Table Of ContentOptical Study of the Free Carrier Response of LaTiO /SrTiO Superlattices
3 3
S. S. A. Seo,1 W. S. Choi,1 H. N. Lee,2 L. Yu,3 K. W. Kim,3 C. Bernhard,3 and T. W. Noh1,∗
1ReCOE&FPRD, Department of Physics and Astronomy,
Seoul National University, Seoul 151-747, Korea
2Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
3Department of Physics and Fribourg Center for Nanomaterials,
University of Fribourg, 1700 Fribourg, Switzerland
8 (Dated: February 6, 2008)
0
0 We used infrared spectroscopic ellipsometry to investigate the electronic properties of
2 LaTiO3/SrTiO3 superlattices (SLs). Our results indicated that, independent of the SL period-
icity and individual layer-thickness,the SLsexhibited a Drudemetallic response with sheet carrier
n densityperinterface 3 1014cm−2. Thisisprobablyduetotheleakageofd-electronsatinterfaces
a ≈ ×
J from the Mott insulator LaTiO3 to the band insulator SrTiO3. We observed a carrier relaxation
time 35 fs and mobility 35 cm2V−1s−1 at 10 K, and an unusual temperature dependence of
7 ≈ ≈
carrier density that was attributed to the dielectric screening of quantumparaelectric SrTiO3.
]
l PACSnumbers: 73.20.-r,78.67.Pt,71.27.+a,73.40.-c
e
-
r
t Recent advances in the growth of atomic-scale mul- confirmation and direct investigation of such interfacial
s
. tilayers of perovskites have opened up new avenues for metallic states. Takizawa et al. recently measured pho-
t
a tailoring their electromagnetic properties. For example, toemissionspectraofLTO/STOSLswithatopmostSTO
m Ohtomo et al. grew superlattices (SLs) consisting of an layer of variable thickness [6]. They observed a metallic
- LaTiO (LTO) Mott insulator and an SrTiO (STO) Fermi edge, indicating the formation of a metallic IF.
d 3 3
band insulator with atomically abrupt interfaces (IFs) However, to date there have been no reports of quan-
n
o [1]. They observed an interesting charge modulation in- titative experimental information on the electrodynamic
c volving electron transfer across the IF from the LTO to properties of the itinerant electrons. Here, we present
[ the STO layers. This had a decay length of 1.0±0.2 nm, spectroscopic ellipsometry measurements of the infrared
2 which is about one order of magnitude larger than ex- (IR) dielectric properties for a set of (LTO)α/(STO)10
v pected for conventional Thomas-Fermi screening. Sub- SLs with α=1,2, 4, and5 unit cells ofLTO layerand10
5 sequent transport measurements have been interpreted unitcellsofSTO.OurIRopticaldatayieldreliableinfor-
1
in terms of an unusual metallic state with quasi two- mation about the intrinsic electrodynamic properties of
4
dimensionalproperties. Thisintriguingexperimentalob- theseSLs. First,theyclearlydemonstratethattheseSLs
3
0 servation has stimulated a number of theoretical inves- contain a sizeable concentration of itinerant charge car-
7 tigations [2, 3, 4, 5], which confirm that so-called “elec- riers. Furthermore, they establish that the sheet carrier
0 tronicreconstruction”[2]canindeedgiverisetoaunique densityisproportionaltothenumberofIFs,anditsabso-
/
t interfacial metallic state. lute value agreescloselywith the theoreticalpredictions.
