Revealing multiple density wave orders in non-superconducting titanium oxypnictide Na$_2$Ti$_2$As$_2$O

0.64 MB·

by  Y. Huang

Revealingmultipledensity waveorders innon-superconducting titanium oxypnictide Na Ti As O
2 2 2
Y. Huang, H. P. Wang, R. Y. Chen, X. Zhang, P. Zheng, Y. G. Shi, and N. L. Wang
Beijing National Laboratory for Condensed Matter Physics,
Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
WereportanopticalspectroscopystudyonthesinglecrystalofNa Ti As O,asistercompoundofsupercon-
2 2 2
ductorBaTi Sb O.Thestudyrevealsunexpectedly twodensitywavephasetransitions. Thefirsttransitionat
2 2
320KresultsintheformationofalargeenergygapandremovesmostpartoftheFermisurfaces.Butthecom-
poundremainsmetallicwithresidualitinerantcarriers.Below42K,anotherdensitywavephasetransitionwith
smallerenergygapscaleoccursanddrivesthecompoundintosemiconductinggroundstate.Theseexperiments
4 thusenableustoshedlightonthecomplexelectronicstructureinthetitaniumoxypnictides.
1
0 PACSnumbers:71.45.Lr,75.30.Fv,74.25.Gz,74.70.-b
2

n
The low temperature broken-symmetry states in low- standingthesuperconductivityinthisfamily. Amongthedif-
a
J dimension materials, such as superconductivity, charge/spin ferentmembersinthefamily,Na2Ti2As2Oappearstobepar-
0 density wave (CDW/SDW), are among the most fascinat- ticularly interesting. The first principle calculations indicate
3 ingcollectivephenomenainsolidsandtheinterplaybetween thatthe compoundhasan SDW groundstate with a blocked
themhasbeenasubjectofconsiderableinterestincondensed checkerboardantiferromagnetic(AFM)order,andtheordered

]
matter physics [1–6]. Most density wave (DW) instabilities stateisnotmetallicbutsemiconductingwithanenergygapof
l
e
(eitherCDW or SDW) are drivenby the nestingtopologyof 0.15 eV [22]. Up to the present, there have been little ex-
-
r Fermisurfaces (FSs), thatis, the matchingof sections of FS perimental studies on the material. It is highly desirable to
t
s toothersbya wavevector2k , wheretheelectronicsuscep- probe its electronic properties and, in particular, to examine
F
.
t tibility has a divergence. Broughtabout by electron-phonon whether such an semiconducting ground state is really real-
a
orelectron-electroninteractions,a singleparticleenergygap izedinNa Ti As Osystem.
m 2 2 2
opensinthenestedregionsofFSs,resultingintheloweringof Inthisworkwepresenttheopticalspectroscopicstudyon
-
d theelectronicenergyofthesystem. Inone-dimensional(1D) Na2Ti2As2O single crystal. Unexpectedly, the study reveals
n system the DW phase transition usually causes an semicon- twoDWphasetransitionsforthecompound. Thefirstoneat
o ductinggroundstate due to the openingof a fullenergygap hightemperature(∼320K)resultsintheformationofalarge
c arisingfromtheperfectnestingofFermisurfaces. However, DWenergygapwith2∆=2600cm−1andremovesmostparts
[
for two-dimensional(2D) or three-dimensional(3D) materi- oftheFSs. Butthecompoundremainsametallicnatureafter

1 als, the CDW or SDW groundstates mostly remain metallic this phase transition. Below 42 K, another DW gap forms
v
duetotheformationofpartialenergygapinducedbytheim- andremovestherestoftheFSstotally. Suchtwostepsphase
3
5 perfectnesting of FSs. To date, there seems no reportedex- transitions,whicheventuallyleadtoasemiconductingground
8 ample of a truly semiconducting ground state caused by the state,werenotanticipatedfromthefirstprinciplecalculation.
7 DWphasetransitionina2Dor3Dsystem. Na Ti As O manifests much more complex than one would
2 2 2
1. Recently,anewsuperconductingsystemBa1−xNaxTi2Sb2O expect.Itislikelytobethefirstprovenexampleofaquasi-2D
0 (T ∼2-5 K) has attracted much attention [7–9]. The system materialundergoingmetal-insulator(M-I)transitiondrivenby
c
4 belongstoatwo-dimensional(2D)titaniumoxypnictidefam- densitywaveinstability.
