Article
Reference
Transport properties in doped Mott insulator epitaxial La
1-xTiO
3+deltathin films
GARIGLIO, Stefano, et al.
Abstract
We report on the transport properties, Hall effect and resistivity, of epitaxial La1-yTiO3+delta thin films. The materials, grown by molecular beam epitaxy, display a temperature independent Hall coefficient and a characteristic T-2 dependence of the resistivity over a wide temperature range, extending from a few Kelvin to 500 K. These transport properties are shown to be consistent with small polaron metallic conduction with a dominant optical phonon mode whose energy, (h) over bar omega (0) = 80 K, is characteristic of the tilt/rotation of the oxygen octahedra in perovskite materials.
GARIGLIO, Stefano, et al . Transport properties in doped Mott insulator epitaxial La
1-xTiO
3+deltathin films. Physical Review. B, Condensed Matter , 2001, vol. 63, no. 16, p. 161103
DOI : 10.1103/PhysRevB.63.161103
Available at:
http://archive-ouverte.unige.ch/unige:114261
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1 / 1
Transport properties in doped Mott insulator epitaxial La
1ÀyTiO
3¿␦thin films
S. Gariglio,1,2J. W. Seo,3,2J. Fompeyrine,2J.-P. Locquet,2 and J.-M. Triscone1
1DPMC, University of Geneva, 24 Quai E.-Ansermet, 1211 Geneva 4, Switzerland
2IBM Research Laboratories, 4 Sa¨umerstrasse, 8804 Ru¨schlikon, Switzerland
3Institut de Physique, University of Neuchaˆtel, 2000 Neuchaˆtel, Switzerland
共Received 8 December 2000; revised manuscript received 8 February 2001; published 6 April 2001兲 We report on the transport properties, Hall effect and resistivity, of epitaxial La1⫺yTiO3⫹␦thin films. The materials, grown by molecular beam epitaxy, display a temperature independent Hall coefficient and a char- acteristic T2dependence of the resistivity over a wide temperature range, extending from a few Kelvin to 500 K. These transport properties are shown to be consistent with small polaron metallic conduction with a dominant optical phonon mode whose energy,ប0⫽80 K, is characteristic of the tilt/rotation of the oxygen octahedra in perovskite materials.
DOI: 10.1103/PhysRevB.63.161103 PACS number共s兲: 71.38.⫺k, 71.30.⫹h, 72.80.Ga, 73.50.⫺h
The discovery of high Tc superconductivity in cuprates1 and the variety of exceptional electronic properties observed in oxides, have recently stimulated numerous theoretical and experimental studies of strongly correlated electronic sys- tems and in particular doped Mott insulators. In these latter materials, the Coulomb electron-electron interaction is re- sponsible for the opening of a gap in the d-band. At half filling, the material is a Mott insulator with an antiferromag- netic ordering driven by the magnetic electron-electron inter- actions. Upon doping, metallicity is recovered with elec- tronic properties strongly dependent on the system and the doping level. Among materials exhibiting electronic correla- tions, LaTiO3 is a compound that has been extensively studied.2 LaTiO3 is known as a Mott insulating Ti3⫹ com- pound, antiferromagnetic below 140 K,3with a distorted per- ovskite structure and a small charge gap of 0.2 eV. This material can be doped by changing the La/O stoichiometry or by substituting Sr or Ba onto the La sites.3–5As the doping level is changed, the electronic properties evolve from a Mott insulator (Ti3⫹) to a band insulator (Ti4⫹), with a me- tallic region in between. The electronic properties close to the metal-Mott-insulator transition have been studied in de- tail in La1⫺xSrxTiO3 by Tokura et al.4It was found that the system behaves as a Fermi liquid up to the vicinity of the metal-insulator transition with a carrier density, measured by Hall effect, proportional to the doping level. A particularly striking T2 temperature dependence of the resistivity, up to room temperature, was observed as well as an increase in the carrier mass as the transition was approached. This behavior has been originally discussed in terms of strong electron- electron correlations although the temperature range over which the T2 behavior is observed is very large as compared to what is observed in transition metals or heavy fermions compounds
