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We report on the crystal structure and ferroelectric properties of epitaxial ZrO$_2$ films ranging from 7 to 42 nm thickness grown on La$_{0.67}$Sr$_{0.33}$MnO$_3$-buffered (110)-oriented SrTiO$_3$ substrate. By employing X-ray diffraction, we confirm a tetragonal phase at all investigated thicknesses, with slight in-plane strain due to the substrate in the thinnest films. Further confirmation of the tetragonal phase was obtained through Infrared absorption spectroscopy with synchrotron light, performed on ZrO$_2$ membrane transferred onto a high resistive Silicon substrate. Up to a thickness of 31 nm, the ZrO$_2$ epitaxial films exhibit ferroelectric behavior, at variance with the antiferroelectric behavior reported previously for the tetragonal phase in polycrystalline films. However, the ferroelectricity is found here to diminish with increasing film thickness, with a polarization of about 13 $\mu$C.cm$^{-2}$ and down to 1 $\mu$C.cm$^{-2}$ for 7 nm and 31 nm-thick ZrO$_2$ films, respectively. This highlights the role of thickness reduction, substrate strain, and surface effects in promoting polarization in the tetragonal ZrO$_2$ thin films. These findings provide new insights into the ferroelectric properties and structure of ZrO$_2$ thin films, and open up new directions to investigate the origin of ferroelectricity in ZrO$_2$ and to optimize this material for future applications.

An analysis of orbital magnetization in band insulators is provided. It is shown that a previously proposed electronic orbital angular-momentum operator generalizes the ``modern theory of orbital magnetization'' to include non-local Hamiltonians. Expressions for magnetic transition dipole moments needed for the calculation of optical rotation (OR) and other properties are developed. A variety of issues that arise in this context are critically analyzed. These issues include periodicity of the operators, previously proposed band dispersion terms as well as, if and where needed, evaluation of reciprocal space derivatives of orbital coefficients. Our treatment is used to determine the optical rotatory power of band insulators employing a formulation that accounts for electric dipole - electric quadrupole (DQ), as well as electric dipole-magnetic dipole, contributions. An implementation in the public \textsc{Crystal} program is validated against a model finite system and applied to the $\alpha$-quartz mineral through linear-response time-dependent density functional theory with a hybrid functional. The latter calculations confirmed the importance of DQ terms. Agreement against experiment was only possible with i) use of a high quality basis set, ii) inclusion of a fraction of non-local Fock exchange, and iii) account of orbital-relaxation terms in the calculation of response functions.

We report the Pockels electro-optic properties of ZrO2 and HfO2 orthorhombic Pbc21 and rhombohedral R3m ferroelectric phases, and we compare them to the well-known LiNbO3 Pockels material from density functional theory calculations using the CRYSTAL suite of programs. Specifically, three essential processes are explicitly investigated: The electronic, the ionic (or vibrational), and the piezoelectric contributions. Our calculations reveal that the ionic part coming from the low frequency phonon modes contributes the most to the electro-optic coefficients of rhombohedral LiNbO3 and of orthorhombic ZrO2 and HfO2. While these low-frequency modes show zero contribution to Pockels coefficients for the rhombohedral phase of the latter compounds., Comment: 29 pages, 5 figures, 15 tables including supplemental material

We report the discovery of three new cases of QSOs acting as strong gravitational lenses on background emission line galaxies: SDSS J0827+5224 (zQSO = 0.293, zs = 0.412), SDSS J0919+2720 (zQSO = 0.209, zs = 0.558), SDSS J1005+4016 (zQSO = 0.230, zs = 0.441). The selection was carried out using a sample of 22,298 SDSS spectra displaying at least four emission lines at a redshift beyond that of the foreground QSO. The lensing nature is confirmed from Keck imaging and spectroscopy, as well as from HST/WFC3 imaging in the F475W and F814W filters. Two of the QSOs have face-on spiral host galaxies and the third is a QSO+galaxy pair. The velocity dispersion of the host galaxies, inferred from simple lens modeling, is between \sigma_v = 210 and 285 km/s, making these host galaxies comparable in mass with the SLACS sample of early-type strong lenses., Comment: 9 pages, 8 figures, accepted for publication in A&A

We present the first case of strong gravitational lensing by a QSO : SDSS J0013+1523, at z = 0.120. The discovery is the result of a systematic search for emission lines redshifted behind QSOs, among 22298 spectra of the SDSS data release 7. Apart from the z = 0.120 spectral features of the foreground QSO, the spectrum of SDSS J0013+1523 also displays the OII and Hbeta emission lines and the OIII doublet, all at the same redshift, z = 0.640. Using sharp Keck adaptive optics K-band images obtained using laser guide stars, we unveil two objects within a radius of 2 arcsec from the QSO. Deep Keck optical spectroscopy clearly confirms one of these objects at z = 0.640 and shows traces of the OIII, emission line of the second object, also at z = 0.640. Lens modeling suggests that they represent two images of the same z = 0.640 emission-line galaxy. Our Keck spectra also allow us to measure the redshift of an intervening galaxy at z = 0.394, located 3.2 arcsec away from the line of sight to the QSO. If the z = 0.120 QSO host galaxy is modeled as a singular isothermal sphere, its mass within the Einstein radius is M_E(r < 1 kpc) = 2.16e10 M_Sun and its velocity dispersion is sigma_SIS = 169 km/s. This is about 1 sigma away from the velocity dispersion estimated from the width of the QSO Hbeta emission line, sigma_*(M_BH) = 124 +/- 47 km/s. Deep optical HST imaging will be necessary to constrain the total radial mass profile of the QSO host galaxy using the detailed shape of the lensed source. This first case of a QSO acting as a strong lens on a more distant object opens new directions in the study of QSO host galaxies., Comment: 6 pages, 5 figures, accepted for publication in A&A Letters. Added new Keck spectroscopy