1
ily, consisting of alternate stacking of conductingoctahedral Single crystal samples of Na Ti As O used in this study
: 2 2 2
v layersTi Pn O (Pn=As, Sb)andotherinsulatinglayers(e.g. weregrownbytheNaAsfluxmethod[24].Figure1showsthe
2 2
Xi Na2, Ba, (SrF)2, (SmO)2) [9–18]. The undoped compounds in-planetemperaturedependentresistivityandmagneticsus-
inthisfamilycommonlyexhibitphasetransitionsbelowcer- ceptibility measuredin a Quantum Design physicalproperty
r
a tain temperatures (e.g. 114 K for Na Ti Sb O [12], 320 K measurementsystem(PPMS)andasuperconductingquantum
2 2 2
forNa Ti As O[11–14,16],45KforBaTi Sb O[7],200K interferencedevicevibratingsamplemagnetometer(SQUID-
2 2 2 2 2
for BaTi As O [17]), as characterizedby the sharp jumpsin VSM),respectively.Clearanomaliesareobservednear320K
2 2
resistivity and drops in magnetic susceptibility. First princi- wheretheresistivitydisplaysasuddenincreaseandthemag-
ple bandstructurecalculationsindicatethatthe phasetransi- neticsusceptibilitya sharpdrop. Belowthephasetransition,
tionsaredrivenbytheDWinstabilitiesarisingfromthenested the resistivity keeps increasing with decreasing temperature,
electronandholeFSs[19–23]. Assuperconductivityemerges reachesamaximumnear150K,thendecreasesslightly. But
onlyincompoundwithlowphasetransitiontemperatureand below roughly 50 K, the resistivity goes up sharply and the
T is further enhanced when the phase transition tempera- compound becomes semiconducting like in the lowest tem-
c
turewassuppressedbydoping,thefamilyoffersanewplay- perature. Suchabehaviorhasnotbeenobservedinanyother
groundto studythe interplaybetweensuperconductivityand memberof the titanium oxypnictidefamily. In the magnetic
DW instabilities. Understanding the electronic properties in susceptibilitycurve,aweakkinkisseennear42K,suggesting
the undoped compounds is an essential step towards under- the emergenceof anotherphase transition. Those anomalies
2

0 100 200 300 1.0
6
330K
cm)4 HH=//a5b T-plane 3 mu/mol) 0.8 32110000000KKKK
(mab 2 -4 10 e R0.6 1.0 1.0
2 ( 0.9 333000KK 0.9 1200KK
0.4 200K 30K
1 0.8 11000KK 0.8 5100K0K
0.7
0 0.7
0 100 200 300 0.2 0.6
T (K) 0 1000 20 0(0cm-13)000 4000 50000.60 100 200 3 ( 0c0m-1)400 500 600
FIG.1:(Coloronline)Thetemperaturedependentin-planeresistivity
0.0
andmagneticsusceptibilityofNa2Ti2As2O. 100 1000 10000
-1
(cm )
FIG.2: (Coloronline)R(ω)spectraforNa Ti As Oatseveralrep-
2 2 2
wererepeatedlyobservedindifferentsamples.Aswillbeseen resentativetemperatures. leftinset: R(ω)spectraupto5000cm−1in
below,opticalspectroscopymeasurementrevealedclearlytwo alinearfrequencyscale;Rightinset: R(ω)spectraupto600cm−1at
distinctDWphasetransitions. lowtemperatures.
