Table Of ContentRearrangement of Van-der-Waals Stacking and Formation
T
of a Singlet State at = 90K in a Cluster Magnet
John P. Sheckelton,a,b Kemp W. Plumb,b Benjamin A. Trump,a,b Collin L. Broholm,b,c,d and
Tyrel M. McQueena,b,c,∗
7
1
0 Insulating Nb3Cl8 isalayeredchlorideconsistingoftwo-dimensionaltriangular layersofSeff =1/2
2
Nb3Cl13 clustersatroomtemperature. Magneticsusceptibilitymeasurementshowasharp,hysteretic
n
a droptoatemperatureindependentvaluebelowT =90K.Specificheatmeasurementsshowthatthe
J
9 transition is first order, with D S≈5 J·K−1·molf.u.−1, and a low temperature T-linear contribution
1
originating from defect spins. Neutron and X-ray diffraction show a lowering of symmetry from
]
el trigonal P3¯m1 to monoclinic C2/m symmetry, with a change in layer stacking from -AB-AB- to
-
r -AB′-BC′-CA′- and no observed magnetic order. This lowering of symmetry and rearrangement of
t
s
t. successive layers evades geometric magnetic frustration to form a singlet ground state. It is the
a
m
lowest temperature at which a change in stacking sequence is known to occur in a Van-der-Waals
-
d solid, occursinthe absence oforbitaldegeneracies, and suggests that designer 2-D heterostructures
n
o maybeabletoundergosimilarphasetransitions.
c
[
1
v
8
1 Introduction
2
5
5 Emergent phenomena among strongly interacting atoms or electrons, such as superconductivity1–3, charge
0
1. density waves4, topological insulators5,6, Kondo insulators7,8, and heavy fermions9, are at the forefront of
0
7 contemporary materials research. Geometrically frustrated magnets are a particularly illustrative class of
1
: stronglyinteractingsystemswherealargedegeneracyofelectronicstatesexistwithinasmallenergyregime
v
i comparedtothemagneticinteractionstrength. Sincetheelectronicdegeneracyarisesfromlatticesymmetry,
X
r geometrical frustration can destabilize the lattice. Here we show that a geometrically frustrated antiferro-
a
magnet built from small transition metal clusters10–15 can succumb to a symmetry-lowering distortion to
evade a degenerate magnetic ground state, even in the absence of orbital degeneracies. This phase change
alsoinvolvesachangeinstackingsequencebetweensuccessivecharge-neutralVan-der-Waals(VdW)bonded
layers.
Specifically, we report the discovery of a paramagnetic and trigonal to singlet and monoclinic phase
aDepartmentofChemistry,TheJohnsHopkinsUniversity,Baltimore,MD21218,USA.
bInstituteforQuantumMatterandDepartmentofPhysicsandAstronomy,TheJohnsHopkinsUniversity,Baltimore,MD21218,USA.
cDepartmentofMaterialsScienceandEngineering,TheJohnsHopkinsUniversity,Baltimore,Maryland21218,USA.
d NISTCenterforNeutronResearch,NationalInstituteofStandardsandTechnology,Gaithersberg,MD20899,USA.
∗E-mail:[email protected]
1
transitioninthecluster-basedmagnetNb Cl ,despiteeachNb Cl clusterharboringasinglyoccupied,non-
3 8 3 13
degeneratehighestoccupiedmolecularorbital(HOMO)andanapproximately1eVgaptodegeneratelowest
unoccupied molecular orbital (LUMO) states. As for Mo O clusters in LiZn Mo O 10, a formal electron
3 13 2 3 8
countyieldsoneS =1/2magneticelectronperNb Cl cluster,whicharearrangedonatwo-dimensional
eff 3 13
triangular lattice. Nb Cl and various stacking variations16–20 have been previously studied. The a -Nb Cl
3 8 3 8
polymorph,with -AB-AB- stacking, isknowntoundergoahystereticmagnetictransition21 withachange in
the magnetic signal at temperatures below T ≈ 90K. Here, this transition is studied via detailed structural
and physical property investigations of both powder and single crystals, revealing a dramatic trigonal to
monoclinic phase transition at T = 90K that quenches the magnetic response but without magnetic order,
i.e. asingletstate. Thereliefofgeometricfrustrationviaorbitalorderingandformationofmagneticorderor
spin singlets, is well-known in compounds containing first-order Jahn-Teller (FOJT) active ions or clusters,
such as NaTiO 22,23, NaVO 24, or GaNb S 25. A similar spin-Peierls distortion in 1D S = 1/2 systems,
2 2 4 8 eff
such as CuGeO 26, NaTiSi O 27, and the titanium oxychlorides/oxybromides28,29, can also be explained in
3 2 6
termsoforbitalordering30.
