, and it was concluded
3 4
0.0
thatthenoninteractingdimerortetramerapproximationisex-
0 100 200 300 400 500 600 700
pected to be violated as a result. However, it is interesting
T (K)
to note that the negative J and positive J determined by
1 2
FIG.5. (a) Magnetic susceptibilityof CrTe3 measured on asingle thefitwouldfavoran“up-down-up-down”spinconfiguration
crystalwithafieldof5Tappliedinplane(inthebcplaneinwhich aroundtheperimeterofthelozenges.
the layers lie) and out of plane (along a*, the stacking direction).
Neutronpowderdiffractionwasusedtolookforfurtherev-
Theinsethighlightstheanisotropydevelopingbelowabout55K.(b)
idence of magnetic ordering in CrTe . Comparison of data
Resultsof fittingthe high temperature magnetic susceptibility data 3
usingmodelsdescribedinthetext. collected at 300 and 10K reveals the presence of additional
scattering at 10K that is absent at higher temperatures (see
Supplemental Material [48]). No additional scattering was
observedin x-raydiffractionbetween300and20K, indicat-
atures(Fig. 5b). Fitting of data above475K givesan effec- ing the feature noted in Fig. 6a is magnetic in nature. The
tivemomentof4.0µ perCr(expect3.87µ forCr3+)anda observation of this magnetic Bragg peak, which is centered
B B
Weiss temperatureof-285K, indicatingrelativelystrongan- near Q=0.945A˚−1 (d=6.65A˚), indicates the onset of mag-
tiferromagneticinteractionsarepresent. neticorder.
Inspection of χ near the temperature at which the weak Further investigation using a single crystal sample at the
heatcapacityanomalywasnotedabove(seeFig. 4a)reveals HB3A diffractometer allowed identification of the magnetic
an anomaly in the magnetic susceptibility as well (Fig. 5a). orderingvector(wavevector)as k=(0.5, 0.5, 0.5) andthe or-
Upon cooling below about 55K anisotropy develops in the dering temperature T =56(1)K, which is consistent with
N
magnetic susceptibility due to a change in slope of the in- magnetizationandheatcapacityresults. Figure6ashowsthe
plane data. This is highlighted in the inset of Fig. 5a. This orderparametermeasurementofthe(0.5,1.5,-0.5)magnetic
behaviorisinterpretedastheonsetofmagneticorder,assup- Braggpeakasafunctionoftemperature.Thetemperaturede-
ported by the neutron diffraction results below. A similarly pendenceof the peak intensity below T was fit to a power
N
weak anomaly is observed in the magnetic susceptibility of lawI(T)∝(1-T/T )2β,whereβ isthecriticalexponent.This
N
the quasi-1D magnetic material CrSb near its Neel temper- is shown on the lower left inset of Fig. 6a. The data obeys
2
ature [52, 53]. In analogy with CrSb , which was shown to this relationship reasonably well down to about 16K below
2
havestronglyonedimensionalmagneticinteractions[54],itis T . Alinearfitonthelog-logplotinthistemperaturerange
N
expectedthatmagneticcorrelationsinCrTe3 developingwell givesavalueofβ=0.37(2),whichissimilartothetheoretical
7
(a) directions along all three crystallographic axes, leading to a
doublingofthemagneticunitcellwithrespecttothenuclear
cellinallthreedirections.Thenearestneighbortetramerscan
be arranged inside the bc plane in two equivalentconfigura-
tions (magnetic domains) that produce stripes aligned along
eitherthe[0,1,1]or[0,-1,1]directions. Thetwomagneticdo-
mains are displayed in Figure 6c and d. Our neutron data
indicatesanalmostequaldomainpopulation(0.502(7)%and
0.498(7)%).Therefinedmagneticmomentis2.0(2)µ ,with
B
the following components along the crystallographic direc-
tions: m = 2.1(1),m = 0.7(1),andm = 1.1(1)µ . The
a b c B
amplitudeoftheorderedmomentissignificantlysmallerthan
β = 0.37(2)
the 3µ moment expected for trivalentCr (S=3/2). Strong
B
covalencybetweenCrandTeordirectCr-Crchemicalbond-
ing could reduce the Cr moment; however, electronic struc-
ture calculations described below give the full 3.0µ mo-
B
mentforCr. Thusthe reducedmomentobservedbyneutron
diffractionmay beascribedto incompletemagneticordering
betweenthespin-lozenges,withresidualdisordermostlikely
(b) along the layer stacking direction. This is supported by the
neutronpowderdiffractiondata, in which the magnetic(0.5,
1.5,-0.5)isbroaderandmoreasymmetricthanthenearbynu-
clear100reflection[48]. Theintra-lozengeorderisexpected
tobecomplete,asevidencedbythesmallvalueofχandlack
ofaCurietailatlowtemperatures(Fig. 5).