a
m There is now a great deal of demand for experimental Ourdataalsohighlightanunusuallystrongtemperature
(T) dependence of the carrier density, which was unex-
-
d pected for bulk metals, but can be explained in terms
arXiv:con ((ba)) Intensity (a.u.)10500 STO200 TLTimO4e0 0(sSeTcO)600LTO800 Intensity (a. u.)111111000000234567 (003c004)005 006 007 008 00900110010* 0012 0013 0014 0015 0016 0017 0018 0019 0020 00210022* 0023 0024 ocPwguoflsOieneWtt2hdthc=reeropa1ylgTt0lusriot−-nleadsmwg5eleldipicTcnhheaoeilnalgralrdryhsSgee-wTenqrfliOtutatdrahtdaeli(inpeits0nslyou0efsre1csLifrt)tiaTrticaouisOcecnusrms/bocS(ssaorPtTsnenrLedOtaitnhDtoieeanSr)sibgLL.nraTsgoutOTfp∼ooTtt/f1hS=0teIdTh0F7oSeOs2nT0tsmhopOIFnie◦stc.Cl,ahusyiliwcanienkerr-
1 spot intensity of reflection high-energy electron diffrac-
10
tion (RHEED) (see Ref. [7] for more details on PLD
10 20 30 40 50
2 (degrees) growth). The RHEED intensity oscillations in Fig. 1(a)
confirmed the controlled growth of alternating LTO and
FIG. 1: (color online) (a) RHEED intensity oscillation
during the initial growth of the (LTO)2(STO)10 SL. (b) STOlayers. Doingthisatahigheroxygenpressurewould
atomic force microscope topographic image (5 5 µm2) of an resultinthegrowthofunwantedLa2Ti2O7 phases,asre-
×
(LTO)1(STO)10SL100nmthickwithsingleunitcellterraces portedpreviously [8]. After growth,all samples were ex-
conserved. (c) X-ray θ-2θ scan of (LTO)1(STO)10. Peaks posedimmediatelytoahigherpressure(P =10−2Torr)
O2
marked with (*) in (c) are reflected from theSTO substrate. forinsitu postannealingatgrowthT for5min,andthen
2
cooled to room T. No changes in the RHEED specu- thicknessofthe SLsis wellbelowourIRwavelength,the
lar spot pattern were observed after postannealing. The entireSLfilmcanbetreatedasasinglelayeraccordingto
atomic force microscope topographic image in Fig. 1(b) the effective medium theory. The resulting effective di-
shows that the SLs retained their single unit cell terrace electricfunctionsthuscorrespondtothevolume-averaged
stepsevenafterdepositionof∼250unitcellsofLTOand dielectricfunctionsofthecomponentsintheSL.Ourop-
STO. Figure 1(c) shows x-ray θ-2θ diffraction, exhibit- tical technique can provide intrinsic values of the bulk
ing well-defined satellite-peaks, confirming the high IF propertiesofthese SLs,whichcanbe comparedwith the
quality and SL periodicity of LTO and STO layers. The preexisting results of transport measurements [1].
full-width half-maximum ≤0.04◦ in ω-scan, which is al- Figures2(a)and2(b)showthe low-T spectra ofσ (ω)
1
most identical to the substrate scan, confirmed the high and ε (ω) for the series of (LTO)α/(STO)10 SLs with
1
crystallinity of the SLs. α=1, 2, 4, and 5. Significantly, all the spectra exhibited
We measured the T-dependent IR optical properties a prominent Drude-like peak at low frequency in σ1(ω)
of the SLs using ellipsometry in the range of 80-5000 and a strongly inductive response in ε1(ω), which pro-
cm−1 (10-600 meV). The far-infrared (FIR) measure- vided unambiguous evidence that these SLs contained
mentsfor80-700cm−1wereperformedwithahome-built sizeable concentrations of itinerant charge carriers. The
ellipsometer attached to a Bruker 66V Fourier trans- stronglyconductingresponsealsoseemedtodampoutIR
formIR(FT-IR) spectrometer atthe IRbeamline ofthe active phonons in the spectra. For quantitative analysis
ANKA synchrotron at FZ Karlsruhe, Germany [9]. For we applied the Drude-Lorentz fitting function:
themid-infrared(MIR)rangeof400-5000cm−1,weused ω2 Sω2
a home-built ellipsometer in combination with the glow- ε˜(ω)=ε∞− pD + 0 . (1)
ω2+iωΓ ω2−ω2−iωΓ
bar source of a Bruker 113V FT-IR spectrometer. The D 0
FIR (MIR) measurement was performed with an angle This is shown in Fig. 2(a) by the solid and dashed lines.