ThephasetransitiontoevadegeometricmagneticfrustrationinNb Cl appearstoproceedviaadifferent
3 8
route. ThestructuralphasetransitionbreakstheC symmetryoftheNb Cl clustersinamannerconsistent
3v 3 13
withasecond-orderJahn-Teller(SOJT)distortion,butwithadramaticchangeinNb Cl layerstackingfrom
3 8
-AB-AB- to -AB′-BC′-CA′-. That such a change in stacking of a VdW material can occur near liquid nitrogen
temperatureisremarkable,but canbe thoughtofasbeingdrivenbyabuckling ofinterfacialCl-atom layers
duetoaninter-layerelectronicinteractionandSOJTdistortioncombinedwithsingletformation. Ourresults
demonstratethe importance of considering multi-site effectsand statesfar from the HOMO in magnetically
frustratedmaterials,andthatchangesinVdWstackingsequencearepossiblewellbelowroomtemperature.
2 Methods
SinglecrystallineNb Cl wassynthesizedbyselfvaportransportinanevacuatedquartztubechargedwitha
3 8
stoichiometricamount of twice re-sublimed NbCl (Strem,99.99%) and powder Nb metal, used as is (Alfa,
5
99.99%). AtemperaturegradientofT =825oCtoT =835oCwasmaintainedoverthereactionvesselfor12
to14daysbeforecoolingto roomtemperature. All sampleswerehandled in agloveboxusing standard air-
freetechniques. High-resolutionsynchrotronX-raydiffractionmeasurements(SXRD)weretakenonpowder
samplesofgroundsinglecrystalsattemperaturesfromT=300KtoT≈90Kusingthepowderdiffractometer
atbeamline11-BMequippedwithaliquidnitrogencryostreamattheAdvancedPhotonSource(APS).Triple-
axis Neutron diffraction measurements of co-aligned Nb Cl single crystals were acquired from T = 300K
3 8
to T = 1.6K on the SPINS spectrometer at the NIST Center for Neutron Research (NCNR). SPINS was op-
erated with a fixed energy of 5 meV, flat analyzer, and a 58Ni guide - 80’ - 40’ - open collimation sequence.
2
-
P3m1
S = 1/2
c b
= Nb
a b = Cl c a
Figure1(a)RietveldanalysisofsynchrotronX-raydiffractiondataatT =300K.Blackdotsaredata,redlineisthe
calculatedfit,bluelineisthedifference,tickmarksareBraggreflectionsforNb Cl (black)andaminorimpurity,
3 8
NbOCl2(orange,0.3(2)wt%). ThehigherQdataaremultiplied×20(4≥Q≥8)and×100(8≥Q≥12). Theresulting
unitcelloftheRietveldanalysisisshownin(b)and(c). TherearetwoNb Cl clustersperunitcellwitheachcluster
3 13
composedofthreeedge-sharingNbCl octahedrameetingatanapicalClatomatoptheNb triangle.Theresulting
6 3
Nb Cl layersareinequivalentascanbeseenbythealternatingdirectionofthecappingClatomandthusforman
3 8
-AB-AB-stackingsequence.Asingleab-planeofNb Cl isshownin(c),formingatriangularlatticeofS =1/2
3 8 eff
triangularclusters.
