We present detailed optical measurements of the mid-infrared (MIR)
excitations in thin films of La2/3Sr1/3MnO3 (LSMO) and La2/3Ca1/3MnO3 (LCMO)
across the magnetic transition. The shape of the excitation at about 0.2 eV in
both samples is analyzed in terms of polaron models. We propose to identify the
MIR resonance in LSMO as the excitation of large polarons and that in LCMO as a
small polaron excitation. A scaling behavior for the low-energy side of the
polaronic MIR resonance in LSMO is established

Deisenhofer, J.

Hartinger, Ch.

Kopp, T.

Loidl, A.

Mayr, F.

English

arXiv

Hartinger, Christine

Mayr, Franz

Deisenhofer, Joachim

Loidl, Alois

Kopp, Thilo (Prof.)

OPUS Augsburg

RAPID COMMUNICATIONSPHYSICAL REVIEW B 69, 100403~R! ~2004!Large and small polaron excitations in La2Õ3„SrÕCa…1Õ3MnO3 filmsCh. Hartinger, F. Mayr, J. Deisenhofer, and A. LoidlEP V, Center for Electronic Correlations and Magnetism, Augsburg University, 86159 Augsburg, GermanyT. KoppEP VI, Center for Electronic Correlations and Magnetism, Augsburg University, 86159 Augsburg, Germany~Received 3 November 2003; published 8 March 2004!We present detailed optical measurements of the mid-infrared ~MIR! excitations in thin films ofLa2/3Sr1/3MnO3 ~LSMO! and La2/3Ca1/3MnO3 ~LCMO! across the magnetic transition. The shape of the exci-tation at about 0.2 eV in both samples is analyzed in terms of polaron models. We propose to identify the MIRresonance in LSMO as the excitation of large polarons and that in LCMO as a small polaron excitation. Ascaling behavior for the low-energy side of the polaronic MIR resonance in LSMO is established.DOI: 10.1103/PhysRevB.69.100403 PACS number~s!: 75.47.Lx, 78.20.Ls, 71.38.2k, 72.80.2rHistorically, polarons were best identified in measure-ments with charge carriers in nonmetals ~e.g., from F centersin alkali halides! or doped semiconductors. More recently,the concept of polaronic excitations has again been in thefocus of solid-state research with the advent of strongly cor-related electronic systems, especially with the discoveries ofhigh-temperature superconductivity and the colossal magne-toresistance in thin films of La2/3Ca1/3MnO3 ~LCMO!.1 Inboth classes of these correlated materials cuprates, and man-ganites, it is now widely accepted that, in the presence of astrong electron-phonon coupling, polaronic effects have to beconsidered an important ingredient to understand the com-plex physical properties of these compounds.2The fingerprints of polarons in the manganites are usuallyassociated with the temperature dependence of high-temperature dc resistivity3 and the occurrence of a midinfra-red ~MIR! excitation in the optical conductivity—termed po-laron peak in the following—which has been observed byseveral authors in both single crystalline4–8 and thin filmmanganites.9–11 Though evidence of the signature of po-larons in the optical conductivity12–14 has been reportedabundantly, the question whether the charge carriers arerather delocalized ~large polarons, LP! or strongly localizedin a locally polarized lattice ~small polarons, SP! remainsstill under debate in the case of manganites.Theoretically, SP and LP have been investigated in severalstudies15–17 on doped manganites, but the observed polaronpeak has been evaluated mainly in terms of the SP model orthrough Gaussian or Lorentzian fits for a phenomenologicaldescription.5,18 Kim et al. reported on experimental evidencefor a LP excitation in polycrystalline LCMO,6 but unfortu-nately they did not identify the LP through a fit to the pro-posed LP model by Emin.19The purpose of this paper is to elucidate the nature of thepolaronic charge carriers by comparison of optical spectros-copy measurements in thin films of LCMO andLa2/3Sr1/3MnO3 ~LSMO!. In contrast to single crystals theuse of thin films has the advantage of a lower conductivitydue to grain boundaries and internal strain. Consequently,screening is effectively reduced—to a level where phononsand polarons are well observable in the optical conductivity,0163-1829/2004/69~10!/100403~4!