Searching for the Slater Transition in the Pyrochlore Cd$_{2}$Os$_{2}$O$_{7}$ with Infrared Spectroscopy

4 Pages·0.35 MB·English

by  W. J. Padilla

Searching for the Slater Transition in the Pyrochlore Cd Os O with Infrared
2 2 7
Spectroscopy
W.J. Padilla and D.N. Basov
Department of Physics University of California San Diego, La Jolla, CA 92093-0319
D. Mandrus
2 Solid State Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831
0
0 InfraredreflectancemeasurementsweremadeonthesinglecrystalpyrochloreCd2Os2O7 inorder
2 to examine the transformations of the electronic structure and crystal lattice across the boundary
of the metal insulator transition at T = 226K. All predicted IR active phonons are observed
n MIT
in the conductivity over all temperatures and the oscillator strength is found to be temperature
a
J independent. These results indicate that charge ordering plays only a minor role in the MIT and
that the transition is strictly electronic in nature. The conductivity shows the clear opening of a
0
gapwith2∆=5.2k T . Thegapopenscontinuously,withatemperaturedependencesimilarto
3 B MIT
that of BCS superconductors, and the gap edge having a distinct σ(ω)∼ ω1/2 dependence. All of

] theseobservables support thesuggestion of a Slater transition in Cd2Os2O7.
l
e
-
r Mott’s classic paper[1] published over half a century the fact that Os5+ is in the 5d3 configurationso that t2g
t
s ago has triggered extensive research on correlated elec- band is near half filling.
t. tron systems which undergo a metal insulator transition The Slater transition is characterized by several hall-
a
(MIT). Both Mott and Hubbard[2] have suggested that
m marks in the frequency domain which so far remained
forsystemsathalffilling,theCoulombrepulsionbetween
- electrons could split the band, thus producing an insu- unexploredinCd2Os2O7. Amongthem,thespecifictem-
d peraturedependence oftheenergygapaswellasthe fre-
lator. Alternatively, Slater in 1951 suggested that an-
n quency dependence of the dissipative response at ener-
o tiferromagnetic order alone could produce an insulator gies above the gap edge that are distinct from the Mott-
c by a doubling of the magnetic unit cell[3]. While there
Hubbard case[10]. Also the analysis of the IR active
[ are numerous examples of Slater / spin-density-wave
phonon modes allows one to verify if a development of
(SDW) insulators in the realm of 1-dimensional (1D)
1 charge ordering is concomitant with spin ordering. De-
v conductors[4, 5], the experimentalsituationathigherdi- spite the fact that IR spectroscopy is ideally suited for
8 mensionsislessclear. Impossibility ofthe Slaterstatein
directly studying the nature of the MIT in solids, the
4 the2Dregimehasbeenrecentlyarguedbasedondynam-
5 ical cluster approximationcalculations[6]. For 3D solids, extremely small size of Cd2Os2O7 single crystals so far
has rendered these measurements impossible. Spectro-
1
spin ordering alone usually generates an energy gap cor-
0 scopic tools available in our lab at UCSD are tailored
ruptingonlyafractionoftheFermisurfacesothatmetal-
2 for investigations of microcrystals,[11] allowing us to fill
lic conductivity persists[7]. In this context the metal-
0 voids in the experimental picture of the insulating state
t/ insulatortransitioninthe3DpyrochloreCd2Os2O7isex- in Cd2Os2O7.
a ceptionallyintriguingsincetransportandmagneticprop-
m erties across the MIT boundary appear to be in accord The near normal reflectance R(ω) of Cd2Os2O7 was
measured from 40 cm−1 to 14000 cm−1 using a Fourier
nd- wthiethfitrhstesSplaetcetrromsceocphiacnsistmud[8ie]s. Ionf tthheisMpaIpTerinwCedre2pOosr2tOo7n. tcrma−ns1fuosrimngspaegcrtarotimngetemroannodchfrroomma1to2r0.00Acmte−st1 itnovo3l5v0in0g0
Our analysis of the infrareddata reveals that the transi-
o polarizedlight displayedno signs of anisotropy,thus un-
tion into the insulating state is driven solely by the elec-
c
polarized radiation was used for a detailed study of the
: tronicinteractionswithoutsignificantinvolvementofthe
v temperature dependence. Samples were coated in situ
crystal lattice. We discuss new facets of the spin-driven
i with gold or aluminum and spectra measured from the
X insulating state in a 3D material.