Measurementswere performedwith the Nb Cl single crystal arrayoriented in both the (hhl) or (h0l) scat-
3 8
teringplanesofthehightemperaturestructure. Low-temperaturepowderX-raydiffraction(PXRD)patterns
were acquired from T = 300K to T = 12K using a Bruker D8 Advance powder diffractometer with CuKa
radiation (l =1.5424Å), a scintillator point detector with 0.6mm slits, and an Oxford Cryosystems PheniX
low-temperatureclosedcyclecryostat. PowderneutrondiffractionatT=300KandT=10Kwasperformed
at the POWGEN diffractometer, Spallation Neutron Source, Oak Ridge National Laboratory (ORNL). Scans
weremeasuredfor4hourseachona0.2gsampleofcrushedNb Cl singlecrystals. Rietveldrefinementsto
3 8
synchrotronandin-houseX-raydiffractiondatawereperformedusingtheGeneralStructureAnalysisSystem
(GSAS)31 andthecommercialBrukerTopassoftwaresuite. Refinementtothelow-temperaturepowderneu-
tron diffraction data was performed using the program FAULTS32 software package to account for random
HT-phasestacking faults(-AB-AB-) intheLTphase. Angle dependentmagneticsusceptibilitymeasurements
3
onsingle crystallineNb Cl wereperformedonaQuantumDesignPhysicalPropertiesMeasurementSystem
3 8
(PPMS) from T = 300K to T = 2K under an applied field of m H = 5T, after first measuring the sample
o
holdertemperaturedependentbackground,whichwassubsequentlysubtractedfromthedata. Specificheat
capacity measurements were taken on a PPMS from T = 300K to T = 2K using the semi-adiabatic pulse
technique and dual slope analysis method. For sensitivity to latent heat, measurements around T ≈ 90K
wereperformedusingasinglelargeheatpulsefromT =85KtoT =110K,andanalyzedviathemulti-point
single slope method33. Resistivity measurements were taken using the four-probe method in the PPMS by
attachingPtwiretosingle crystalline Nb Cl usingDuPont4922Nsilvercompositionpaint. Thesamplewas
3 8
measuredfromT=300KtoT ≈275Kwheretheresistivityexceededtheinstrumentthresholdduetoavolt-
meterimpedanceof≈16MW . Bandstructurecalculationswereperformedonthehigh-andlow-temperature
phasesofNb Cl . Convergencewasachievedwitha8×8×4and4×7×4k-pointmeshforthehigh-andlow-
3 8
temperature phases respectively, using the ELK all-electron full-potential linearized augmented-plane wave
(FP-LAPW)codeusingthePerdew-Wang/Ceperley-Alder LSDAfunctional34.
3 Results
ResultsofRietveldrefinementstopowderSXRDdataatT =300Kofthehigh-temperature(HT)P3¯m1phase
are shown in Fig. 1. The HT phase unit cell [Fig. 1(b)] consists of two Nb Cl clusters per unit cell in
3 13
a -AB-AB- bilayer stacking order where A and B refer to independent Nb Cl layers and AB constitutes a
3 8
single bilayer,sinceadjacent Nb Cl layersareinequivalent due toalternatingdirectionsoftheNb capping
3 8 3
Cl atoms. No atomsoccupy the two inequivalent spaces betweenNb Cl layers, leaving only Van-der-Waals
3 8
(VdW) interactions between interfacial Cl layers as the net attractive force. Rietveld refinement to powder
synchrotron diffraction data [Fig. 1(a)] show low-Q diffraction peaks that are asymmetric and not fit well
(broad calculated peaks) due to a combination of instrumental low angle peak asymmetry and significant
stackingfaults. Theexcellentoverallqualityofthefitishighlightedbythezoomedregions. Toassesswhether
ornotamoresubtledistortionispresentathightemperatures,fitstospacegroupswithsymmetryelements
systematically removed (P3¯, P3m, P3, and C2/m) do not improve the fit, either statistically or qualitatively.
ThelowtemperaturesynchrotrondatanearT ≈90K showno indicationofasymmetry-loweringstructural
distortion(seeESI†). TheseresultsfromtheHTphaseareinagreementwiththestructurepreviouslyinferred
fromsinglecrystalX-raydiffraction19,35.