/$22.50 69 1004even in the metallic phase. This allows the detailed analysisof polarons from the respective optical data.We demonstrate that the distinctive shape of the polaronpeak in LCMO differs significantly from the one in LSMOallowing to distinguish between SP in LCMO and LP inLSMO. A striking characteristic of the polaron peak inLSMO is the observed scaling behavior for the low-energyside ~see Fig. 2!. We will confirm this scaling in a weak-coupling evaluation, analogous to that of Tempere andDevreese for an interacting many-polaron gas.20As the lattice distortion is of major importance for theeffect of charge-carrier localization, the structural differencesbetween LCMO, which is orthorhombically distorted, andLSMO, which reveals a rhombohedral symmetry, representpromising conditions to find distinct regimes of the electron-phonon coupling strength a and, consequently, to distinguishbetween competing polaronic models.Thin films have been prepared using a standard pulsedlaser deposition technique.21 They were grown onto singlecrystalline substrates: LSMO on (LaAlO3)0.3(Sr2AlTaO5)0.7and LCMO on NdGaO3. The typical thin film thickness wasbetween 200 nm and 400 nm. X-ray analysis revealed arhombohedral structure for LSMO and a preferred growthalong the @100# axis. For LCMO an orthorhombic structurewas found and the growth direction was @110#. Below roomtemperature the reflectivities of the sample and the pure sub-strate were measured using the Fourier-transform spectro-meters Bruker IFS 113v and IFS 66v/S, to cover the fre-quency range from 50 to 40 000 cm21. In addition, the re-flectance for frequencies from 10 to 30 cm21 was calculatedfrom the measured complex conductivity data, which wereobtained by submillimeter-transmission measurements usinga Mach-Zehnder-type interferometer. This setup allows themeasurement of both the transmittance and the phase shift ofa film on a substrate. The combined data sets were used for aKramers-Kronig analysis to obtain the optical conductivitys , the real part of the complex conductivity.In Fig. 1 we present s(n) for LSMO ~upper panel! andLCMO ~lower panel! at different temperatures. In the case ofLCMO, with a Curie-temperature TC5243 K, the spectra inthe complete frequency range were measured both in theparamagnetic ~PM! and in the ferromagnetic ~FM! regime.©2004 The American Physical Society03-1RAPID COMMUNICATIONSHARTINGER, MAYR, DEISENHOFER, LOIDL, AND KOPP PHYSICAL REVIEW B 69, 100403~R! ~2004!The data for LSMO, as shown in the upper panel of Fig. 1,only cover the FM regimes. We defined TC as the inflectionpoint and TMI as the point of the maximum in the dc-resistivity curve.In LCMO (d5200 nm) an almost symmetric but stronglytemperature-dependent maximum is observed in the MIRrange which suffers a continuous loss of the spectral weightupon increasing the temperature up to TC . Above TC thetemperature dependence is negligible. The maximum movesfrom 1800 to 5300 cm21. The loss in spectral weight can beexplained in terms of a decreasing carrier mobility.22 Thesefindings are in agreement with previous studies of Ca-dopedmanganites.6,10 For LSMO (d5400 nm), in contrast, there isa sharp onset which, along with the asymmetric peak, shiftsby approximately a factor of 2 in energy in the range 6 K,T,295 K. This trend continues up to the insulating phase,where the reflectivity data ~not shown! do not change anyfurther.23The prominent feature of the optical spectra, on which wewill concentrate in the following, is the distinctly differentshape of the polaron peak for LSMO and LCMO. In LSMOthe excitation is clearly asymmetric with a steep rise belowand a long tail above the peak position, whereas for LCMO abroader hump is visible which is more symmetric about itsmaximum ~compare Fig. 1!. A fit with standard single-polaron models highlights the remarkable qualitative differ-FIG. 1. ~Color online! Optical conductivity s for 6K<T<295 K. Straight lines represent data in the FM, dashed and dottedlines indicate the PM phase. Upper panel: LSMO (d5400 nm).The dotted line is to guide the eyes for the shift of the maximum ofthe MIR excitation. Lower panel: LCMO (d5200 nm).10040ences and allows a preliminary identification ~see the respec-tive optical spectra at 6 K in Fig. 2!. For the LP fit we tookthe phenomenological approach by Emin19 which assumes aphotoionization of the charge carriers from self-trapped intofree-carrier states. The threshold behavior of the respectiveoptical conductivitys~v !5np643e2m1v~k~v !R !3@11~k~v !R !2#4~1!reproduces the observed upturn at the low-frequency side ofthe polaron peak. Here, k(v)5A2m\(v2v0)/\ , with thetemperature-dependent threshold frequency for the absorp-tion v05E0 /\52pn0 ~see inset of Fig. 2!. E0 is interpretedas the energy difference between the localized ground stateand the lowest continuum state. The radius of the hydrogenicground state of the polaron is R, the density of polarons isnp , and m is the ~effective! mass of the free-carrier states atthe band minimum. For m53me (me is the free electronmass! and n05540 cm21, we find R/a50.8 with the