{'fraction_non_alphanumeric': 0.02799750208159867, 'fraction_numerical': 0.01894254787676936, 'mean_word_length': 4.512908777969019, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Far infrared properties of the rare-earth scandate DyScO3

We present reflectance measurements in the infrared region on a single crystal the rare earth scandate DyScO3. Measurements performed between room temperature and 10 K allow to determine the frequency of the infrared-active phonons, never investigated experimentally, and to get information on their temperature dependence. A comparison with the phonon peak frequency resulting from ab-initio computations is also provided. We finally report detailed data on the frequency dependence of the complex refractive index of DyScO3 in the terahertz region, which is important in the analysis of terahertz measurements on thin films deposited on DyScO3.


I. INTRODUCTION
DyScO 3 , together with other rare-earth scandates (RScO 3 ), has recently received considerable attention, since it is considered to be among the best substrates for the epitaxial growth of high-quality ABO 3 perovskite-type thin films 1 . On such thin films it is possible to induce ferroelectric and multiferroic properties tailoring their lattice constants by changing R in RScO 3 . For example, SrTiO 3 exhibits strain-induced ferroelectricity if grown on a RScO 3 substrate 2 . Furthermore, scandates are considered to be some of the most promising candidates to substitute SiO 2 as gate dielectric in MOSFET, thanks to the high value of their static dielectric constant ǫ 0 2,3 . SrTiO 3 /DyScO 3 heterostructures are also widely used for applications in the terahertz (THz) range 4 .
We remark that scandates are increasingly used as substrates for film growth and that the optical investigation of a film often allows basic studies which can be difficult when only small size single crystals are available. In particular, the large and flat surface of a film permits accurate optical measurements in the far-IR and THz regions, which have an important role in studying superconducting films 5 . When the radiation penetration depth is larger than the film thickness the optical response of the substrate affects the measured far-IR/THz spectrum, and the complex dielectric functionǫ(ω) = ǫ 1 (ω) + iǫ 2 (ω) of the film material cannot be obtained through the Kramers-Kronig (KK) transformations. In this case more elaborate procedures 6,7 must be used to extract theǫ(ω) of the film from the reflectance or transmittance data, which require the knowledge of the substrate complex refractive index n(ω) = n(ω)+ik(ω). While the far-infrared properties of common perovskites-like substrates as SrTiO 3 and LaAlO 3 are well known [8][9][10] , no far-IR data are available in the DyScO 3 case.
For this system, theoretical calculations of the phonon modes have been reported 3 , which could be compared only with data from recent Raman investigations 11,12 .
Moreover, both infrared (IR) and Raman spectroscopy are of interest in investigating the structural properties of oxide materials with the perovskite structure, since the study of the optical phonons can provide direct information on even subtle structural distortions of the ideal perovskite structure.
We have performed reflectance measurements in the IR region on a DyScO 3 single crystal, at a number of temperatures in the 10-300 K range. The infrared-active phonons of DyScO 3 have been investigated for the first time, allowing a direct comparison with the results of the ab initio calculations 3 . Moreover the frequency and temperature dependence of the complex refractive indexñ(ω) in the far-IR/THz region has been obtained.

II. EXPERIMENTAL DETAILS AND RESULTS
Reflectance measurements were performed at near-normal incidence on the 110 surface of a DyScO 3 (DSO) single crystal. The sample was glued with silver paint, to ensure thermal contact, on an optically black cone 13 mounted on the end of a Helitran cryostat's coldfinger. Such cone was aligned, with the use of three tilting screws, so to have the sample surface perpendicular to the incident radiation. By employing a home-built reflectivity unit, measurements were performed over a broad energy range (50÷12000 cm −1 ) with a Michelson interferometer at a spectral resolution of 2 cm −1 .
To obtain the absolute value of the reflectivity R(ω) we employed the overfilling technique 13 . A metallic film of Au is deposited in situ on the sample surface and used as reference. This allows not only to prevent thermal disalignment but also to take into account any effect of diffraction due to the sample size or diffusion if the sample surface is not mirror-like.
The optical reflectivity R(ω) is plotted up to 800 cm −1 in Fig. 1 at various temperatures.
Several phonon lines, which show a weak temperature dependence, can be observed in this spectral region. At higher frequencies R(ω), in agreement with the insulating properties of the DyScO 3 crystal, is nearly flat and constant at a value of about 0.1 up to the highest measured frequency (see Fig.2).

