Evaluation of similarities and differences of LiTaO3 and LiNbO3 based on high-T-conductivity, nonlinear optical fs-spectroscopy and ab initio modeling of polaronic structures

Different aspects of ferroelectric LiTaO3 (LT) such as polaronic defects, optical response and electrical conductivity are investigated by the most recent theoretical and experimental approaches. Comparing the results with the state-of-the-art knowledge of the widely studied LiNbO3 (LN), we evaluate the general assumption that there is little difference between the aforementioned properties of LT and LN. First-principles calculations reveal the existence of point defects in LT qualitatively compatible with the polaronic picture established in LN. Though, peculiar differences with respect to the individual binding energies and polaronic deformation can be revealed. Accordingly, (sub-)picosecond transient absorption measurements show pronounced differences in the kinetics in the sub-ps time domain of small polaron formation and, even more pronounced, in the long-term evolution identified with small polaron hopping. In contrast, (sub-)ps transient luminescence, attributed to the relaxation of self-trapped excitons in LN, shows very similar kinetics. Electrical conductivity measurements are performed in air as function of temperature. Up to about 600 °C they demonstrate similar temperature dependence for the two materials, from which rather comparable activation energies can be extracted. However, in the high-temperature range from about 600 °C to 920 °C both materials show noticeable differences. The results suggest that the fundamental microscopic understanding of LN can be in part transferred to LT. However, due to differences in structure, energetic landscape and temperature behavior, discrepancies between the two materials bear a striking potential for novel applications, even at high temperatures.


Introduction
Since the discovery of its ferroelectric nature in 1949 [1], LiNbO 3 (LN) has become one of the most employed electro-acoustic and electro-optical materials for technological applications. Its uncommon, unusually large and favorable properties [2,3] are indeed exploited in a wealth of applications. Correspondingly, LiNbO 3 is one of the most intensively investigated ferroelectrics [4][5][6][7][8][9][10][11][12][13][14][15]. The effort of the ferroelectric community, in particular in the last 50 years, has led to unprecedent deep insight in the physical mechanisms determining the materials characteristics. A row of material properties, including its optical response, can be interpreted and modeled within the concept of quasiparticles called polarons and their dynamics [16]. Furthermore, LiNbO 3 has become a testbed for generations of scientists, trying to tailor its optical properties or elucidate and enhance technologically relevant effects (e.g. the bulk photovoltaic effect [17]). Many of the material's properties are largely determined by intrinsic defects [18,19], which are present in high concentrations due to the Li-deficient growth (congruent composition). Structural models based on Nb vacancies [20] or Li vacancies [21,22] have been proposed by different scientists to explain the congruent composition. Vibrational spectroscopy has provided valuable information concerning the material composition [4, 5, 11-13, 23, 24]. Summarizing, LiNbO 3 has been the drosophila of the optically active ferroelectrics, on which a wealth of ideas, technologies and procedures have been tested [25][26][27][28]. In addition, high-temperature properties are attracting increasing interest, since the piezoelectric coefficients of LN are very high compared to high-temperature stable piezoelectric crystals such as langasite (La 3 Ga 5 SiO 14 [29,30]), and thus LiNbO 3 based actuator applications are desired. Related investigations of the thermal stability and of the atomistic transport processes has been performed as function of Li content [31][32][33].
At the same time, our knowledge of similar ferroelectric crystals such as ferroelectric LiTaO 3 is rather limited. Lithium tantalate is, like LiNbO 3 , an opical crystal [34,35], which is the functional material in devices exploiting its bulk [36,37] or surface properties. LT crystallizes within the R3c space group below the Curie temperature as lithium niobate [2,38,39], and within the space group R3c above it [40,41]. The lack of a comprehensive literature about LT might be in part due to the common assumption that the properties of structurally and electronically similar ferroelectric crystals such as LN and LT differ only slightly, and a corresponding systematic is not necessary. Also, some of the crystal physical parameters in LT, such as electro-optic coefficient, do not reach the magnitudes found in LN. However, it is also reported that LT features severe fundamental differences to LN, for example the Curie (940 K vs 1480 K) [42] and melting (1923 K vs 1526 K) [43] temperatures, as well as the coercive fields (17 kV cm −1 vs 40 kV mm −1 ) [44] are very different in the two compounds. These aspects are of particular relevance in applications where ferroelectric poling, transport along ferroelectric domain walls, or high-temperature stability are exploited.