latticeconstant a53.88 Å and np.431021 cm23 at 6 K. We chal-lenge this phenomenological approach below and propose amicroscopic modeling.The SP is interpreted in terms of the Holstein small-polaron theory. It has been proposed to apply an extension ofthe standard SP optical conductivity formula24,14 to the low-temperature optical spectroscopy:25,26FIG. 2. ~Color online! Comparison between fit and experimentfor the MIR excitation of LSMO ~upper panel! and LCMO ~lowerpanel! at 6 K using a LP model @Eq. ~1!, solid line# and a SP model@Eq. ~2!, dashed line#. Inset: polaron binding energy for LCMO(2Eb) and for LSMO (E0).3-2RAPID COMMUNICATIONSLARGE AND SMALL POLARON EXCITATIONS IN . . . PHYSICAL REVIEW B 69, 100403~R! ~2004!s~v ,T !5s~0,T !sinh~4Eb\v/D2!4Eb\v/D2e2(\v)2/D2. ~2!Here s(0,T) is the dc conductivity, Eb is the SP bindingenergy, D[2A2EbEvib, and Evib is the characteristic vibra-tional energy being kBT in the high-temperature regime and\vph/2 at low temperatures (kBT,\vph , vph is a phononfrequency!. Equation ~2! reproduces the broad resonancewith a maximum at 2Eb ~inset of Fig. 2!. The low-energy SPabsorption is well represented by the optical conductivity,Eq. ~2!. However, one would have to consider the conse-quences of a high polaron concentration for the absorption inorder to understand the slow decay on the high-frequencyside.As shown in the inset of Fig. 2, the binding energy 2Ebincreases towards the metal-insulator transition at TMI , andremains constant above TMI reflecting the significant role ofmagnetic interactions in a polaronic system as well as theimportance of electron-phonon interactions in the formationof the insulating phase. For LSMO the increase of E0 isweaker corresponding to a weaker electron-phonon interac-tion. As TMI is above room temperature for LSMO, s of theinsulating phase was not accessible in our experimentalsetup.Concerning LCMO, the SP picture is well accepted andboth the high-temperature dc resistivity3 and the rather sym-metric line shape close to the maximum of the polaronicexcitation suggest that the transport is controlled by incoher-ent tunneling of SP. For LSMO, the interpretation of thepolaron peak in terms of LP is not as obvious. However, anobservation related only to LSMO proves to be most valu-able in restricting the possible scenarios.If we scale the frequency by the T-dependent thresholdvalue n0 and the optical conductivity by its maximum valueat the polaron peak, we find a universal low-energy slopeindependent of temperature ~see Fig. 3!. This scaling signi-fies that the low-energy scattering processes which contrib-FIG. 3. ~Color online! Rescaled optical conductivity of LSMO:s is scaled by the maximum of the resonance, n is scaled by thethreshold value n0 of the onset of the polaronic peak. For Ds wesubtracted a constant background sbg5370 V21 cm21 ~cf. Fig. 2,Ref. 27!. The scaling at the low-frequency slope is nearly indepen-dent of the precise value of sbg .10040ute to the absorption for this frequency range relative to n0are of the same origin independent of temperature, relatedband narrowing, and other energy scales.We challenge that Emin’s phenomenological approach isapplicable here: ~i! it would reproduce the scaling if the di-mensionless polaron radius %[RA2mE0/\ were the samefor all temperature sets; however, % varies from 0.6 to 0.8, arange of values too large to convincingly support the scaling;~ii! the polaron radius R/a50.8 is small and local latticeeffects have to be accounted for; ~iii! there is no hole-bandminimum available to which the excited charge carrierscould scatter. Furthermore, the energy difference from themobility edge below which the trapped polarons would re-side to the hole-band minimum would have to be the thresh-old frequency. This frequency is about 540 cm21 at 6 K andis too small for the addressed energy difference.Consequently the modeling has to be revised as to imple-ment LP’s with finite mass and a finite density of chargecarriers ~Fermi edge!. In weak-coupling theory, the generali-zation of the single-polaron absorption by Gurevich, Lang,and Firsov28 ~GLF! ~dotted curve in Fig. 4, a is the couplingstrength!,sGLF~v !5anp23e2m1v0S v0v D3A vv021, ~3!to the situation of many-particle absorption was carriedthrough by Tempere and Devreese for a Coulomb gas.20 Theoptical conductivity for a similar approach, which builds onthe Hubbard model, is presented by the solid curve in Fig. 4.For the manganites in the ferromagnetic, metallic regime, wetake the following standard simplifications for the low-temperature evaluation: ~a! only one spin direction prevails~spinless fermions! due to double exchange and strongHund’s coupling; ~b! there are two degenerate orbital statesFIG. 