◦ ◦
of incidence of the linearly polarizedlight of 82.5 (80 ), TheparametersoftheDrudetermarethescatteringrate
i.e. close to the pseudo-Brewster angle of the SLs. De- Γ , and the plasma frequency ω2 = 4πne2/m∗, where
D pD
tails about the ellipsometry technique are given in Ref. n,e,andm∗ arethedensity,charge,andeffectivemassof
[9, 10]. Here, we only point out that the ellipsometry is the itinerant charge carriers, respectively. The parame-
a self-normalizing technique that directly measures the tersoftheLorentztermthataccountsforthebroadMIR
complex dielectric function ε˜(ω)[=ε1(ω)+iε2(ω)], with- band are the oscillator strength S, the width Γ, and the
out the need for Kramers-Kronig analysis. We also resonant frequency ω . A broad MIR band is commonly
0
measured the T-dependent spectroscopic response of a observed in conducting oxides and has been interpreted
bare STO substrate that was treated thermally under in terms of either the inelastic interaction of the itiner-
the same growth and annealing conditions of T and antcarriers,a secondtype ofcarrierin abound state,or
PO2 as the SLs. Then we used a uniaxially anisotropic low-lying interband transitions. As LTO is well-known
single-layer model [10] to obtain the in-plane compo- tohaveweakbroadMIRbands,the Lorentzpeakwith a
nent [11] of ε˜(ω), and the related optical conductivity small value of S can be reasonably interpreted to be the
σ˜(ω)[=ε˜(ω)ω/4πi=σ1(ω)-iε1(ω)ω/4π]oftheSLs. Asthe lowestintersited-d(i.e.,U-3J)transitionofLTO[12]. An
overview of the fitting parameters for the low-T spectra
is given in Table 1.
Most importantly, we noted that all the SLs have
14 20
-1 cm)1102 (a) CInochoehreernetn (tD (Lruodreen)tz) 1--42000 ((((LLLLTTTTOOOO))))1245////((((SSSSTTTTOOOO))))11110000(bp)* scouanrrrpsireuirsgsign.egsltTyiohhnisigohofbωsOepkrDva,amtaioontnod mathnoudtsivMahtiigelldhisdu[es2n]tsoiotfiefosallooqfwufaruseipe-
-1
3 (10 12468 ((((LLLLTTTTOOOO))))1245////((((SSSSTTTTOOOO))))11110000 3 -1-1 (10cm)112460001123155000000000 K K2KKKK000 3 (0c0 m(0LT-1O)4)20/(0S0TO(c)51)0000 tLpwTeroO-Id/FiSm,TneOnshseiIeoFtns=a.lnmWNdeIet,adwlleiirctihvsettdhaettehtoetthaslahtSeeLtdtechvaiecrlkroinpeesrssdinednastinhtdye
0 0
100 1000 100 1000 TABLE I:Drude-Lorentzfittingparameters for optical spec-
-1 -1
Wavenumber, (cm ) (cm ) tra of (LTO)α/(STO)10 SLs measured at 10 K.