Thetemperaturedependentmagneticsusceptibility of single crystalline Nb Cl uponcooling and warm-
3 8
ing is shown in Fig. 2(a) for fields parallel and perpendicular to the c crystallographic axis. Whereas pre-
vious reports show that Nb Cl has hysteretic magnetization with a clear transition around T ≈ 90K21, we
3 8
find the susceptibility effectively vanishes for T <90K upon cooling. Hysteresis is observed, in that upon
warming from the low-temperature (LT) phase to the HT phase, this transition occurs at a higher tempera-
4
Figure2(a)Nb3Cl8susceptibilitywithappliedfieldparallel(k)andperpendicular(⊥)tothecrystallographicc-direction.
Curie-Weissfitstock m oH dataisshownasablackline,forbothhigh-andlow-temperatureregions.(b)Neutron
diffraction(ND)intensityofthe(001)reflectionofNb Cl ,whichgrowsuponenteringtheC2/mphase.Theinsetshows
3 8
the(001)peakatT =1.6KanditsabsenceatT =130K.(c)Heatcapacityovertemperaturevs. temperaturefor
Nb3Cl8. PeaksaroundT ≈100Karefirst-orderheatingandcoolingtransitionsbetweenthetwophases.Theinset
showsasinglecrystalgrownbyvaportransport.TheorangebackgroundcorrespondstotheLTC2/mmonoclinic
phase.
ture than upon cooling. An analysis of the inverse susceptibility data for T >140K yields a Curie constant
C =0.484 emu·K·molf.u.−1·Oe−1 (p =1.97, consistent with S = 1/2) and a Weiss temperature of
eff eff
q =−51.2K. The fit is shown as a solid black line in Fig. 2(a), for 140K≤T ≤300K and is continued
as a dashed line at lower temperatures. The values vary less than 5% between the two crystal directions,
indicating any HT anisotropyis small. The upturns observed belowT ≈ 30K account for ≈2% of the high-
temperature spins, consistent with a small number of impurity spins or edge states. The fit shown below
T ≈90K inFig.2(a)istoaCurie-Weiss law, c = C +c where c =0.8×10−4 emu·Oe−1·mol f.u.−1 and
T−q o o
q =−4K.
5
Fig.2(b)showstheresultsofneutrondiffractionrockingscansoftheNb Cl (001)reflection. Compared
3 8
totheHTphase,theLTphasehasasignificant increaseintheintensityofthe(001)reflection,whichtracks
thetransitionbetweentheLTandHTphases,withconsistenthysteresis.
Heat capacity measurements on Nb Cl are shown in Fig. 2(c). The cooling (blue) and warming (red)
3 8
transitionsareconsistentwiththesusceptibilityanddiffractiondata. Theamountofentropyassociatedwith
the transitions is obtained from S(T)=R0TCv·T−1dT assumingCv≈Cp, after a smooth curve to account for
the background is subtracted. This results in an entropy change D S=5 J·K−1·molf.u.−1, which is 85% of
the full entropy change of a two level system, R·ln(2)=5.76 J·K−1·molf.u.−1. This may suggest the bulk
hasasingletgroundstatewithagaptothefirstexcitedstate.
An analysis of the low temperature C ·T−1 versus T2 data (Fig. 3), however, reveals a significant lin-
P
ear contribution to the specific heat, indicative of metallic behavior, despite Nb Cl being an insulator at
3 8
all accessible temperatures. Measurements on two separate single crystal pieces yield two different linear
contributions, g =13 and 18 mJ·K−2·mol f.u.−1 for samples 1 and 2 respectively [Fig. 3(a) and (b)]. The
observationofvaryingvaluesoftheT-linearcontributiontothespecificheatsuggestsitsoriginisnotintrinsic
butratherduetodefectsthatalsogiverisetotheCurietailinlowtemperaturesusceptibilitydata[Fig.2(a)].