Figure 2 and 3 show the reflectance R(ω) and real part
of conductivityσ (ω) spectra at differenttemperatures. The
1
insets show R(ω) and σ (ω) spectra in a linear frequency curveofBCStheoryforadensitywavephasetransition,im-
1
scale. The measurement technique is the same as we pre- plyingthatthetransitionisasecondorderphasetransition. It
sented before [25]. At 330 K, a temperature higher than shouldbeemphasizedthatthelow-ωR(ω)intheDWordered
the phasetransition,R(ω) showsa typicalmetallic response. stateincreasesfastertowardsunityatzerofrequencythanthat
R(ω) approaches unity at zero frequency and drops almost at330K.Asaconsequence,onecanseearathersharplow-ω
linearly with increasing frequency. This well-known over- reflectanceedge.ThisindicatesclearlythattheFermisurfaces
dampedbehaviorindicatesratherstrongcarrierscattering. A areonlypartiallygappedandthecompoundsarestillmetallic
strikingfeatureisthatR(ω)isstronglysuppressedbelow2600 belowTs.
cm−1belowthephasetransitiontemperatureatT =320K.Ac- Surprising results were observed at low temperatures. As
1
cordingly,aremarkablepeakstructureemergesinσ (ω)and seenintherightinsetofFig.2,below50K,anewsuppression
1
becomesmorepronounceduponcooling(leftinsetofFig. 3). featureappearsinR(ω) atmuchlowerenergyscale, roughly
ItisatypicalDWenergygapcharacterintheopticalconduc- below300cm−1. Abovethisenergylevel,thereisaslighten-
tivity spectrum, which is determinedby the ”type-Icoherent hancementofreflectance. Thischaracterbecomesmorepro-
factor” for DW order [26, 27]. The spectral change across nounced as the temperature decreases. It is very similar to
the phase transition is rather similar to that seen for its sis- the spectral change arising from the opening of DW energy
tercompoundNa Ti Sb O,wherethephasetransitionoccurs gapaswehaveexplainedforthephasetransitionat320K.In
2 2 2
at114K [25]. Thepeakpositionin σ (ω) roughlygivesthe theσ (ω)spectra,thesuppressionofconductivityatlowfre-
1 1
gap value of 2∆ =2600 cm−1(∼ 0.32eV). This leads to the quencycould be clearly seen below 50 K. Nevertheless, due
1
ratio of the energy gap relative to the transition temperature to theemergenceofstrongphononmodes, thepeak position
2∆ /k T ≈11.5at10K.Thevalueisalsoclosetothethatob- could not be unambiguously resolved. Overall, this second
1 B 1
tainedforNa Ti Sb Ocompound[25]. Notably,thisvalueis gapfeatureis muchweaker thanthe first oneat 320K. This
2 2 2
muchlargerthantheBCS(Bardeen-Cooper-Schrieffer)mean couldbeattributedtothesmallresidualcarrierdensitybeing
fieldvalueof3.52foradensitywavephasetransition[1].This leftafterthefirstDWphasetransition. Judgingfromthesup-
means that the transition temperature is significantly lower pressionfrequencyinR(ω)andthespectralweightanalysisas
than the mean field transition temperature. It might be due beingpresentedbelow,thegapvalueisestimatedtobeabout
tohighlytwo-dimensionalelectronicstructurewhichleadsto 2∆ =300 cm−1. Combined with the anomalies in resistivity
2
strong fluctuation effect and suppresses the actual ordering andmagneticsusceptibilityatT =42K,theobservationyields
2
temperature. The 2D nature of the compound is well sup- compellingevidenceforthedevelopmentofanewDWorder.