coated surface were used as a reference. This method,
r
a The pyrochlore Cd2Os2O7 was first characterized by discussed previously in detail[12], allows one to reliably
Sleight et al.[9]. The metal-insulator transition in the obtain the absolute value of the reflectance by mini-
resistivity has been found to occur at the same tem- mizing the errors associated with non-specular reflec-
perature ≃ 226 K as the antiferromagnetic transition in tion and small sample size. We inferred the complex
susceptibility measurements. No evidence of concurrent conductivity σ1(ω)+iσ2(ω) by use of Kramers-Kronig
structural changes were detected through X-ray diffrac- (KK) analysis after extrapolating data to ω → 0 and
tion(XRD)analysis. Thoroughexaminationoftransport ω → ∞. Various low frequency extrapolations (Drude,
and magnetism in Cd2Os2O7 has been recently reported Hagen-Rubens)were used; howeverthe data did notsig-
by Mandrus et al.[8] with a Slater picture delivering a nificantly depend on the particular method of low-ω ex-
coherent interpretation of all experimental data. This trapolation. We employed the usual ω−4 dependence for
particular mechanism in Cd2Os2O7 may be favored by the high-energy extension of the data[13].
2

0
0
0
0
0 1
2
1 K 0
K K 5K K K K 4
2 5 20 0 0 0
tFeImGp.e1r:atuRr29eeflsefcrto22am2Knce4020Ko22fcms0Ki−n211glte0Koc201ry00s0Kt0a15lcmC5K−d12.O380sI2nOs-1em)7tasthovwasriothues FKIrGam. 2e:rsR-Keraolnpiagrtanoaflythsiesoopntiacallocgosncdaulec.tivAitygaaps ocabntabineedsebeny
entire energy ran9ge ch2ara1cter0ized f5or ro2om tempcerature and to develop continuously as th0e temperature is reduced. The
0 2 222 1 0( 00
0025K on a log scale. 6y reductioninspectralweighto00ccurringintheinfraredregionis
10 3c compensatedbyashifttohigh80erenergies. Theinsetshowsthe
0 K n hardening Real part of the o1ptical conductivity as obtained
1 25 0e byKramers-Kroniganalysisonalogscale. Agapcanbeseen
4u to develop continuously as the temperature is reduced. The
Fig.1 shows the infrared reflectance 3takqen between reduction in spectral weight occurring in the infrared region
25 K and room temperature from an unpoelished facet iscompensatedbyashifttohigherenergies. Theinsetshows
0
0of Cd2Os2O7 crystal with dimensions le2ss thFran 0.5x0.7 thehardening of the347 cm−1 phon))on at low T.
8mm2. Thereflectanceatroomtemperatu3reis highandis 0 -1-1
metallic in nature. R(ω) decreases with decreVasing tem- 0 mm
peratur7einthe infraredregion. Although00theereflectance 6 cc
VV decreOases0monotonically0,itchangeslit0tle3nearmroomtem- tween the two s0egments at 818 cm ( (−1 can be chosen as a
peratur2ea0ndatlowtem0peratures. Depression o0fR(ω) is quantitativeme0asureoftheenergyyygap2∆. Theω1/2 be-
ee s 0 0 0 0 cc
mm mostOsigni2ficantinthev1icinityoftheMIT:betwe0en225K haviorcan be re0cognizedat0highennr temperatures as well.