a Stabilityofpossiblemagneticstructureswerecomparedus-
b c ing DFT calculations. Non-magnetic (NM), ferromagnetic
(FM), and several antiferromagnetic (AFM) structures were
(c) (d) considered. Table I shows the optimized lattice parameters
from DFT calculations performed using different magnetic
configurations and calculational methods. All calculations
used a 2x1x1 supercell model. As expected, neglecting the
c c long rangevan der Waals interaction(PBE) stronglyoveres-
b b timates the a-axis length. Of the magnetic models used, the
a a AFM2 structure is the closest approximation to the experi-
mental structure, which would require a 2x2x2 supercell to
representexactly.InAFM2(andAFM3)everylozengewithin
FIG. 6. (a) The order parameter (magnetic Bragg peak intensity) onelayerhasthesameup-down-up-downconfiguration,while
measured using the (0.5, 1.5, -0.5) reflection. The insets show an in the experimental structure each layer contains stripes of
ω-scanforthisreflectionmeasuredat4and300K,andthefitused lozengeswithup-down-up-downanddown-up-down-upcon-
todeterminethecriticalexponent β usingtheorderparameterdata figurations. All of the magnetic structures considered are at
downto40K.(b)ThemagneticstructureofCrTe3determinedfrom least330meVmorestablethantheNMstate. Amongthedif-
singlecrystalneutrondiffractionat4K.Panels(c)and(d)showtwo
ferent magnetic configurations, AFM2 and AFM3 are more
domainconfigurationswithinthelayers;solidandopencirclesrep-
stable than FM and AFM1 by about 30meV. Although this
resentmomentsdirectedoutofandintothepage,respectively. The
isnearthelimitofprecisionforthecalculations,itdoessup-
layersstackantiferromagnetically.
port the experimentally determined magnetic structure. The
calculations give a magnetic momentof 3.0µ per Cr. The
B
associated density of states in AFM2 state is includedin the
predictionforthe3DHeisenbergmodel. SupplementalMaterial[48].
To evaluate the possible spin configurations, a magnetic Somevariationinthe relaxedlattice constantsis observed
symmetryanalysishasbeencarriedoutusingthetoolsavail- whendifferentmagneticconfigurationareusedinthecalcula-
ableattheBilbaoCrystallographicServer[64].Thebestfitof tions(TableI).Inparticular,thein-planelatticeparameters(b
the43independentmagneticreflectionshasbeenobtainedus- andc)are aresignificantlyaffectedbythe inclusionof mag-
ingamagneticstructuremodeldefinedbythemagneticspace netism. Thisisidentifiedasanindicationofmagneto-elastic
group PS1 , shown in Fig 6b. In this model, each lozenge- couplinginCrTe3,whichwasalsonotedaboveinthetemper-
shaped tetramer has an up-down-up-downspin arrangement, aturedependenceofthelatticeparameters(Fig. 2).
with the alternating nonequivalent Cr sites carrying antipar- Results of inelastic neutron scattering experiments are
allel spins. The successive tetramers alternate their spins’ shownin Fig. 7. At 1.6K clear evidenceof dispersivemag-
8
TABLEI.Latticeparametersandenergies(relativetoNM,thenon-magneticstate)fromDFTcalculationsusingthemagneticconfigurations
andmethodslisted.ForthevdW-DFcalculationstheOptB86bfunctionalwasused.
configurations description method a(A˚) b(A˚) c(A˚) β(deg.) E-ENM (eV/F.U.)