Toquantifythisargument,theC(T)datawerefittoanequationaccountingfortheintrinsicsamplebehavior
withaSchottkyanomalytermforthelowtemperatureimpurityspins,C·T−1=b ·T2+g +(R)(D )2 eD /T ,
T T [1+eD /T]2
where g is the T-linear contribution, b is the lattice contribution, R is the ideal gas constant, and D is the
Figure3LowtemperatureCP·T−1versusT2dataontwopieces(a,b)ofthesamebatchofNb3Cl8. Dotsaredata,
linesarefitstotheequationshownin(b).Thevaluesofg extractedfromfitstothedataare≈40%differentforthetwo
piecesofNb Cl crystal,suggestingtheoriginoftheT-linearcomponentisfromimpurityspins. Theinsetin(b)shows
3 8
thevalueoftheSchottkygapasafunctionoffieldextractedfromfitstodataonsample1(greensquare)andsample2
(blackdots),whichyieldag-factorof1.5(1).
6
Figure4(a)NeutrondiffractionatT =10KindicatesLT-Nb Cl adoptsC2/mspace-groupsymmetry. Blackdotsare
3 8
data,redlineiscalculatedfit,bluelineisdifference,andtickmarksareBraggreflectionsforLT(black)andremnantHT
(orange)phaseNb Cl . InsetsshowHT(green)andLT(black)datafromneutronandX-raydiffractionatT =10Kand
3 8
T =12K,respectively,showingthesplitHT(202)trigonalreflection.HTandLTphaseNb Cl structuresareshown
3 8
perpendicular(b)andparallel(c)toNb Cl layers.(b)Changesinintra-clusterNb-Nbdistances(red)andinter-cluster
3 8
Nb-Cl-Nbbondangles(black)depicteffectonintra-layersuperexchangepathways.Ashiftinlayerstacking(c)is
observedfromaHT-aaa-bilayer(-AB-AB-layer)toLT-abc-bilayer(-AB′-BC′-CA′-layer)order.OrangeClatoms
highlightpuckeringofClatomlayerswhichdriveclosestpackingandstackingorderrearrangement.
Schottkyanomalygap. Asinglevalueofb andasinglescalefactorforthelowtemperatureSchottkyanomaly
wasused forall fieldsof sample2 [Fig.3(b)]. Thefield dependenceof the Schottkyanomaly gap is shown
in the inset to Fig. 3(b), which is used to extract a g-factor of 1.5(1) for the impurity spins contributing to
the anomaly. We thus reason the T-linear specific heat of Nb Cl may originate from a distribution of bro-
3 8
ken singlets (giving rise to defect spins) that interact through the majority phase as in Ba CuSb O 36 and
3 2 9
Sr CuO 37.
2 3
7
Table1AtomicparametersofLT-Nb Cl fromRietveldrefinementtoneutrondataatT =10K.ThespacegroupisC2/m
3 8
withlatticeparametersa=11.6576(1)Å,b=6.7261(1)Å,c=12.8452(1)Åandb =107.6087(2)o. Allsitesarefully
occupiedandthermalparametersweresetequalforallatoms,witharefinedvalueofBiso=0.10(6). Thefitqualityis
givenbyaRwp=3.59.
Atom Wyck. site x y z
Nb-1 4i 0.9734(10) 1/2 0.2470(10)
Nb-2 8j 0.1558(10) 0.2980(10) 0.2550(10)
Cl-1 4i 0.7046(10) 0 0.1231(10)
Cl-2 4i 0.2157(10) 0 0.1473(10)
Cl-3 4i 0.1271(10) 1/2 0.4013(10)
Cl-4 4i 0.1239(10) 0 0.3656(10)
Cl-5 8j 0.9595(10) -0.2490(10) 0.1209(10)
Cl-6 8j 0.3725(10) 0.2606(10) 0.3622(10)
Low temperature powder X-ray and neutron diffraction was used to determine the LT structure. The
LT phase has a characteristic pattern of peak splitting, indicating a structural distortion to a C2/m phase.