6000a8n0Kdd1d5a02tKa.i)sT1,-whmeithacbins1o-elxupt(Weer vi1maleu snetaolfatchceurraeflcye,cteaqnucive1afloerntthtoe Idnestchriebeladttweritshp1eactlrinae(aFrigd.e3100p)etnhdeenueueincter.agTapheretgeimonpeirsabtuerset
C K qq
1tsphchraoetnenaotnins2g5inKist.hgAersaidntuefrmaalrplyeedrrareteduguriceoenids. lNuonwovteaerbiellidyn,gthaslelefvprehereoanleolesntcsrtoraonr292nge adneIpdt25Keσnis1d(ienωns)cter∝uocωft1ivt/0h2ee-1rtmoeigncithoenarsrseaicc400sttipeorlnoiztebteFreFreetdhtweinedeetnhveetlhoinepsmσet1e(noωtf)oFf∝igt.h3ωe.
still visible in the room temperature data. In00the in- energy gap in C00d2Ocs2O7 through the spectra of the ef-
0set to Fig7.1 we plot the reflectance over the enti1re range fective spectral1weightNeff(ω)= 1π20R0ωσ1(ω′)dω′. The
4characOterized for room temperature and 25K. magnitude of N (ω) depicted in Fig.4, is proportional
eff
Fig.2 s2hows the real part of the conductivity σ1(ω) at to the number of carriersparticipating in the opticalab-
s
differenttemperatures. Theroomtemperaturespectrum sorption up to a cutoff frequency ω, and has the dimen-
O 0
cσa1n(ωb)ed=adσ2e0q/u(1at+elωy2dτe2s)caritbleedaswtiftohraωs<im1p0l0e0Dcrmud−0e1mwhoedreel ssipoenctorfalfrweeqiugehntc00oyccsuqrurainregdi.n20Tthheeinsitgrnaigfiacpanrtegrieodnuicstitornanisn-
σ0 is tChe DC conductivity and τ is the relaxati1on time. ferred to the en1ergy region0above 3∆. Interestingly, the
0This behavior is followedby a somewhat slowerdecrease spectral weight does not b0ecome completely exhausted
20than that prescribed by the Drude form, and an inter- until16000cm−1implyingt1hattheenergyrangeasbroad
1 0 8 6 4 2 0
bvwiaistninbdelesfesieanstuttrhheeeacItoRn2t2rie0ng0ui0oonucm.s o−Ap1292Kse.ntSeinemvgpeoreafrla225Katsutgrraoepnigwsipltohhwoaenrod1.endrs220Kaosatnr0.ieec )0.ta(wrsaRI4nm0.0s210K pi∆toior≃0.tna.1n0t4200K0.iknBsTigM25KhtIsT150Kiinstoinvtohleveodriigninthoefmtehtealininsusulalatitnogr
reduction of σ1(ω) in the infrared. In the 25 K spec- state in Cd2Os2O7 may be0reached through the analysis
00trumthe intra0ga8pconductiv0ityis6frequenc0y indepe4ndent0 ofthe p2ho0nonspectra. 00The pyrochlorestructure belongs
1.0(apart from t0he0.sharp phon0on pe0.aks). A0t ω abov0.e the0 to the0.sp0ace group Fd0.¯3m and reveals seven IR active
0 5 0 5 0 5
3gap edge the 2spectrum reve2als the ω1/2 d1ependence ex-1 modes[15, 16]. We observe phonon peaks at 86 cm−1,
pectedforaSlatertransition[10,14]. Anintersectionbe- 108 cm−1, 200 cm−1, 347 cm−1, 371 cm−1, 440 cm−1,
ecnatcelfeR
) mc mhO( ytivitcudnoC laeR
1- 1-
3
E /D (meV)
0 4 8 12 16 20 24 28 32 36
010000 Cd Os O
4 2 2 7
2 K K K
O7 0 0 5
0 5 2
FIG.3:sInf2raredregionofth2erealcond1uctivityatT <TMIT. 00
The expOected theoretical frequency depe0ndence5o0f the1g0ap0 150 200 250 3005
0edge (σ1(ω2) ∼ ω1/2) is shown for each temperature as a 1
0dashed dline. A linear fit for the region below the gap edge