共
in transition metals the T2 behavior is observed at most up to 20 K兲
.6 Also, the ratio A/␥2, A being the coefficient of the T2term in the resistivity and␥ the specific heat coefficient, measured in La1⫺xSrxTiO3 is much larger than what is observed in other transition metals exhibiting a T2 behavior. It is also striking to notice that the T2behavior of the resistivity is in fact observed more clearly for x⫽0.5, far from the metal insulator transition, where the carrier ef- fective mass is not very large and the electronic correlationssubstantially reduced. On the same system, in 1992, Fujimori et al.7have reported on photoemission experiments allowing to study the changes in the electronic properties as a function of the doping level. An interesting peak in the photoemission spectra, 1.5 eV below the Fermi level, was observed. This feature, not predicted by band theory and tentatively attrib- uted to the lower Hubbard band, had a maximum intensity for x⫽0 but did not disappear or shift even at high doping levels (x⫽0.9), a result, as pointed out by the authors, dif- ficult to understand since the short-range Coulomb repulsion should become less important far from the Mott insulator and the band theory should recover. In 1996, the same group8did interpret its photoemission data, and in particular the 1.5 eV peak as a signature of the polaronic nature of the charge carriers. Their results suggest a rather small polaronic radius of 2.7 Å, consistent with a high carrier concentration. Recent experiments, close to the band insulator, also suggest polaron hopping as a transport mechanism in La2/3TiO3.9 In the co- lossal magnetoresistance materials, such as La1⫺xCaxMnO3, the temperature dependence of the resistivity below the ferromagnetic-antiferromagnetic transition, is also close to T2. This behavior has been studied in details and several ideas have been developed to explain this behavior observed below 100 K.10 Recently, Zhao et al.11 have proposed that the experimental resistivity data can be understood if small polaronic transport is the dominant conduction mechanism in these materials. Taking also into account the contribution of two-magnon scattering due to the ferromagnetic state, the data can be well fitted to the theory. The results suggest that only a low lying optical phonon mode (
ប
0⫽80 K兲
contrib- utes substantially to the resistivity. This mode is characteris- tic of perovskite materials, related to the tilt/rotation of the oxygen octahedra, and strongly coupled to the carriers.12In this paper, we have studied the transport properties, resistivity and Hall effect, of epitaxial films of La1⫺yTiO3⫹␦. We find that the resistivity behavior can be perfectly explained by small polaron transport theory with a dominant phonon mode at an energy of 80 K. This energy, very similar to the one found by Zhao et al.11 in La1⫺xCaxMnO3, is in agreement with Raman data on LaTiO3 and suggests that there is some universality in the transport behavior of metallic perovskites, related to the
structure of the materials and to the strong electron phonon interaction present in these compounds.
The system studied here, LaTiO3, is a distorted perovskite Mott insulator with an O-Ti-O buckling angle of about 10 degrees. Doping is achieved by changing the La/Ti and/or the Ti/O ratios, leading to a modification of the Ti valence, ionic radius and unit cell volume.3,13 Epitaxial thin films of La1⫺yTiO3⫹␦
共
LTO兲
were deposited, using a molecular beam epitaxy system and a chemical block-by-block deposi- tion method.14The La and Ti evaporation rates, typically one unit cell per minute, were measured and controlled with quartz monitors and mass-spectrometers leading to a preci- sion on the La/Ti ratio of about 5–10 %. Several series of LTO samples have been grown at a substrate temperature of 800 °C on共
001兲
LaAlO3共
LAO兲
, and共
001兲
MgO.In situ reflection high energy electron diffraction analyses show a relaxation of the epitaxial strains and a 2D growth.