In order to evaluate the validity of the general assumption that there is only little difference between LN and LT, we identify at fist the most representative properties of the model system LN. LN is one of the most important opto-electronic materials, with a multitude of further applications in surface acoustic devices and sensors. Therefore polaronic structures, optical response and transport properties are chosen as characteristic and crucial aspects of LN. This list of properties is of course not exhaustive, however it suffices to provide a representative description of the material. In a second step, we perform an independent investigation of the selected properties in LN and LT, using the most advanced methods available to highlight differences and similarities between the two materials.
Commercially available LN samples are strongly Li deficient and their composition is referred to as congruent. Congruent crystals are characterized by a substantial concentration of point defects. Among these, Nb Li antisites are able to localize electrons in their close neighborhood, resulting in the formation of small electron polarons. It might thus be expected that electron polarons also exist in the isomorphic and isoelectronic lithium tantalate, which also crystallizes in a congruent composition. However, the proof of the existence of small polarons in LiTaO 3 is still missing. Although vacancies [45] and defect clusters [46] have been investigated from first principles, a detailed theoretical description of polaronic defects in LT elucidating the interplay between atomic and electronic structure is not available in the literature.
In this work, we at first explore the possibility of polaron formation in LiTaO 3 . The goal is the identification of defect centers compatible with the polaronic picture. We provide an atomistic description of polaronic defects at the microscopic scale based on ab initio models within the DFT +U method. This method allows for the accurate modeling of strongly correlated electrons such as the Ta 5d orbitals, and is thus essential for an accurate modeling of the investigated materials. Free polarons, for which an atomistic description is missing both in LN and LT, as well as intrinsic bound small polarons or bipolarons are considered. We demonstrate that structural properties, the electronic band structures as well as the spatial extension of the squared wavefunctions of isolated Ta 4+ Li antisites and nearest-neighbor Ta 4+ Li − Ta 4+ Ta pairs are compatible with the polaronic picture. Similarities and differences with corresponding structures in LN are discussed.
In a second step, we perform (sub)picosecond time-resolved absorption and luminescence spectroscopy to investigate the optical response dynamics of congruent LT and LN single crystals. It is already widely accepted, that (ultrafast) absorption spectroscopy is a powerful tool to inspect the formation dynamics on the sub-ps time domain and the hopping and recombination regime that is reported up to milliseconds. In contrast, transient luminescence on the sub-ps to ps-time scale is associated with the relaxation dynamic of self-trapped excitons. The latter is investigated in this study with the recently introduced technique of femtosecond fluorescence upconversion spectroscopy, modified for the inspection of weakly luminescing solid state samples [47]. Accordingly, the results presented here are the first reported for LiTaO 3 in the difficult to access (sub)picosecond time range, providing insight into the early stages of carrier localization phenomena. As to be expected from the findings in the energetic landscapes of the polaronic states, the transient absorption reveals significant differences in the sub-ps time-domain of formation kinetics. More pronounced, we find an increase of the lifetime in the transport hopping regime, while overall kinetics are less manifold. In the transient luminescence, in contrast, on ultrashort timescales both samples show practically identical kinetics. Assuming its origin from optically generated self-trapped excitons as in LN, it can be concluded that the features related to the ideal LT lattice are not very much altered when compared with LN.
Finally, measurements of electrical conductivity are performed in the temperature range from about 350 • C to 920 • C for congruent LiNbO 3 and LiTaO 3 crystals. Up to 600 • C, the activation energies have similar values. Furthermore, the magnitude of the conductivity of both materials differs only slightly. At 600 • C, Czochralski grown LN and LT exhibit conductivities of 2.6 × 10 −4 and 3.0 × 10 −4 S m −1 , respectively. Consequently, similar transport mechanisms appear to be dominant. However, in the high-temperature range from about 600 • C to 920 • C both materials show noticeable differences. The activation energies cannot yet be determined as the underlying transport mechanisms are currently not clear.
The results of these investigations suggest that although the fundamental microscopic understanding of LN can be transferred to LT, differences in structure, energetic landscape and temperature behavior are present, which bare striking potential for novel applications even at high temperatures.