2 C
is also shown. The intersection of the two fits can be taken
345
asameasureoftheenergygap2∆. Theinsetshowstheopti-
calenergygap asdetermined)bythemethoddescribedabove
1
(opencircles),andtheexpec-tmedthe3or4et0ic aTldeempenpdeenrcae(tsuolried (K)
)
1cu0rv0e0). 1
0 (c 335 -m
6 0
1 c
-2) and 615 cm−1 in the 25Kw spect3ru3m0[17]. Both the fre- FIG. 4: Effective spectral w00eight vy (s. cutoff frequency for
m quencypositionandtheoscillatorstrengthofallphonons temperatures as indicated. T0he topcaxis is in energy units
Vc (with the exceD pt i/o nD o(fTth=e034)7 c3m2−51 resonance) are in- normalized by twice the gap1energy.enThe upper inset shows
e300dependent of temperature (lower inset of Fig. 4). The thetemperaturedependenceofthe3u47 cm−1phononandthe
m12347cm−10mode8assi6gned4to th2e O6I00I0−Os−OII bend[15] BCS gap function is also plotted, (qsolid curve). The lower
(eff1shows w0ea1.k ha20.rd9en2i0.nKg at0.T <0.TM0.IT. The key outcome insetshowsthetemperaturedependerenceofallsevenphonons.
N of the examination of the phonon spectra in Figs.1,2, is F
0
that no3new p2ho2n5onKmod1e)s appear at T = TMIT and
-
tehx1ep0elK)co0twe-d50Tfodrattah2ef2oird0eCaKdl2pOyrso2Occmh7lodrie4sps0ltar0yusctounrley. the 7 modes the energy gap in the electronic conductivity displayed
80thaTthe (tehee02xdpevereilmo2pemn1tea0nltKeovfitdheen(icnes0uplraetsienngtsetdataebionvCeds2uOggs2eOst7s itnheFMigI.2T[w19h,ic2h0]i.s Tcohnesissetceon0ntdwoitrhdetrhteraSnlasitteironpiicstuinreaoc-f
occuurrs w20ithout1v5is0iblKe signws of charge ordering. Exam- cordwithearlierspecifichea50tandmagneticsusceptibility
inatiton of the IR-active phonons has proven to be one data[8].
of thae m50ost se n2sit5ivKe tests for th2e0c0har ge-ordered state. Further support for the Slater hypothesis in the con-
r
Quitee co1mmonly additional lattice modes appear in the text of the Cd2Os2O7 data is provided by the electronic
0phonpon0spectra or a dramatic redistribution of the spec- conductivity. We first note that our data reveals sev-
4tralmweig0ht between several resonances takes place pro- eral hallmarks of the Bardeen-Cooper-Schrieffer (BCS)
1
videed the system reduces its symmetry in the charge- electrodynamics expected for systems with spin density
ordeTred0regime[18]. We failed to 0detect any of these waves[5], including the ratio of 2∆/k T ≃ 5.1 (ex-
B MIT
effe1c t0s. 5Furthermore, a detailed ana0lysis o5f 0the x1-r0ay0 1p5ec0ted2in0a0mo2d5ifi0ed B3C0S0theorythat takesinto account
diffractiondatadidnotproduceanyindicationsforstruc- the scattering of electrons by phonons, as for the canon-
Temperature (K)
tural ch0anges at T < T [8]. These observations al- ical SDW Chromium)[21, 22] as well as a characteristic
MIT
0low us to conclude that the metal-insulator transition in declineofthegapvalueatno0n-zerotemperatures[19,20].