ported by the large value of the anisotropic ratio of the re- From the gap value, we obtained the ratio of the energygap
sistivities ρ (T)/ρ (T) ∼ 400 [24]. Similar gap ratios were relative to the transition temperature 2∆ /k T ∼10 for the
c ab 2 B 2
alsoobservedinotherlow-dimensionaldensitywavemateri- secondtransition,whichissimilartothevalueforthefirstDW
als, e.g. (TaSe ) I [1]. The right inset of Fig. 3 shows the phase transition. It deserves to remark that the earlier mea-
4 2
plotoftheenergygap∆ ,extractedfromtheopticalmeasure- surementofanisotropicratioofresisitivitiesbyMontegomery
1
ment,asafunctionoftemperature.Thedatapointsfollowthe technique on Na Ti As O showed a very sharp drop below
2 2 2
3

6000 6000
6000
330K
10000 -1-1 cm) (241000000 32110000000KKKK (eV)0001...011826 BCS gap curve -1-1 (cm)1 4000 eDinxrteuprde-erbim-aLneodnr et3taen3lrt zmd0 afKitta -1-1 (cm)41000 100K
-1 cm) 00 1000 2000 -13000 4000 5000 00..00040 50 100150200250300350 2000 Drude component 2000 DW gap 1
-1 (cm) T (K) Drude
(1 00 1000 2000 (cm -31)000 4000 5000 00 1000 200 0(cm -13)000 4000 5000
100K 6000
1000
50K
3200KK -1 m) 4000 10K 0.9 nnoorrmmaalliizzaaeedd 1/p2 0.9
10K -1 (c1 DW gap 1 1/0.6 0.62 p
2000 0.3 0.3
100 DW gap 2
100 1000 0.0 0.0
-1 00 1000 2000 3000 4000 5000 0 50 100 150 200 250 300 350
(cm ) ( cm-1)
T (K)
FIG.3:(Coloronline)σ (ω)spectralforNa Ti As Oatlowtemper-
1 2 2 2
atureoverbroadrangeoffrequencies. Leftinset: Theconductivity FIG.4:(Coloronline)Theexperimentaldataofσ1(ω)at330K,100
spectraupto5000cm−1inalinearfrequencyscale. Rightinset: the Kand10KtogetherwiththeDrude-Lorentzfits;Rightbottompanel:
plotofenergygap∆1,extractedfromtheopticalmeasurement,asa Thevariationsof1/τandω2pnormalizedtothevaluesat330Kasa
function of temperature. The data points follow the curve of BCS functionoftemperature.
theoryforadensitywavephasetransition(thedashedcurve).
dleandlasttermsaretheDrudeandLorentzcomponents,re-
50K[24],implyingareconstructionofbandstructureatlow spectively. The Drude term captures the contribution from
temperature,whilenosuchabruptchangeinanisotropicresis- freecarriersandtheLorentzcomponentsdescribetheexcita-
tivities was seen in Na Ti Sb O crystals. Those anisotropic tionsacrossthegapandinter-bandtransitions.Itisfoundthat
2 2 2
resistivitydataalsosupportthepresenceofthesecondphase theexperimentaldatabelow5000cm−1at330Kcouldbere-
transitionbelow50K. producedapproximatelybyoneDrudetermandoneLorentz
At 10 K, the lowest measurement temperature, the re- component. After the first phase transition, another Lorentz
flectancevalueisfiniteandsmallerthanunityatthezerofre- peak (DW gap 1) is added. As the temperature is lowered
quency limit. In σ (ω), the Drude componentis absent and below 42 K, a third Lorentz term (DW gap 2) develops and
1
phonon structures become dominant. The very small low- takes place the Drude component completely. A list of fit-
frequencyspectral weight is likely due to the effect of finite ting parametersis displayedin table I. The fitting resultsfor
measurementtemperature(10K).Theresultsindicatethat,in threerepresentativetemperaturesareshowninFig. 4. Itillus-
the ground state, the Fermi surfaces would be fully gapped tratesclearlythatthecompoundundergoestwo phasetransi-
andthecompoundbecomesasemiconductor. In2DDWma- tionswithdifferentenergygapscales.
terials, one usually observes enhanced metallic behavior be- Itisworthnotingthattheplasmafrequencyat330K(above
lowthetransitionbecausethepartialDWenergygaptendsto thefirstphasetransition)isabout23000cm−1whichisalmost
removetheelectronsthatexperiencestrongerscattering[28]. equal to Na Ti Sb O, while 1/τ ≈2000 cm−1is much lager
2 2 2
Althoughthere are a few examplesof nonmetallic2D CDW thanNa Ti Sb O[25]. Thisexplainsthelagerresistivityval-
2 2 2
systems,theoriginofthesemiconductingbehaviorisactually uesofNa Ti As Ocompound. Thevariationsofplasmafre-
2 2 2
not due to true FS nesting but Mott physics [29–31]. LaTe quencyandscatteringrate1/τnormalizedtothevaluesat330
2
was suggested to be a 2D FS nesting driven semiconducting Kasafunctionoftemperaturearedisplayedintherightbot-
CDWsystem[32],however,morerecentstudyindicatedthat tompanelofFig. 4. Providedthattheeffectivemassofitin-
thenonmetallicbehaviorwasinfactcausedbythelocalization erantcarriersdoesnotchangewith temperature,the residual
effect due to the presence of defectsin conductingTe layers carrierdensityat100Kisonly10%ofthatathightempera-
[33]. Inthisregard,Na Ti As Omaybethefirstexampleof ture. Meanwhile,the scatteringrate alsoreducesby90%. It
2 2 2
FSnestingdrivensemiconductingmaterial. indicatesthattheopeningofpartialdensitywavegapremove
To analyze the evolution of both the itinerant carriers and theelectronsnearFermilevelwhichbearstrongerscattering.