Computational approach
The Vienna ab initio simulation package VASP [48,49] is employed to perform first-principles total-energy calculations within the spin-polarized density functional theory. We consider a number of valence electrons equal to 3 per atom for lithium (1s 2 2s 1 ), 13 for niobium (4s 2 4p 6 4d 3 5s 2 ), 11 for tantalum (5p 6 5d 3 6s 2 ), and six for oxygen (2s 2 2p 4 ). The projector-augmented wave (PAW) [50,51] method is employed to account for remaining core electrons. Following the tests performed in reference [52], we chose to employ the semi-local exchange-correlation functional proposed by Perdew, Burke, and Ernzerhof (PBE [53]). We furthermore make use of a plane wave basis containing waves up to a kinetic energy of 400 eV to expand the electronic wave functions. The atomic positions are self consistently optimized until Hellmann-Feynman forces lower than 0.001 eV Å −1 are present on each atom. 2 × 2 × 2 k-point meshes generated with the Monkhorst-Pack algorithm [54] and centered to the Γ-point are employed to perform the energy integration in the Brillouin zone. Convergence tests show that within this approach leads to converged results concerning total energies and forces.
Isolated free and bound polarons are modeled with rhombohedral cells of 2853.68 Å 3 for LT and 2869.59 Å 3 for LN containing 270 atoms. The correct treatment of the d orbitals of Ta and Nb is typically problematic in DFT due to the strong electronic correlation. The strong on-site Coulomb repulsion of such electrons is accounted for in this work by the approach commonly referred to as the DFT +U method. Within this method, a strong intra-atomic interaction is introducted in a (screened) Hartree-Fock like manner, as an on-site replacement of the L(S)DA [55]. In the present investigation, we apply the simplified approach proposed by Dudarev et al [56]. The rotationally invariant DFT +U functional is thereby described by The indices i and j run over all the electronic levels of the Ta 5d or Nb 4d orbitals. U is the spherical averaged Hubbard correction, which models the enhanced Coulomb interaction. The eigenstates ε i are then calculated as the derivatives of equation (1) with respect to the occupation numbers n i : As a consequence of the Hubbard correction, the lower Hubbard subband (occupied d orbitals) is shifted downwards, while the upper Hubbard subband is shifted to higher energies [58]. In the approach applied in this work the shift is proportional to the difference U = U − J, which can be interpreted as an effective U. J, an approximation of the Stoner exchange parameter, is the screened exchange energy, which is roughly equal to 1 eV [59]. According to the tests performed in reference [42,60,61], we chose U = 4 eV for LN and U = 5 eV for LT. Different values shift the position of the localized defect states within the band gap, without qualitatively modifying the behavior of the polaronic defects. This approach has led to the reliable description of intrinsic and extrinsic polarons in LiNbO 3 [62][63][64].

Picosecond transient absorption and luminescence
Transient absorption kinetics is studied using a conventional, home-built pump-probe-technique based on a regeneratively amplified Ti-sapphire laser and an optical parametric amplifier (OPA) as described in reference [47]. Both samples are excited at a repetition rate of 1 kHz using intense, frequency-doubled fs-laser pulses (λ = 400 nm, τ = 60 fs, E = 65 μJ). The OPA is tuned to generate probe pulses in the near-infrared spectral range (λ = 910 nm). The transmitted probe pulse for a specific temporal delay between the pump and probe pulse is recorded and analyzed with a thermoelectrically-cooled 2D-CCD-array attached to a Czerny-Turner monochromator. The detected spectra are spectrally integrated to obtain a signal I proportional to the transmitted pulse energy. For each temporal delay, the absorbance is calculated via where I(t 0) is the spectrally integrated pulse signal for time delays at which the probe pulse arrives at the sample before excitation. The apparatus response function has a full width at half maximum of ≈130 fs.
Transient luminescence on the (sub-)ps-timescale is investigated applying broadband fs-fluorescence upconversion spectroscopy [65] adapted to the inspection of single crystals in reflection geometry (for a detailed description of the experimental setup see reference [47]). The same fs laser pulses as in the absorption measurement are used to excite the samples. The emitted luminescence is collected with an off-axis Cassegrain reflector and imaged onto a BBO crystal. There it is superposed with intense, tilted and compressed fs-laser pulses (λ = 1340 nm, τ = 45 fs, E = 50 μJ) provided by the OPA for non-collinear sum-frequency mixing. For fixed time delays, the generated sum-frequency spectra are again recorded with the monochromator-CCD-detection system. The Gaussian-shaped apparatus response function of this experimental setup has a full width at half maximum of 160 fs.