Ex situ ⫺2 diffractograms of the films can be indexed with only
共
00l兲
reflections. Finite size effect oscillations around the共
00l兲
peaks were observed, indicative of good structural coherence throughout the film. The c-axis param- eter is found to be between 3.95 and 3.93 Å depending on the doping level. The rocking curve around the共
001兲
reflec- tion is typically 0.1°. Oscillations in low angle scans suggest a flat surface, and atomic force microscopy reveals a peak- to-valley height of about two unit cells and a root-mean- square roughness of 4 Å. To control the doping level in the films, we tuned the oxygen content during the deposition while keeping the La/Ti ratio共
within 5%兲
constant. For samples grown in low oxygen pressures (10⫺8– 10⫺7 Torr兲
, a metallic behavior over most of the temperature range was observed, whereas for higher oxygen pressures (10⫺6– 10⫺5 Torr兲
a semiconducting behavior was observed with eventually the formation of ferroelectric La2Ti2O7.15 To quantify the doping level of the films we measured the Hall effect as a function of temperature to obtain the carrier den- sity. The carrier density can then be related to the doping level using the results of Tokura et al. (La1⫺xSrxTiO3) who observe a linear relation between the doping level and the carrier density up to the vicinity of the Mott insulator.4 To unambiguously define the doping level, we use x*⫽Ti3⫹/(Ti3⫹⫹Ti4⫹), which varies from 0 to 1 as one goes from the band insulator to the Mott insulator.16The transport properties of the metallic films have been studied in details on patterned samples. Resistivity and Hall effect paths were prepared by lithographic processing and dry etching. Figure 1 shows a characteristic result for the Hall constant RH as a function of temperature in the range where metallic transport is observed. The inset shows the Hall voltage as a function of magnetic field, between ⫺5 T to 5 T, at 150 K. As can be seen from the data the Hall constant is essentially indepen- dent of temperature with a sign corresponding to electrons.
Using the standard free carrier Hall effect formula RH⫺1
⫽en, where e is the electron charge, n the carrier density, one finds that the metallic films have typically a carrier con- centration between 5–12 1021electrons per cubic centimeter corresponding to a doping level of x*⫽0.3– 0.7, typically in between the band and Mott insulator. Figure 2 shows the resistivity as a function of temperature for a LTO thin film,
25.0 nm thick with a carrier concentration of 1.2 1022 cm⫺3, plotted between 4 K to 600 K. Measurements at very low temperatures
共
15 mK兲
did not reveal any superconductivity17 and we systematically observe, below a characteristic tem- perature TM⫺I, that the resistivity increases as the tempera- ture is reduced, as shown in the inset of Fig. 2, pointing to an insulating ground state. At higher temperatures, the resistiv- ity is roughly proportional to T2, this region will be analyzed in details below. Above room temperature the measurements were performed in an oxygen flow up to 600 K. Above 550 K, the resistivity behavior changes dramatically and in- creases steeply as the temperature increases. This high tem- perature increase of the resistivity is not reversible. To avoid difficulties related to changes in the composition and/or film quality, we restricted our analyses to temperatures below 500 K where the resistivity is unaffected by thermal cycling.The T2 resistivity behavior observed at intermediate tem- peratures has often been taken as a result of strong electron- electron correlations resulting from the proximity to the Mott insulating state. The resistivity behavior observed in Fig. 2, FIG. 1. Hall coefficient of a LTO 22 nm thick film as a function of temperature. Using the standard free electron formula one finds that the carrier density is n⫽1022 cm⫺3. Inset, transverse voltage as a function of magnetic field measured at 150 K.
FIG. 2. Resistivity of a LTO thin film as a function of tempera- ture. A steep increase of the resistivity at high temperatures and a following irreversibility in the cooling suggests a change in the doping level above 550 K. In the metallic range, the resistivity displays a temperature dependence close to T2. Inset,between 15 mK and 10 K.