Rietveld refinement to neutron diffraction data at T = 10K, shown in Fig. 4(a), indicates a 16% remnant,
random HT phase stacking pattern in the LT structure. The resulting structure is summarized in Table 1
and change in symmetry unique octahedral Nb-Cl bond lengths in Table 2. Considerable stacking faults
and the remnant HT phase stacking present in the LT phase warranted use of FAULTS32 to model the LT
structurewith all thermalparametersrestrainedto beequal tominimize refinableparametersand yield the
most statistically significant model. The primary effect of the phase transition on the Nb Cl clusters is
3 13
showninFig. 4(b)and (c). Thediscrete Nb Cl clusters (2.81Åintra-and 3.93Åinter-cluster Nb-Nb bond
3 13
distances) in the HT phase [Fig. 4(b)] are characterized by “molecular” C point group symmetry and a
3v
S =1/2magneticelectronequally distributedovertheentire cluster (blueshading). Theclustersforma
eff
triangular lattice thatare stackedin a-AB-AB- sequence. Thetransitionto theLT phase [Fig.4(b)and (c)]
results in removal of the threefold rotational symmetry of the HT clusters, so that only a C2/m a-c mirror
plane remains. The result is a scissoring of the clusters, whereby the HT phase equilateral Nb triangu-
3
lar cluster becomes isosceles, resulting in one decreased (2.72Å) and two increased (2.86Å) Nb-Nb bond
lengths and two inequivalent NbCl octahedra, consistent with the SOJT effect. The transition modulates
6
inter-cluster Nb-Cl-Nb superexchange pathwaysbydecreasing and increasing these bondangles [Fig. 4(b)]
resulting inapseudo-one-dimensional state. Further,accompanying thephase transitionare changesto the
nearest-neighbor(NN)inter-andintra-clusterdistances,heredefinedasthedistancebetweenthegeometric
centroidofNb clustertriangles. Whiletheintra-layerclusterdistancesareshorterandchangefromasingle
3
NN distance of 6.7457Å (HT) to 6.7294Å and 6.7261Å (LT)—suggestive of 1D chains—the change in NN
inter-layerdistanceisgreater,from7.3585Å(HT)to7.1887Å(LT),consistentwithinter-layersingletforma-
tion. Theclusterscissoringhasapronouncedeffectontheinterlayerstackingarrangement. IntheHTphase,
Cl atoms at bilayer edges are flat triangular layers, resulting in a simple closest packing of chlorines from
the top of one bilayer with the bottom of the next and thus, a -AB-AB- arrangement. In the LT phase, the
8
Table2Changesintheniobium-chlorinebondlengthsofsymmetryuniqueNbCl octahedrainNb Cl clusters
6 3 13
betweentheHTandLTNb Cl phases. BondlengthsareseparatedandlabeledbyuniqueClatomswithinan
3 8
octahedra.DuplicatelengthswithinaNbCl octahedraarelabeledassuch. Nb istheapical(i.e.non-scissored)Nb
6 A
ion,Nb representthetwo“scissored”Nbions. AlldistancesareinAngstroms(Å).
B
HT(P3¯m1) LT(C2/m)
Nb -Cl 2.483(13)
Nb-Cl 2.437(2) A A1
A
Nb -Cl 2.423(13)
B A2
Nb -Cl 2×2.552(11)
A B1
Nb-Cl 2×2.530(1) Nb -Cl 2.548(10)
B B B2
Nb -Cl 2.497(13)
B B3
Nb -Cl 2×2.407(12)
A C1
Nb-Cl 2×2.464(1) Nb -Cl 2.435(12)
C B C2
Nb -Cl 2.371(12)
B C3
Nb -Cl 2.513(13)
Nb-Cl 2.640(1) A D1
D
Nb -Cl 2.646(10)
B D2
scissoringmotionresultsinabucklingofthechlorinelayersashighlightedinFig.4(c),wherecrystallograph-
ically equivalent orange Cl atoms emphasize the Cl-layer crimping distortion—the lowest interfacial energy
betweenthesenowstaggeredlayersrequiresashiftinstackingtoa-AB′-BC′-CA′-pattern. Here,A/A′,B/B′,
etc is used to relate the LT structure to the former HT (AB-designated) layers. The resultant shift in inter-
and intra-layer structure, however, is not concomitant with long-range magnetic order. The observation of
a structural distortion by powder X-ray diffraction suggests the increased intensity of (001) neutron Bragg
diffraction[Fig. 2(b)] hasa structural—not magnetic—origin. Changes in the measured single crystal neu-
tron diffraction data are consistent solely with nuclear diffraction associated with the P3¯m1 to C2/m phase
transition.