NM non-magnetic vdW-DF 7.854 10.841 11.180 117.5 0.000
FM ferromagnetic vdW-DF 7.888 11.507 11.696 118.9 -0.330
AFM1 FMlayers,AFMstacking PBE 8.202 11.487 11.647 117.7 –
AFM1 FMlayers,AFMstacking vdW-DF 7.877 11.523 11.696 118.9 -0.336
AMF2 AFMlayers*,FMstacking vdW-DF 7.946 11.177 11.624 118.1 -0.363
AFM3 AFMlayers*,AFMstacking vdW-DF 7.935 11.178 11.623 118.1 -0.362
*layerscomposedoflozengeswithidenticalup-down-up-downspinconfigurations,seetext.
ergiesforaspin-3/2lozengemodelgiveninEq. 3ofRef. 63,
6
200 K one would expect to observe two localized magnetic modes
30 nits) at3.4meVand6.0meV.Instead,dispersivemagneticexcita-
V) 20 4 b. u tionsareobservedindicatingthepresenceofsignificantinter-
(me y (ar tgertoraumndersctaotuep.liPnrgesliamnidncaorynsainstaelnytsiwsiitnhdthicealtoesngth-raatntgheeoerxdceirtead-
E 10 2 nsit tion spectrum can be reproduced using a spin wave model
e
nt based on three exchange couplings, which includes the two
i
0 0 intra-tetramer couplings (J and J ) and one antiferromag-
1 2 3 4 5 1 2
|Q| (Å-1) netic inter-tetramerinteraction (J3). Similar dispersive mag-
netic excitations have been observed in Na RuO [63], and
3 4
6
coppertelluratecompoundsCu Te O Cl andCu Te O Br
30 1.6 K s) 2 2 5 2 2 2 5 2
nit [65],thatwerepreviouslyproposedtoconsistofcoupledspin
V) 4 b. u tetrahedra and exhibiting magnetic long-range order at low
e 20 ar temperatures.
m y (
E ( 10 2 nsit
e
int IV. SUMMARYANDCONCLUSIONS
0 0
1 2 3 4 5
|Q| (Å-1) CrTe3 is an easily cleavable magnetic material with a
unique layered crystal structure. The results presented here
suggest significant magneto-elastic coupling in CrTe and
FIG. 7. Contour plots of INS intensity from CrTe3 powder versus 3
energyandmomentumtransfermeasuredatT=200K(upperpanel) reveal low dimensional magnetic correlations extending to
and1.6K(lowerpanel). Thedatawerecollectedusinganincident aboveroomtemperatureandlongrangemagneticorderbelow
energyofEi=50meV. TN=55K.Thestructurecontainslozengeshapedtetramersof
Cr thatadoptan up-down-up-downspin arrangementaround
their perimeters in the magnetically ordered state. There is
stripe-like ordering among tetramers within planes and anti-
ferromagneticstackingbetweenplanes. Transportproperties
netic excitations are seen that could be associated with the
show semiconducting behavior consistent with a small band
magnetic ordering, which, according to the diffraction data,
gap well above T . This may arise from a Mott-Hubbard
arisesbelowabout56K.Thespin-wave-likeexcitationsprop- N
agate out of the ordering wave-vector, at Q≈0.945A˚−1 and mechanism since Cr3+ has half-filled t2g orbitals, although
stronghybridizationbetweenCr andTe is indicatedbyelec-
extend up to approximatively 25meV. The inelastic scatter-
tronic structure calculations. Based upon the observed elec-
ing intensity decreases with increasing wave-vector, follow-
tronicandmagneticproperties,bulkCrTe crystalsshouldbe
ingthedecayofthemagneticformfactor,whichconfirmsthe 3
of interest for the study of low dimensionalmagnetism, and
magnetic nature of these excitations. At 200K , the inten-
thecleavabilityofthematerialmakesitanexcitingcandidate
sity of inelastic scatteringbecomesmuchweakerand broad-
for exploring magnetism in monolayer materials and for in-
ensin bothenergyandmomentumspace, consistentwith an
corporationintovanderWaalsheterostructures.
evolutiontoaparamagneticstate. Phononscatteringbecomes
more prominent at larger wavevectors above 4A˚−1. For an
isolatedtetramerscenario,dispersionlessexcitationswouldbe
expectedwithaQdependencearisingfromthedynamicstruc- ACKNOWLEDGEMENTS
ture factor dependent on intra-tetramer atomic separations.
Usingtheexchangevaluesdeterminedfromthemagneticsus- ResearchsponsoredbytheUSDepartmentofEnergy,Of-
ceptibility,andthecalculationsfortheallowedexcitationen- fice of Science, Basic Energy Sciences, Materials Sciences
9
andEngineeringDivision,andScientificUserFacilitiesDivi- andAndrewF.Mayforhelpfuldiscussionsthroughthecourse
sion (neutronscattering). TheauthorsthanksBen S. Conner of the work, and Radu Custelcean for use of and assistance
withthesinglecrystaldiffractometer.
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