Experimental techniques providing highest temporal resolutions are powerful tools for the study of charge-carriers and excitons with strong lattice coupling in ABO 3 perovskite-like ferroelectrics, as the formation of these transients in such materials is extraordinarily fast ( 300 fs [47,[66][67][68]). Photoluminescence spectroscopy is of special importance where the absorption feature of a transient is experimentally inaccessible, however it has been seldom applied to ABO 3 ferroelectric solids [47]. To the best of our knowledge, the transient absorption and the photoluminescence features of LiTaO 3 with a sub-picosecond temporal resolution were not investigated so far.

Conductivity measurements
The electrical conductivity of LiNbO 3 and LiTaO 3 single crystals is determined by AC impedance spectroscopy in the frequency range from 1 Hz to 1 MHz using an impedance/gain-phase analyzer (Solartron 1260). The measurements are performed in a tube furnace that allows heating up to 1000 • C in air at atmospheric pressure while heating at a rate of 1 K min −1 from room temperature (RT).
An electrical equivalent-circuit model consisting of a constant phase element (CPE) connected in parallel with a bulk resistance R B is fitted to measured data. The bulk conductivity σ is subsequently calculated from the relation σ = t(AR B ) −1 , where t and A are the thickness of the sample and the electrode area, respectively. Further, the activation energy E A is extracted from the Arrhenius relation where σ 0 , k B and T are a constant pre-exponential coefficient, the Boltzmann constant, and the absolute temperature, respectively. The activation energy E A can be extracted from equation (4) provided that a single conduction mechanism dominates in a sufficiently large temperature range. This fact is reflected by a constant slope in the Arrhenius representation that can be attributed to E A . The slope used here is denoted by E σT and follows from The consideration of σT is motivated in section 3.3.

Crystal growth and sample preparation
Optical measurements are conducted on rectangular plates of congruent lithium niobate (9 × 10 × 0.2 mm 3 , X-cut) and lithium tantalate (7 × 8 × 0.5 mm 3 , Z-cut) grown by the Czochralski method at the WIGNER Research Center for Physics, Budapest, and at the University of Osnabrueck, respectively. Both samples are cut and polished to optical quality. Transient luminescence and absorption are both detected for ordinary (probe) polarisation.
The crystals for the study of the electrical properties are prepared by the Czochralski method at the Institute of Microelectronics Technology and High Purity Materials, Russian Academy of Sciences, Moscow, and subsequently prepared as polished X-cut rectangular plates with dimensions of 8 × 20 × 1.6 mm 3 . Further, Pt-electrodes with a thickness of ∼3 μm are deposited by screen printing (print ink: Ferro Corporation, No. 6412 0410). After screen-printing, the specimens are annealed at 1000 • C for about 30 min.

Results and discussion
3.1. Polaronic defects 3.1.1. Free polarons Free small polarons are quasiparticles that are formed in crystals with large lattice polarizability, when the electron (or hole)-lattice interaction is large enough to overcome the Coulomb repulsion and localize the carrier at substantially one lattice site [16]. Electrons self-trapped at the regular Nb 5+ (4d 0 ) ions of the LN lattice are paradigmatic examples of free small polarons. Although the optical absorption bands caused by free polarons in LN have been measured [16], a quantitative structural model based on atomistic calculations is still missing. This is probably due to the fact that the additional electron is strongly localized and therefore difficult to model within conventional DFT.
The presence of an electron at the regular Nb 5+ (Ta 5+ ) lattice site affects the crystal morphology in its neighborhood. According to our calculations, the Nb (Ta) ion moves into a more central position within the oxygen octahedron, which expands by 2.20% in LN and 2.39% in LT. The bond distances of the Nb (Ta) ion (at which the free polaron is localized) with the first oxygen neighbors are reported in table 1. Although the magnitude of the lattice expansion is slightly larger in LT than in LN, the corresponding distortion costs elastic energy of ca 500 meV in both materials. This suggests a similar high lattice polarizability for both compounds.
The band structures calculated for a supercell containing the free polaron in LN and LT are shown in figure 1. The defect state related to the self trapped electron is clearly observable and is located 0.65 eV below the conduction band in LN and 0.69 eV in LT. Calculations performed with supercells of different size and extrapolation to infinite supercells suggest the free polaron level at about 0.60 eV below the conduction band for both LN and LT. This is compatible with the onset of the free-polaron related optical absorption as measured in LN [16].