FIG. 2: (color online) (a) Optical conductivity spectra of
Drude Lorentz
t(hLTeOco)hαe/r(eSnTtO(D)1ru0daet)1a0ndKin(cwoihtehrevnetrt(iLcaolreonfftsze)tcs)o,ntcroinbtuatiinoinnsg. α1 ωp62D.0(cm10−71) ΓD128(c(m3−)1) 75(S11) ω9020((cm9−51)) 1Γ98(0c(m−5810))
(b) SL real dielectric constant spectra as a function of pho- 2 6.6×107 144(±8) 51(±22) 980(±240) 1530(±1200)
ton wavenumber at∗10 K. The arrow indicates the screened 4 5.1×107 105(±6) 87(±20) 780(±200) 1630(±1000)
plasmafrequencyωp[=ωpD/√ε∞]. (c)T-dependentσ1(ω)of 5 6.1×107 122(±2) 126±( 8) 750(±65) 1740(±350)
(LTO)2/(STO)10. × ± ± ± ±
3
the number of LTO/STO IFs N of the SL [13]. Figure merous recent controversial studies and some debate in
I
3(a) shows n values within error-bars dependent on oxide electronics circles have centered on the discontin-
sheet
∗
the detailed assignment of m based on the analysis of uous IF polarity of LaAlO /STO [21] especially regard-
3
our ellipsometric data in the framework of the extended ing the origin of conduction due to the oxygenvacancies
Drude-model. Thisdirectlyyieldstherenormalizedmass [22]. AsindicatedbythearrowinFig. 3(a),therangeof
m∗/me =(ωp/ω)2(ε0−ε1)/((ε0−ε1)2−ε22). Notethatall nsheet values of LaAlO3/SrTiO3−δ grown at low oxygen
ofourSLsexhibitaverysimilarvalueofn ≈3×1014 pressure [23] is so wide that it also overlaps our experi-
sheet
cm−2 with m∗ =1.8m [14], which agrees well with the- mental value of n ≈ 3×1014 cm−2 as well as with
e sheet
oretical predictions [3, 5, 15]. the theoretical values [3, 5] of electronic reconstruction
Here,weshouldmentionthattheDrudetermisonlya at the LTO/STO IF. However, according to the recent
phenomenologicaldescription, and its microscopic origin report by Herranz et al., LaAlO3/STO films were all in-
is not clear. One possible explanation is in terms of a sulating orhighly resistivewhen cooledina high oxygen
chemicalintermixingofLaandSrionsacrosstheIFsbe- pressure environment from the deposition T to room T
cause LaxSr1−xTiO3 solidsolutions are metallic [16]. As [24]. We performed a similar in situ oxygen annealing
indicatedbythesolidcirclesinFig. 3(b),theexperimen- processtocompensateforpossibleoxygenvacancies,but
tal data of bulk LaxSr1−xTiO3 solid solutions reported our LTO/STO SLs still exhibited metallic behavior.
byFujishimaetal. [17]showthattheωpD valueincreases Another interesting aspect concerns the strong T de-
from x = 0.1 to 0.7, while it decreases above 0.7 due to pendence of n(T). Figure 2(c) shows the T dependence
the strong electron correlation effect as a function of in- of σ (ω) for (LTO)2/(STO)10, which are characteristic
1
creasing x. However,our SL data follow a different path of all SLs. Figure 4(a) shows that n(T) increased sig-
although the value of ωpD is expected to increase when nificantly by almost 30% between 300 K and 10 K. The
goingfromα=1toα=5,asshownbythesolidsquares corresponding n(T) in a conventional normal metal is
in Fig. 3(b). Moreover, the well-defined superstructure typicallyoftheorderof1%,evenforoxideswithstrongly
peaks in our x-ray diffraction data and the abrupt IFs correlated electrons. For the cuprate high-T supercon-
c
seen on cross-sectional transmission electron microscopy ductors, for example, it is smaller than 10% [25]. Even
(not shown) confirm that the extent of La and Sr inter- the opposite T dependence is observed for doped semi-