III. ANALYSIS AND DISCUSSION
DyScO 3 has an orthorhombically-distorted perovskite structure with space group P nma with a 20-atom primitive cell. Therefore, one expects, as in the isostructural LaMnO 3 manganite 14-17 , 60 phonons, among which 24 are Raman active (corresponding to the ir- In order to perform the KK analysis 6 , we first performed a Lorentz fit on R(ω) so to extrapolate its behavior as ω → 0. We have fitted the low-frequency part of R(ω) (i.e. below 400 cm −1 ) in order to obtain a careful description in the THz region. This procedure resulted in a convincing extrapolation of the experimental data down to zero frequency and in reliable results in the far-IR once the KK transformations are performed. We remark that data have been collected up to 12000 cm −1 , so to avoid problems in the KK procedure due to the high-frequency extrapolation of the spectra. The resulting ǫ 2 (ω) are reported in Fig.   2 for frequencies below 600 cm −1 at selected temperatures. To determine the central frequency of the phonon modes and their temperature dependence, we have fitted ǫ 2 (ω) within the Lorentz model by using: where A j , ω j and γ j are respectively the mode strength, the central frequency and the damping of each phonon mode j. The resulting curves obtained with ǫ ∞ ∼ 4 are in good agreement with the data, as shown for T= 10 K and 300 K in Fig.3. The phonon frequencies resulting from the fits are reported in Table I and tentatively compared with the calculations of Ref. 3 As our measurements were performed without polarizing the incoming beam no information about the polarization of the phonon peaks can be extracted from the experimental data. We made a tentative assignment by simply comparing the phonon frequencies obtained from the fit with the computed ones. Taking into account the complexity of this class of materials, we believe that the overall agreement between theory and experiment should be considered as reasonable.
Most of the phonons harden their central frequency with decreasing T and reduce their half-height half-width γ, as expected and in good agreement with the behavior found in Ref. 12 at higher temperatures. A closer inspection of data shows that the broad peak, visible at 300 K just below 200 cm −1 is due to two different phonon modes at 190 cm −1 and at 199 cm −1 (see Table I). The apparent splitting of such peak is due to the softening of the more intense mode (at 190 cm −1 ) to 185 cm −1 and the simultaneous hardening of the second mode. Some other weak modes also show a light softening by decreasing T as reported in Table.I. This softening might correspond to subtle lattice modifications (still within the P nma crystal structure) as T decreases. To the best of our knowledge, the Tbehavior of the DyScO 3 lattice parameters has been investigated between 298 -1273 K, that is the temperature range of interest for perovskite thin film growth 19 , while no data exist at lower temperatures. Therefore one cannot link unambiguously the modifications in the IR-active phonon response to a structural rearrangement.  This finding supports the theoretical prediction 3 that in DyScO 3 the high value of the static dielectric constant ǫ 0 , i.e.ǫ(ω → 0), is associated with low-frequency ionic vibrations. On the basis of the employed procedure, ǫ 0 is given by ǫ ∞ + j A j (see Eq.1). Since the fitting procedure provides the A j value for each mode (as reported in Table I), we find that the phononic contribution to ǫ 0 , i.e. j A j is large, of about 21, mainly due to the phonon mode at 135 cm −1 . Moreover we find a total static dielectric constant ǫ 0 ≈ 25, as the sum of ǫ ∞ ∼ 4 and the phononic contribution, in excellent agreement with theory 3 and experiments on single crystals 2 .
Finally we report in Fig.4 the frequency dependance of the complex refractive index n = n + ik in the THz region as directly obtained fromǫ = ǫ 1 + iǫ 2 . Below 100 cm −1 n is nearly flat reaching a value of about 5 for ω → 0, while the vanishingly small k value indicates the absence of an appreciable absorption in the same spectral region.

IV. CONCLUSIONS
We have presented here the first experimental data on the IR phonon spectrum of the rare earth scandate DyScO 3 . In the temperature range between 10 and 300 K no dramatic changes occur in the phonon response indicating that the P nma structure is stable down to the lowest measured temperature. The overall agreement with the recent ab initio calculations is to be considered satisfactory. We finally note that the present work can provide reference data and extrinsic peak selection for future infrared investigations of thin films grown on DyScO 3 substrates.