C00d2Os2O7 is driven s00olely by electronic p00rocesses with- Th00e generalformof the0conductivity spectra is also con-
o0ut not0iceable indica5tions for5in0v0ol0vemen0t of the lat- 10s0is0t5e0ntwiththe BCSpic1t5ur0e0w0heretype2coherencefac-
t2ice. Another impor1tant fact pertaining 1to the nature torsleadtoanovershootbetweenthedataatT ≪T
MIT
of the insulating state is the continuous development of an-d1T >T at frequencies above the gap. As pointed
) mc mhFOre( qytuiveintccuyd (ncomC )laeRMIT
1- 1-
4
out above, the behavior of the low-T spectra above the in which antiferromagnetic fluctuations are perceived as
gapedgeareadequatelydescribedwiththeσ1(ω)∼ω1/2 alikely causeof the pseudogapstate. Finally,it is worth
dependence, as is expected for a Slater transition. This mentioningthatotherpyrochlorecompoundsrevealvery
finding is important because the ω1/2 dependence is dis- different properties at the verge of the metal-insulator
tinctfromtheω3/2 dependence observedinthe Hubbard transition. For instance, the transition to the insulating
limit[10]. regime in the closely related Tl2Ru2O7 system appears
Given the experimental evidence discussed above, the to be of first order and additionally is accompanied by
Slater mechanism emerges as a viable model of the charge ordering effects judging from the transformations
MIT in Cd2Os2O7. Therefore, this compound may be of the phonon spectra[25]. It is yet to be determined
the first well documented case of a three-dimensional what microscopicfactors define the peculiar characterof
SDW material[23], subject to further direct verification the MIT in Cd2Os2O7.
of the spin structure. An unexpected feature of the Work performed at UCSD was sponsored by the U.S.
antiferromagnetically-drivenMITisamismatchbetween Department of Energy under Contract No. DE-FG03-
the TMIT ≃ 200K and the frequency range involved in 00ER45799. Work at Oak Ridge National Laboratory is
the redistribution of the spectral weight in the insulat- managedby UT-Battelle, LLC, for the U.S. Department
ing state Ω ≃ 20000K. Similar mismatch is commonly of Energy under Contract No. DE-AC05-00OR22725.
found throughout the spectroscopic studies of the so-
called pseudogap state in high-T superconductors[24],
c
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[2] J. Hubbard,Proc. R.Soc. London A 276 238 (1963). located at 440 cm−1 can be resolved easiest in Fig.1 in
[3] J.C. Slater, Phys. Rev. 82 538 (1951). the lower temperature data sets.
[4] L. Degiorgi, M. Dressel, A. Schwartz, B. Alavi, G. [18] E. Buixaderas, S. Kamba, J. Petzelt, M. Savinov, N.N.
Gruner,Phys. Rev.Lett. 76 3838 (1996). Kolpakova, European Physical Journal B 19 9 (2001).
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B MIT
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Solid StateComm. 14 357 (1974). the lattice parameters show an abrupt change at T <
[10] G.A. Thomas, D.H. Rapkine, S.A. Carter, A.J. Millis, T . While a depression of the conductivity has been
MIT
T.F.Rosenbaum,P.Metcalf,andJ.M.Honig,Phys.Rev. observed in this work, it is difficult to judge on the T-
Lett.73 1529(1994). dependence of the gap and on the form of σ1(ω) across
[11] S.V. Dordevic, N.R. Dilley, E.D. Bauer, D.N. Basov, the gap. This as well as the large 2∆k T ∼ 20 ra-
B MIT
M.B.Maple,L.Degiorgi, Phys.Rev.B 6011321 (1999). tio pose problems for a SDW interpretation of the data.
[12] C.Homes,M.A.Reedyk,D.A.Crandels,andT.Timusk, SeeT.Katsufuji,Y.Okimoto,T.Arima,andY.Tokura,
Appl.Opt.32 2976 (1993). Phys. Rev.B 51 4830 (1995).
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Mineralogist 57 255 (1972).
[17] Of these seven phonons, six can easily be resolved in