mixing is negligible. conductors where n(T) decreases as the carriers become
As other candidates of extrinsic origin, it is also trapped at low T. Thus, the increase of n(T) at low T
necessary to consider the possibility of oxygen excess also cannot be explained by the electron-doping effect
LaTiO3+δ [18] or La vacancy La1−xTiO3 [19] of LTO, of oxygen vacancies of STO. However, we note that the
and oxygen deficiency of STO [20]. The former possibil- quantum paraelectric behavior of incipient ferroelectric
ity can be excluded as our data for ωpD do not exhibit a STO exhibits a significant increase in dielectric permit-
corresponding change as the relative volume fraction of tivity (ǫSTO) as T decreases. Therefore, we can explain
0
the LTO layers is altered by a factor of 5 between α=1 the increase of n(T) in the context of electronic recon-
and 5. On the other hand, serious consideration should struction at an IF. The charge transfer across the IF of
begiventothelatterpossibilityofoxygendeficiencyand LTO/STO (and thus n ) should be affected by the
sheet
thus metallic SrTiO3−δ layers. It is noteworthy that nu- dielectric screening of the STO layer. The larger value
of ǫSTO thus gives rise to the larger screening length of
0
theelectroniccharges,andthisallowsmorechargestobe
4 transferred across the LTO/STO IF. (See also the the-
-2 (cm)n11sheet001156 (a) ((0OKLL.ak5TTna OOecm-h))oa//tr((olSSa eTT etOO ta ))al16.l.0 LaAlO/SrTiO33- et al.(Kalabukhov ) 4-1 (10 cm)pD23 (b[L)a]=n (FLuajixsShrim1-xaT eiOt a3l.) oretical predictio n of the coh4erent carri er density4a0s a
1 (LTO) /(STO)10 %)140 (a) (b)
FdiIcGa1t.0e31s04:.0th(ceov[lLoa0arl.u]2/o(e[nSolri]fn+e[a0L).n4a]()iad)eanl0s.6h0e.5etep00−e.0rpIe0Fr.2[.LuaTn]0/ih(.t4[eSScruse]0p+ole.l[l6rLiladaatrt]i0)cel.eia8ns,ea1in.n0d- (T)/(300K) (nn110200 -14 123 (10 sec) (((LLLTTTOOO)))124///(((SSSTTTOOO)))111000 123000 2-1-1 (cmVs)
(LTO)5/(STO)10
thedashed and dotted lines represent theoretically predicted 80 0 0
values reported by Kancharla [5] and Okamoto [3], respec- 0 100 200 300 10 100
Temperature (K) Temperature (K)
tively. The vertical arrow shows the range of nsheet in
LaAlO3/SrTiO3−δ IF from Ref. [23]. (b) Comparison of SL FIG.4: (coloronline)T dependenceof(a)thecarrierdensity,
ωpD with solid-solution [17] and the ideal doping of [La]=n and (b) the relaxation time and mobility of free carriers for
as a function of La and Srcomposition. (LTO)α/(STO)10 SLs.
4
function of ǫ by Kancharla [5].)
0
Figure4(b)displaystherelaxationtimeoffreecarriers
τ(T)[= Γ−1(T)]. As all of our LTO/STO SLs showed a
D ∗ Electronic address: [email protected]
significantly reduced ΓD, which is at least one order of [1] A. Ohtomoet al.,Nature419, 378 (2002).
magnitude smallerthan adoped Mottsystem[26], fairly [2] S. Okamoto and A. J. Millis, Nature 428, 630 (2004).
high mobility µ(10 K) ≈ 35 cm2V−1s−1 was obtained [3] S.OkamotoandA.J.Millis,Phys.Rev.B70,241104(R)
∗ ∗
according to the relation µ = eτ/m with m = 1.8m . (2004).
e
It wouldbe interesting to consider whether signaturesof [4] S. Okamoto and A. J. Millis, Phys. Rev. B 70, 075101
novel phenomena, such as the quantum Hall effect, may (2004), S. Okamoto and A. J. Millis, ibid. 72, 235108
(2005), S. Okamoto and A. J. Millis, Physica B-Cond.
beobservableintheLTO/STOSLs. Themeasuredvalue
of τ ≈ 3.5×10−14 s at 10 K yields ωcτ = 0.01−0.02, NM.aAtt..S3p5a9ld,i1n3,7P8h(y2s0.0R5e)v,.SL.eOttk.a9m7o,t0o5,6A80.2J.(2M00il6l)is,,Za.nSd.