4. ~Color online! Comparison of the low-temperature MIRoptical conductivity to s(n) from various model calculations: thesolid line refers to the weak-coupling approach of Tempere andDevreese modified for an on-site Hubbard interaction, well approxi-mated by Eq. ~4!; the dashed line is the result of the phenomeno-logical approach for self-trapped large polarons by Emin, Eq. ~1!;the dotted curve is the weak-coupling single-polaron result ~GLF!,Eq. ~3!.3-3RAPID COMMUNICATIONSHARTINGER, MAYR, DEISENHOFER, LOIDL, AND KOPP PHYSICAL REVIEW B 69, 100403~R! ~2004!~the two eg levels!; ~c! the interaction is represented by thelocal Hubbard U for two fermions on the same site in two egorbital states. We adjust the parameters as follows: the den-sity of charge carriers is np5631021 cm23, which is thestoichiometric number of doped holes and which is in therange of what has been estimated from Hall measurements.29Using m.3me , consistent with specific-heat measure-ments,30 we then estimate E f /h53270 cm21. Since n05540 cm21 for the 6 K data, we fix the ratio hn0 /E f50.17, i.e., we are in the adiabatic regime. Finally, we varyU/E f in the range 0.1–5. For values of hn0 /E f,0.3, theabsorption shape is nearly independent of U/E f , except thatthe magnitude of smax scales down with increasing U/E f .For U/E f50.1, we have smax5a(2.373103) V21 cm21which should fit the data with a of the order of 1.For the considered frequency range above the threshold,we are always sufficiently close to the Fermi edge in order toapproximate the frequency dependence of the imaginary partof the dielectric response by (v2v0), the number of excitedlow-energy particle-hole pairs. The scaling of the low-frequency slope ~as suggested in Fig. 3! is implementedthrough the increase of the number of particle-hole pairs withincreasing frequency ~relative to the Fermi edge!. The de-crease at the high-energy side is controlled by a 1/v3 factor,most easily identified in the force-force correlation functionform of the conductivity. Consequently, we expect the opticalconductivity to approachs~v !}S v0v D3S vv0 21 D . ~4!Indeed, this formula matches the frequency dependence of10040the numerically calculated s(v) ~solid line in Fig. 4!. Themodel reproduces the observed shape of the polaron peakquite convincingly and it accounts for the scaling. However,it does not provide a mechanism for the observed shift of thethreshold with temperature—which is probably controlled bythe electron-phonon coupling strength. This necessitates toextend the considerations to intermediate or strong-couplingsituations, first and foremost in the adiabatic limit. Such anevaluation is not available yet. It has to involve the collectiveresponse of the Fermi sea to the formation of a potential wellduring the absorption process which leads to singularities inthe optical conductivity, well known from the x-ray edgeproblem. Recoil of the polaronic lattice deformation, whichis taken up in the excitation process of the charge carrier tothe Fermi edge,31,32 flattens the singularity and might be re-sponsible for the observed shape. Though the consequencesfor the shape of the absorption spectrum are speculative, thesingular response is supposed to be present in any modelwith a sudden creation of a heavy or localized scatterer in thepresence of a Fermi sea, and it will have to be investigated.Apart from these considerations, the simple modeling pre-sented above already characterizes the observed polaron ex-citations sufficiently well and we are in the position to iden-tify the nature of the polaronic processes in LSMO andLCMO films as large and small polarons, respectively.We acknowledge discussions with K.-H. Höck, T. S. Nun-ner, R. Hackl, A. Nucara, and P. Calvani. We thank J. Gold-fuss and W. Westerburg for placing the samples at our dis-posal. The research was supported by BMBF ~Grants Nos.13N6917, 13N6918A! and partly by DFG through SFB 484~Augsburg!.1R. von Helmolt et al., Phys. Rev. Lett. 71, 2331 ~1993!.2P. Calvani, Optical Properties of Polarons ~La Rivista del NuovoCimento, Bologna, 2001!.3D.C. 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Large and small polaron excitations in La2/3(Sr/Ca)1/3MnO3 films

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Large and Small Polaron Excitations in La2/3(Sr/Ca)1/3MnO3 Films

Large and Small Polaron Excitations in La2/3(Sr/Ca)1/3MnO3 Films

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