Density functional theory (DFT) band structure calculations for Nb Cl , shown in Fig. 5, were used to
3 8
gaininsightintothenatureofthemagneto-structuraltransition. Inagreementwithpreviouscalculationsfor
discrete Nb Cl clusters18, the HT Nb Cl band structure confirms the highest occupied molecular orbital
3 13 3 8
(HOMO)ofeachclusterisanon-degeneratea orbitalthatisfarinenergyfromtheexcitedstateorbitalsand
1
therefore,notconventionally(i.e. tofirst-order)Jahn-Telleractive. ThebandscorrespondingtoeachNb Cl
3 13
clusterHOMO[greenandorangeband,onefromeachoftwoclustersperunitcell,Fig.5(a)]aresplitatthe
G -point from orbital overlap between the magnetic electrons in adjacent clusters resulting in the formation
of a bonding/anti-bonding pair of states. The band structure calculation of the LT phase, Fig. 5(c), shows
shifted bands with respect to the HT phase. Notably, the HT bonding/antibonding states [from Fig. 5(a)]
have an increased gap and the degenerate e states have been raised and lowered in energy (i.e. orbital
degeneracy was broken) upon entering the LT phase. Breaking the degeneracy of the first excited states
upon entering in the LT phase is consistent with a second-order Jahn-Teller distortion from orbital mixing.
ThecalculationsinFig.5(a)and(c)havenospin-polarization(SP),spin-orbitcoupling(SOC),orelectronic
interactionviaaHubbardU. Undertheseconditions,HTNb Cl isclearlypredictedtohaveafinitedensityof
3 8
9
Figure5BandstructurecalculationsontheHT[(a)and(b)]andLT[(c)and(d)]structuresofNb Cl . Calculationsin
3 8
(a)and(c)areperformedwithoutspinpolarization(SP),spin-orbitcoupling(SOC),oraHubbardU. Calculationsin(b)
and(d)areperformedwithSP,SOC,andHubbardU=4eV.ThetransitionobservedinNb3Cl8isdrivenbya
second-orderJahn-Tellerdistortiondrivenbyinteractionof(a)HTphasee(blue)anda orbitals.TheHTphase
1
possessesabonding(green)andanti-bonding(orange)pairofstatesfromthenon-degenerate(a )valencebandsat
1
theG -pointfromaninteractionbetweeninterlayerclusters.TheHTphaseeorbitalsaresplitupontransitionintothe(c)
LTstate. ToreproducetheexperimentallyobservedinsulatingbehaviorintheHTcalculation,theHubbardU andSOC
mustbeincluded(b),whichsplitsboththenon-degeneratea andebands.Forcomparison,inclusionofaHubbardU
1
intheLTcalculationsisshownin(d)(seeESI†). ThespecialpointsoftheBrillouinzoneinboththeHTandLT
calculationsarelistedintheESI†.
statesattheFermilevelandthusbemetallic,inconsistent withresistivitymeasurements. Thisdemonstrates
the importance of correlations in producing the observed behavior of this compound. Intriguingly, we find
that solely SOC or solely a Hubbard U (onsite electron-electron interaction), are not sufficient to produce
an insulator in the HT phase (see ESI†). Including both SOC and U simultaneously, Fig. 5(b), is sufficient
to produce an insulator. In this calculation, Nb moments were assumed to align with the crystallographic c
axis,andbeorientedantiferromagneticallybetweenlayerswithatotalmomentof≈0.5m perclusterinthe
B
HTphase. Giventhelimitations ofDFTin describingcorrelatedmaterials,thissemi-quantitative agreement
is reasonable. In contrast, LT Nb Cl is almost predicted to be insulating by DFT, even in the absence of
3 8
10