In order to determine how far the self trapped charge carrier is localized at the Ta and Nb lattice site or rather delocalized over several unit cells, we have calculated the charge density difference between a supercells with and without the free polaron. The result of this procedure is shown in figure 2. The electron captured upon 5+/4+ transition is strongly localized at substantially one lattice site, which is typical for small polarons. The squared wavefunctions are rather similar to the Ta or Nb d z 2 orbitals building the bulk conduction band.

Bound small polarons
In LiNbO 3 , an electron is localized at the Nb 5+ Li (4d 0 ) site by the electron-lattice interaction, which results in a consistent lattice distortion. With respect to the free polarons, the positive potential due to the antisite defect additionally binds the electron. Thus, the charged antisite, Nb 4+ Li (4d 1 ), is usually addressed to as a bound (small) polaron.
The signatures in the optical spectra of LiNbO 3 can be interpreted within the polaronic picture. In the absorption spectra the photoexcited peak at roughly 1.6 eV is assigned to bound small polarons. Furthermore they are involved in different processes determining the material's optical response [16]. It is therefore not surprising, that different research groups have theoretically modeled niobium antisites in LiNbO 3 [62,[69][70][71][72][73]. We have simulated differently charged Nb Li antisites with the computational approach described in section 2.1 in order to have a term of comparison for possible polaronic defects (Ta Li antisites) in LT. The polaronic distortion upon single (Nb 5+ Li → Nb 4+ Li ) and double (Nb 5+ Li → Nb 3+ Li ) electronic capture is pronounced, as shown in table 2. The corresponding electronic structure, with the typical polaron-related electronic state which lowers its energy with increasing occupation, is shown in figures 3(a) and (b). The calculated data closely reproduce small bound polarons in LiNbO 3 as described, e.g. by Nahm and Park with a similar approach [62].
A similar, detailed description of tantalum antisites in LiTaO 3 is not available, though. Here, we focus on the description of the atomic and electronic structure of bound small polarons in LiTaO 3 , as calculated with the previously described spin-polarized DFT +U approach.    If a Li is replaced by a Ta atom in LiTaO 3 , the lattice rearranges locally. As a consequence of the smaller ionic radii of Ta ions with respect to Li (see table 3), the oxygen octaedra around the substitutional is contracted with respect to the ideal lattice, as shown in table 4.
In the charge state 5+ the Ta Li antisite hs the electronic configuration 5d 0 and is isovalent with the replaced Li + ion. The average Ta Li -O distance shrinks from 2.164 Å to 2.023 Å, and a localized defect level  is formed very close to the conduction band edge (blue and red bands in figure 3(c)). This electronic level can accommodate up to two electrons. If an electron is localized at the Ta Li defect, the shallow state in the spin-up channel becomes a mid-gap level (see figure 3(d)), while the corresponding empty state in the spin-down channel is within the conduction band. This behavior is unexpected, as Coulomb repulsion should shift upwards upon occupation. However, the energy release due to the lattice relaxation stabilizes the system. The average Ta Li -O interatomic distance grows from 2.023 Å to 2.082 Å due to the Coulomb repulsion as a consequence of the electron localization. This is similar in magnitude to the behavior of the Nb Li antisite in LN and is typical for a polaronic system. Similarly to LN, antisite-induced flat electronic states are present in proximity of the conduction band in LT. Upon electronic capture these levels are  To give an estimate of the wavefunction localization in bound polarons in LiTaO 3 , we plot the charge density difference of the antisite in the two configurations Ta 4+ Li (5d 1 ) and Ta 5+ Li (5d 0 ) in figure 4. Similarly to free polarons in the same system, the squared wavefunctions are strongly localized in the neighborhood of the antisite, which is the hallmark of small polarons. The strong resemblance with the atomic Ta d z 2 states suggests a minor hybridization of these orbitals.

Bipolarons
The capture of a second electron at a Nb Li antisite in LiNbO 3 leads to the formation of a nearest-neighbor pair Nb 4+ Li − Nb 4+ Nb (4d 1 − 4d 1 ). The pair is stabilized by the formation of a new bond along the z-axis. Accordingly, the distance between the involved atoms is strongly reduced (see table 2). The described defect pair is commonly accepted as model for bound bipolarons.