thedensitywavegapexcitationsinaquantitativeway,weuse ThischaracterissimilartoNa Ti Sb O,butthescatteringrate
2 2 2
aDrude-Lorentzmodetofittheσ (ω)spectrainabroadfre- of Na Ti As O is less reduced. Thoseevolutionsagreewell
1 2 2 2
quencyrange[26]: withthe temperaturedependenceofresistivity. Theitinerant
carrier density becomes zero at the lowest temperature sug-
ǫ(ω)=ǫ∞− ω2+ωi2ωp /τ +XN ω2−ωS2i2−iω/τ . (1) gtheestsiencgotnhdeDreWsidouradlerF.ermi Surface has been fully gappedby
D i=1 i i
Aspectralweight(SW)analysisgivesmoreinsightintothe
Here,theǫ∞ isthedielectricconstantathighenergy,themid- developmentofthetwoorders. Thespectralweightshownin
4
TABLEI:Temperaturedependenceoftheplasmafrequencyω andscatteringrateγ =1/τ oftheDrudeterm,theresonancefrequencyω,
p D D i
thewidthγ=1/τ andthe square root of theoscillator strength S of theLorentzcomponent(all entriesin103 cm−1). One Drudemode is
i i i
employedathightemperatures. LorentztermsresponsiblefortheDWordersareaddedatlowtemperatures. Thelowestenergyinter-band
transitionisalsodisplayed.
ωp γD ω1 γ1 S1 ω2 γ2 S2 ω3 γ3 S3
330K 23 2 – – – – – – 5 8 23
300K 13 1 – – – 1.2 2.5 20 5.4 8 23
200K 4.1 0.3 – – – 2.2 1.9 22 5.4 7.5 23
100K 2.4 0.1 – – – 2.5 1.8 22.7 5.4 7.5 23
50K 2.3 0.09 – – – 2.6 1.6 22.5 5.4 7.5 23
10K – – 0.3 0.44 2.6 2.6 1.5 21.5 5.4 7.5 23

First,thetwostepsphasetransitionswerenotanticipatedfrom
the calculations. Second, the value of energy gap in the or-
7
10
-2 m) deredstate fromfirstprinciplecalculations(0.15eV)is only
-1 c 6 half ofthe gapvalueobservedfor the first DWphase transi-
10
ht ( tion,butfourtimeslargerthanthatforthesecondDWphase
weig 105 333000K transition. Apparently, further theoretical work is needed to
al 200 resolve the discrepancy. A more realistic approach to the
ctr 100 groundstateistoconsiderfirstametastableintermediateDW
Spe 104 50 state driven probably by the strongest nesting instability of
20
10K FSs, and then to examine further possible instability on the
3
10 basisoftheintermediateDWstate.
10 100 1000 10000
-1 It also deserves to remark that, although the optical mea-
(cm )
surement revealed formation of two energy gaps at different
FIG.5: (Coloronline)Frequency-dependent spectralweightatdif-
temperatures, the measurement could not determine where
ferent temperature. The curvatures indicated by arrows reflect the
theFSsaregapped.Momentumresolvedexperimentalprobe,
effectofspectralweightredistributionscausedbyDWgapopenings.
such as angleresolvedphotoemission,should be used to de-
terminethe gappedregionsandcorrespondingwave vectors.