∗
where the cyclotron frequency ωc = eB/m with the Popovic and S. Satpathy,ibid. 94, 176805 (2005).
magneticfieldB ≈20Tandm∗ =1.0−2.5me. Fromthe [5] S.S.KancharlaandE.Dagotto,Phys.Rev.B74,195427
obtained carrier density and mobility of our LTO/STO (2006).
SLs, we determined that the mean free path of the con- [6] M. Takizawa et al.,Phys. Rev.Lett. 97, 057601 (2006).
ductingelectronsisabout10nm(≈25unitcellslong)at [7] H. N.Lee et al.,Nature433, 395 (2005).
[8] A. Ohtomoet al.,Appl.Phys. Lett.80, 3922 (2002).
10K.Itisremarkablethattherewasarecentobservation
[9] C. Bernhard, J. Humlicek, and B. Keimer, Thin Solid
ofthequantumHalleffectinZnO-basedheterostructures Films 455-456, 143 (2004).
below1K[27],inwhichthecoherencelengthoftheelec- [10] R. M. A. Azzam and N. M. Bashara, Ellipsometry and
tron was considerably longer than those in other oxides. Polarized Light (North-Holland,Amsterdam, 1987).
In summary, our use of IR spectroscopic ellipsometry [11] Okamoto et al. [3] suggested sharp optical transitions
showedthatalltheLTO/STOSLsexhibitedaDrude-like along the c-axis due to bound states of quantum well-
metallicresponseregardlessoftheSLperiodicityandthe like structures in IR energy region (with t 0.3 eV).
∼
individual layer-thicknesses, even after in situ post an- However, the large refractive indices (>10) due to con-
◦
ducting IFs make the refraction angle 5 . Therefore,
nealing in oxygen. Our data yielded a nearly constant ≤
theelectricfieldofinfraredwavesisalmostparalleltothe
n per IFof∼3×1014 cm−2 with smallΓ of∼120
sheet D in-planedirection,anditallowsdiscussionofthein-plane
cm−1, and a sizeable mean free path of ∼25 unit cells at response only.
10K.WenotethattheunusuallystrongT dependenceof [12] J. S. Lee, M. W. Kim, and T. W. Noh, New J. of Phys.
n can be interpreted qualitatively as quantum paraelec- 7, 147 (2005).
tric behavior of STO with theoretical prediction of the [13] For (LTO)1/(STO)10 and (LTO)1/(STO)6, it is rather
ambiguoustodefinethenumberofIF.Here,wecounttwo
leakageofd-electronsfromLTOtoSTOacrosstheIF.A
IFs(bothsides)perLTOlayerforconsistencywithother
pictureofelectron-dopingbytheoxygenvacancyofSTO,
SL samples. Hence, the nsheet of (LTO)1/(STO)10 and
which has been the subject of recent debate on similar
(LTO)1/(STO)6 may be reduced due to overestimated
systems of LaAlO3/STO, is insufficient to explain our NI.
observations in LTO/STO SLs. Hence, we note the dif- [14] Note m∗ = 1.62me from the thermoelectric experiment
ference between an LTO Mott insulator and an LaAlO3 for LaxSr1−xTiO3 by T. Okudaet al., Phys. Rev. B 63,
band insulator, and suggest that the strongly correlated 113104 (2001).
[15] The values from the theoretical calculations of 6.5
d-electronsofLTOshouldplayanimportantroleinelec- 1014 cm−2 and 3.4 1014 cm−2 are obtained∼by int×e-
tronic reconstruction and the resultant metallic state at ∼ ×
grating the coherent d-electron density curves displayed
a polar (LTO) and nonpolar (STO) oxide IF.
in Figs. 2 and 2(a) of Refs. [3] and [5], respectively.
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as well as Y.L. Mathis for support at IR-BL of ANKA.
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tiatives (Functionally IntegratedOxide Heterostructure) [23] A.Kalabukhovetal.,Phys.Rev.B75,121404(R)(2007).
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project 200021-111690/1),and the Division of Materials [25] A. Toschi et al.,Phys.Rev.Lett. 95, 097002 (2005).
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and POSTECH.