In LiTaO 3 , when a second electron is hosted in the defect level represented in figure 3(d), the system experienced a deep modification of the electronic and atomic structure. The corresponding electronic structure is displayed in figure 5(b). In case of double occupation, the Ta Li antisite and the nearest-neighbor Ta Ta move toward each other along the [111] crystallographic axis by 0.240 Å. This major lattice relaxation is clearly explained by the electronic charge distribution. The difference between the Ta 3+ Li antisite (nominal electronic configuration 5d 2 ) and the Ta 4+ Li antisite (electronic configuration 5d 1 ) is plotted in figure 6(b). The squared wavefunction does not only surround the antisite as in the case of small bound polarons, but reaches the nearest-neighbor Ta at a regular Ta lattice site. Similarly to the Nb Li -antisites in LN, new bond is created by the hybridization of an antisite electronic state with a 5d orbital of the Ta Ta . The system is thus stabilized by the formation of a covalent bond. More important, the charge distribution suggests that the system is more appropriately described as a nearest-neighbor pair Ta 4+ Li − Ta 4+ Ta (5d 1 − 5d 1 ) than as a Ta 3+ Li (5d 2 ) defect. The doubly charged antisites are thus compatible with our knowledge of bipolarons, that consist of coupled free polarons and small bound polarons. Again, the microscopic description of  Concluding, we point out that we have demonstrated in previous studies that the Nb 5+ Li antisite in LN is a so called negative-U system, for which a double charge transition is energetically favored [70]. This appears to be in good agreement with the optical studies demonstrating that the bound small polaron Nb 4+ Li is a metastable state. Small polarons are created by illumination and have a lifetime of about of 10 −3 seconds [16]. On the other hand, bipolarons are stable systems, which have been assumed both in chemically reduced LN [16] and LT [16,74], even if they can be dissociated both optically and thermally. Bipolarons are associated to the broad peak in absorption spectra at 2.5 eV in chemically reduced LN and LT [16].
Summarizing, the calculations reveal that the behavior of Ta Li antisites in LiTaO 3 and Nb Li antisites in LiNbO 3 is similar and typical of polaronic defects. This large family of lattice-carrier quasiparticles is thus not the exclusive hallmark of lithium niobate but also exist in other ionic oxide crystals. However, although polarons in LN and LT are at a first sight identical, differences in binding energies and electronic structures lead to different absorption spectra. Furthermore, as the polaron binding energy is related to the activation energy in transport processes [16], different transport mechanisms might characterize LN and LT.

Optical response 3.2.1. Transient absorption
The transient absorbance of LT and LN after fs-pulse excitation probed at a wavelength of 910 nm is shown in figure 7. Both kinetics exhibit a steep increase with a small intermediate maximum, which is usually assigned to two-photon absorption of a pump and probe photon [75]. It is therefore used to define time zero. For the congruent LN sample a clear two step decay of the transient absorbance is observed. While the first one has a decay constant of ≈0.7 ps, the second one appears on the picosecond time scale and may correspond to the faster decay observable in the data published by Beyer et al [76]. The slower decay can be assigned to absorption of hopping bound polarons [16,67,76].
Probing the transient absorption of LT at the same wavelength shows a similarly fast increasing signal but a very different longtime behavior. In contrast to the congruent LN sample a rather constant signal is observed for almost 100 ps followed by a very slow decrease. Surprisingly, the transient absorbance of congruent LT resembles the signal observed in heavily Mg-doped lithium niobate [47]. A clear assignment of the observed transient absorption to antisite bound small polarons is therefore not possible. However, based on the calculations presented here, it is not surprising that antisite bound small polaron hopping in LT and LN is not identical.
In both samples, the transients are generated within a few tens of fs, which is in accordance with small polaron formation observed in LN [66][67][68]. The rise time of the transient absorption upon the laser pulse is commonly attributed to the time necessary for thermal cooling of hot carriers and the reorganization of the regular lattice. A lower bound for the latter process is mainly determined by the phonon frequency that is reported in the order of 0.1-1 THz in polar oxide crystals [16]. This corresponds to the determined rise time of the transient signals for LT and LN of 100 fs (see figure 7).
Novel model approaches of upcoming studies thus can be easily validated in two different systems. Moreover, taking LiNb 1−x Ta x O 3 solid solutions into account, the role of intrinsic disorder and/or defect structure for carrier localization phenomena can be studied in its very detail and may be of major importance for applications at room and/or elevated temperatures.