Another important issue is that, although the optical exper-
Fig. 5 is defined as Ws = R0ωcσ1(ω)dω, where ωc is a cut- iment indicated typical DW phase transitions, the measure-
off frequency. Thesmall step structuresbelow200K in low mentcouldnottellwhetherthephasetransitionswereCDW
frequency region, between 100 and 600 cm−1, are ascribed orSDWsincebothordershavethesamecoherentfactorand,
to the phonons. At very low energy, the Ws at 330 K has therefore, the same energy gap character. Other techniques
highest value due to the large Drude component. Below the that are capable to probe magnetism should be used to re-
300 K , the spectral weight is severely suppressed at about solve the issue. A recentNMR measurementon BaTi Sb O
2 2
2000 cm−1and recovered at a higher energy. This indicates polycrystalline sample revealed an absence of internal field
the formationof an energygap. Moreover,anothersuppres- at the Sb site, which therefore favored an CDW origin [34].
sion at low-ω region becomes eminent at 20 and 10 K. The Nevertheless,thisresultisactuallyinagreementwiththefirst
SW approaches approximately to zero at finite frequency at principlecalculationswhichindeedpredictedaCDWground
10K,indicatingtheinsulatorcharacter.Thesuppressionisan state for BaTi Sb O [23]. On the contrary, the first princi-
2 2
indication of the second energy gap opening which leads to ple calculations on Na Ti As O indicated a semiconducting
2 2 2
theM-Itransition. WenotethatthespectralcurvaturesofWs SDW ground state with a blocked AFM order [22]. There-
near 200 - 300 cm−1at 10 and 20 K are rathersimilar to the fore,sensitivemagneticprobesshouldbeappliedparticularly
thosenear2000-3000cm−1at100and200K,asindicatedby toNa Ti As Ocompound. Resolvingthoseissuesisofgreat
2 2 2
twoarrowsinFig. 5. Therefore,thetemperaturedependence significanceinviewoftheprofoundrelationshipbetweenthe
of the SW suppressionreflects two differentDW energygap density wave (SDW or CDW) and superconductivity in this
openingsbelow320and42K,respectively. family.Thepresentstudyisexpectedtomotivatemoreexper-
TheobservationoftwoDWphasetransitionsistotallyun- imentalandtheoreticalstudiesonthematerials.
expected. Although a FS nesting driven SDW semiconduct- Toconclude,wehavestudiedthein-planeopticalproperties
ing ground state is obtained from the first principle calcula- ofNa Ti As Osinglecrystal,asistercompoundofsupercon-
2 2 2
tions[22],theexperimentalobservationsdifferintwoaspects. ductorBaTi Sb O.Unexpectedly,thestudyrevealedtwoden-
2 2
5
sity wave (DW) phase transitions. The first transitionat 320 [8] P.Doan etal.,J.Am.Chem.Soc.134,16520(2012).
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[11] AxtellIIIetal.,J.SolidStateChem.134,423(1997).
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[12] T.C.Ozawaetal.,J.SolidStateChem.153,275(2000).
drivesthecompoundintosemiconductinggroundstate. This
[13] T.C.Ozawaetal.,J.E.Chem.Mater.13,1804(2001).
makes Na Ti As O the first proven quasi-2D DW semicon-
2 2 2 [14] T.C.Ozawaetal.,J.Cryst.Growth265,571(2004).
ductor driven by FS nesting as in 1D materials. The study [15] T.C.Ozawaetal.,Sci.Technol.Adv.Mater.9,033003(2008).
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[18] R.H.Liuetal.,Chem.Mater.22,1503(2010).
ACKNOWLEDGMENTS [19] W.E.Pickett,Phys.Rev.B58,4335(1998).
[20] deBianietal.,Inorg.Chem.37,5807(1998).
TheauthorsacknowledgeusefuldiscussionswithZ.Y.Luand [21] D.J.Singh,NewJ.Phys.14,123003(2012).
J. L.Luo. ThisworkwassupportedbytheNationalScience [22] X.W.YanandZ.Y.Lu,J.Phys.: Condens.Matter25,365501
(2013).
FoundationofChina(11120101003,11327806),andthe973
[23] A.Subedi,Phys.Rev.B87,054506(2013).
project of the Ministry of Science and Technologyof China
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(2011CB921701,2012CB821403).
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