S. GARIGLIO et al. PHYSICAL REVIEW B 63 161103共R兲
161103-2
however, can also be understood if polaronic transport is considered. As described for crystalline semiconductors,18 there are three different regimes of transport. At low tem- peratures, the electrons are bound and an activated resistivity is observed ( decreases as T increases
兲
, at higher tempera- tures a polaronic band is formed, and a small polaron metal- lic transport is observed. The heavy particles are scattered by phonons and thus the resistivity increases with increasing temperature. Above 1/2⌰
D, where⌰
D is the Debye tem- perature, the mean free path is smaller than the lattice spac- ing and hopping conduction is observed, decreases again as T increases. The data shown in Fig. 2 are consistent with this scenario assuming that the latter hopping high tempera- ture regime is masked by changes in oxygen stoichiometry discussed above.To better understand whether the observed behavior is related to polaronic transport, we focused our attention to the
‘‘metallic’’ region which extends over a temperature range that is large enough to perform a detailed fit to the data. For polaronic transport in the metallic regime19the Hall constant should take the form:
RH⫽␥⬜
en,
共
1兲
where e is the electron charge, n the carrier density, and␥⬜
a constant close to 1 implying that the Hall constant is es- sentially probing the carrier concentration. If small polaron metallic conduction is considered, the resistivity should take the form:19
共
T兲⫽共ប
2/ne2a2tp兲
Asinh2
共ប
0/2kBT兲 共
2兲
assuming only one low lying optical mode 0 with strong electron phonon coupling. In the above formula, a is the lattice constant, A is a constant depending on the electron- phonon coupling strength and tp is the hopping integral of polarons. Figure 3 shows the resistivity as a function of tem- perature between 4 and 300 K for a 22.0 nm thick film with n⫽1022 cm⫺3. The line on Fig. 3 is a fit to:
共
T兲⫽
0⫹C/sinh2共ប
0/2kBT兲
.共
3兲
As can be seen, the fit is excellent with 0⫽0.20 m
⍀
cm, C⫽2.3 ⍀
cm, andប
0/kB⫽80 K.20The interesting point is that the phonon frequency obtained from the fit is very similar to the one extracted by Zhao et al. from their own resistivity fits on La1⫺xCaxMnO3. This soft mode seems to be characteristic of the tilt/rotation of the oxygen octahedra in perovskite materials. In LaTiO3, Raman data21gives clear evidence for the existence of a soft mode at an energy of about 100 K, reinforcing substantially our interpretation of the resistivity data. Additionally, if small polarons transport is the correct interpretation of the resistivity data, it would allow to unify the picture emerging from transport and pho- toemission experiments. These results thus strongly suggest that the physics at intermediate doping levels in La1⫺yTiO3⫹␦ is dominated by electron-phonon interactions and not by electron-electron correlations. Comparing the data on La1⫺yTiO3⫹␦ and on La1⫺xCaxMnO3 suggest that there is some universality in the transport properties of me- tallic perovskite systems. This universality being related to the existence of a soft mode, intimately related to the struc- ture of the perovskites and the proximity of these systems to ferroelectricity. Although difficult experimentally, growing materials closer to the Mott insulating state and studying their transport properties is important to probe the range over which transport is dominated by polaronic effects. Finally, we notice that if the phonon modes of a perovskite, in a bilayer or trilayer stack, are not confined, they will affect the scattering rates in the adjacent layers. This is essentially in- dependent of whether that perovskite is metallic or not. In- sulating perovksites with a high dielectric constant are cur- rently being investigated as replacement gate oxides for SiO2 in CMOS devices.22 However, so far the reported p- and n-mobility23 remained below those currently achieved with SiO2, which might be precisely related to the phenomenon discussed in this paper.In conclusion, we have grown epitaxial films of the doped Mott insulator La1⫺yTiO3⫹␦ compounds. The transport properties of these films, including Hall effect and resistivity have been studied. At low temperatures the resistivity always increases as the temperature is decreased suggesting an insu- lating ground state. At higher temperatures a metallic regime is observed. The resistivity behavior can be perfectly ex- plained if small polaronic metallic transport is assumed with a dominant optical phonon mode with
ប
0⫽80 K. This mode, observed in Raman experiments on LaTiO3, seems also to dominate the transport properties of colossal magne- toresistance compounds. Our results and analysis strongly point to a physics at intermediate doping levels in La1⫺yTiO3⫹␦ dominated by electron-phonon interactions and not by electron-electron correlations.We thank G. Zhao for useful discussions on polaronic transport. This work was supported by the Swiss National Science Foundation.
FIG. 3. Resistivity of a LTO 22 nm thick film with n
⫽1022 cm⫺3. The continuous line is a fit of the resistivity to a polaronic conduction mechanism. Details of the fit are discussed in the text.
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16While the Hall effect gives an estimate for the total average dop- ing level (3y⫹2
␦
), it does not allow to disentangle how much carriers are induced through La deficiency or additional oxygen.Indeed, the oxidation mechanisms are complicated in LTO.
Since the perovskite LaTiO3structure is already very dense, it is not clear how a small quantity of additional oxygen can be in- corporated without very large local distortions to the structure.
In such a case, it seems easier that doping proceeds via La vacancies, while preserving the overall perovskite structure. On the other hand, for a large quantity of oxygen, this becomes easier when all the additional oxygen can be concentrated in one additional plane in the structure.
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20Although on Fig. 3 the fit is shown between 4 and 300 K, a fit of similar quality is obtained between 4 and 500 K.
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