Transient luminescence
After fs-pulse excitation, both LT and LN show a weak but broad photoluminescence in the blue-green spectral range [77]. Within the error of the experiment, broadband fluorescence upconversion spectroscopy performed in this study and in reference [47] indicates no temporal-stokes shift within the lifetime of the luminescence signal. The spectra are thus integrated to increase the signal-to-noise ratio leading to the kinetic traces shown in figure 8. For both samples, a steep increasing luminescence signal is observed around time zero followed by an equally fast first decay. The latter can be described with an exponential function having a decay time of ≈100 fs. Subsequently, the luminescence signal decays exponentially on a picosecond timescale (τ = 1 ps). Within the error of the experiment and except for the peak intensity around time zero, both kinetic traces are practically identical. The luminescence peak around time zero seems to increase with longer illumination times and may thus be related with pump light scattered by an increasingly degraded surface.
The experimental study of the sub-ps kinetics of photoluminescence is a comparably new technique for the inspection of carrier localization phenomena. Based on early findings of Blasse et al [78] and the recent systematic studies of Messerschmitdt et al [79], Krampf et al [47], and Corradi et al [80], the RT luminescence may be assigned to the presence of self-trapped excitons bound to the regular Nb-O octahedra in LN. Though the underlying physics still is under investigation, a clear relation to the lattice dynamics is out of question and thus is used as additional fingerprint in the present study.
It is interesting to verify the presence of a sub-ps luminescence in LT crystals, as well, for two reasons: (i) to best of our knowledge it is the very first observation of a room-temperature luminescence kinetics in LT crystals and (ii) it validates the similarities of the (nonlinear) optical responses of the regular LN and LT lattice upon single sub-ps pulse exposure. In particular, the very high consistency in the temporal evolution of the luminescence on a timescale up to 5 ps is remarkable.
As excitons with strong lattice interaction located at Nb-O-and Ta-O-octahedra share a common electronic structure [81][82][83], we assume the same microscopic processes in LN and LT. In both cases, the transients are formed on a timescale 200 fs which is comparable to the formation time of small polarons in LN estimated to be in the range between 1.5 fs and 300 fs [66][67][68].

Electrical conductivity
The electrical conductivity is obtained from complex impedance spectra as described in section 2.3. Thereby, the low frequency intercepts of R B -CPE semicircles in the complex impedance plane are interpreted as bulk resistance and subsequently converted in the bulk conductivity. A Nyquist plot, showing the data in the complex plane, is exemplary given in figure 9 for both studied crystals at 600 • C. As seen from the figure, slightly depressed semicircles with almost similar resistance are obtained. Thereby, it must be noted that  As seen from the figure, both samples exhibit similar electrical conductivities. A slightly different slope is observed, which needs to be evaluated in detail. Figure 10(b) shows the related slopes E σT in the temperature range from about 350 • C to 920 • C.
Below about 600 • C the slopes are constant for both materials. The behavior indicates that the conductivity is governed by a single thermally activated process. Therefore activation energies can be assigned which are E A = 1.29 ± 0.04 and 1.37 ± 0.03 eV for LN and LT, respectively. In case of LN, the evaluation, i.e. averaging of the slope, is carried out above 405 • C, since the slopes scatter below. However, it can be assumed that E A is constant down to at least 370 • C. At the latter temperature the evaluation for LT is started. Earlier, it has been shown in reference [84] that the electrical conductivity of congruent LT shows an activation energy of 1.19 ± 0.05 eV in the temperature range from 350 • C to 800 • C. For congruent LN an activation energy of 1.31 eV is found above about 500 • C [32]. The authors conclude that the conductivity is governed by mobile lithium ion vacancies. Similarly to LiTaO 3 , our previous studies [31,32] show that the lithium ion migration via lithium vacancies is the dominating transport mechanism in LiNbO 3 . Accordingly, the product σT must be used to determine the activation energy [84]. Due to the strong similarity of the conductivity as measured in this work for LN and LT, it is plausible to assume that also in LT the lithium ion migration via lithium vacancies plays a major role below about 600 • C. Indeed, the ab initio calculations predict the spontaneous formation of Li vacancies, which are exotherm for a wide range of Fermi energy values within the LT fundamental gap [45].
Above 600 • C the behavior differs. LT shows a slightly decreased slope E σT with respect to the situation below 600 • C. Moreover, the slope is constant. In contrast, the slope for LN increases gradually with increasing temperature which indicates a transition range with contributions of two or more conduction mechanisms. The increasing activation energy is consistent with data from [31] showing an activation energy of 1.37 ± 0.01 eV at 700 • C. However, for our data, the activation energy cannot be determined. In case of LN the slope is not constant whereas in LT the underlying conductivity mechanism is not known. As a consequence it is not clear for LN whether the activation energy must be determined for σT or σ. The essential and most obvious result is that the electrical conductivity of LN and LT differ noticeably above 600 • C.
At this point, we want to emphasize that the correlation of the defect structure and the high-temperature transport properties of LiNbO 3 and LiTaO 3 requires further studies of oxygen and cation diffusion as well as of different defect types at elevated temperatures. Although the first steps toward this correlation have been performed, such complex investigations are beyond the scope of the current work and will be performed in subsequent research.

Conclusions
In order to examinate the general assumption that LN and LT crystals are to a great extent alike, and understand how far the knowledge collected in the last decades on LN is generally valid, we have performed a parallel investigation of polaronic structures, optical response and electrical conductivity of LN and LT.
First principles calculations reveal the existence of point defects in LT compatible with the polaronic picture established in LN. Structures compatible with our knowledge of free polarons (Ta 4+ Ta ), small bound polarons (Ta 4+ Li ) and bipolarons (Ta 4+ Li − Ta 4+ Ta ) have been modeled. They are characterized by a major rearrangement of the atomic structure and, in the case of bipolarons, by the formation of a covalent bond between Ta atoms. The charge distribution analysis confirms the localized nature of the polaronic states, which can thus be addressed as small polarons. Although polaronic defects in LN behave similarly to their counterpart in LT, differences in the electronic structure suggest differences in the optical response and in charge transport.
Due to the comparable electronic structure and to the occurrence of similar polaronic defects, the appearance of transient absorption and transient luminescence as optical phenomena in LT can be expected. With respect to the kinetics, qualitative similar behaviors in LN and LT are expected. Experimentally, it is widely established for LN that the presence of small polarons bound to a Nb Li antisite defect center, to regular Nb Nb sites or of Nb 4+ Nb − Nb 4+ Li bipolarons results in pronounced optical fingerprints in the visible and near-infrared spectrum. Time-resolved spectroscopy studies performed in the present work additionally enable to clearly validate small polaron formation and hopping transport. The observation of a transient absorption in LT crystals upon single pulse exposure thus represents a sufficient condition to assume the presence of polarons with strong coupling to the lattice in LT, as predicted by theory. Remarkably, the signal appears in a spectral region (λ = 910 nm) that is quite similar to the Nb Li small polaron in LN, so that electrons coupled to Ta Li antisite defect centers might be reasonably assumed at its origin. A much more striking finding is the observation of a rise time of the transient absorption upon the laser pulse, that is a characteristic feature of small polaron formation. From the comparison of transient absorption and transient luminescence between LT and LN, we find that the transient absorption features much longer relaxation lifetimes together with a simplified decay path. LT here resembles rather a Mg doped LN sample than a congruent one including a large density of antisite defects. At the same time, transient luminescence appears with striking similarity in the sub-ps to ps time regime in both crystals. Considering both findings, we can conclude that the defect alterations strongly affect the small polaron hopping while the 3D lattice structure does not influence the macroscopic features.
Electrical conductivity measurements in air in the temperature range from about 350 • C to 920 • C demonstrate similar activation energies and magnitudes of electrical conductivity for LN and LT samples below 600 • C, thereby indicating closely related conduction mechanisms. As the dominating transport mechanism in LN is due to Li transport via Li vacancies, it is plausible to assume that also in LT this transport channel plays a major role. This is in turn in agreement with the ab initio calculations, which predict the spontaneous formation of Li vacancies, which are exotherm for a wide range of Fermi energy values within the LT fundamental gap. Above 600 • C the electrical conductivity of LT and LN differs. For example, LN shows a gradually increasing slope E σT with temperature which indicates a transition range with contributions of two or more conduction mechanisms. For our data, the activation energy cannot be easily determined, as the slope is not constant and the underlying conductivity mechanisms are not yet known. Detailed investigations of the high-temperature conductivity are subject to subsequent studies.
The results suggest that the knowledge of the physical mechanisms gathered on LN can be transferred to some extent to other ferroelectric oxides such as LT and related solid solutions. However Curie and melt temperature in LN and LT are very different. Thus, solid solutions of the two materials will offer the possibility to exploit and tune the temperature dependence of many materials properties. This makes LiNb 1−x Ta x O 3 solid solutions a promising and exciting field of research for the near future.