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We present a first-principles study of the low-temperature rhombohedral phase of BaTiO$_3$ using Hubbard-corrected density-functional theory. By employing density-functional perturbation theory, we compute the onsite Hubbard $U$ for Ti($3d$) states and the intersite Hubbard $V$ between Ti($3d$) and O($2p$) states. We show that applying the onsite Hubbard $U$ correction alone to Ti($3d$) states proves detrimental, as it suppresses the Ti($3d$)-O($2p$) hybridization and drives the system towards a cubic phase. Conversely, when both onsite $U$ and intersite $V$ are considered, the localized character of the Ti($3d$) states is maintained, while also preserving the Ti($3d$)-O($2p$) hybridization, restoring the rhombohedral phase of BaTiO$_3$. The generalized PBEsol+$U$+$V$ functional yields good agreement with experimental results for the band gap and dielectric constant, while the optimized geometry is slightly less accurate compared to PBEsol. Zone-center phonon frequencies and Raman spectra are found to be significantly influenced by the underlying geometry. PBEsol and PBEsol+$U$+$V$ provide satisfactory agreement with the experimental Raman spectrum when the PBEsol geometry is used, while PBEsol+$U$ Raman spectrum diverges strongly from experimental data highlighting the adverse impact of the $U$ correction alone in BaTiO$_3$. Our findings underscore the promise of the extended Hubbard PBEsol+$U$+$V$ functional with first-principles $U$ and $V$ for the investigation of other ferroelectric perovskites with mixed ionic-covalent interactions.

High-resolution angle- and spin-resolved photoemission spectroscopy reveals new features of the electronic structure of the ferromagnetic triple-layered ruthenate Sr$_4$Ru$_3$O$_{10}$. There are narrow spectral peaks $\sim$30 meV below the Fermi-level in two regions of the Brillouin zone: a hole-like band at the zone-center and a saddle-point van Hove singularity at the zone edge. Below T$_c$ each feature is almost completely spin-polarized, with opposite sign polarization and with strong Kondo-coherence-like temperature-dependent spectral weight variation suggestive of strong Hund's metal correlations. In addition, there are distinct Fermi surfaces for wide electron-like minority spin bands around the zone center and narrow hole-like majority spin Fermi surface contours around the zone corners. The origin of these features is in general agreement with density functional calculations, if they are shifted to reduce the exchange splitting, and scaled to take into account effects of correlation. Furthermore, the deduced narrow band origins from the tri-layer splitting of $d_{xz/yz}$ orbitals implies a layer-specific spin-polarization contribution from the narrow bands. Over a larger energy range, net spin-majority polarization of incoherent Ru $d$-bands is observed to extend down to the top of the oxygen bands, where additional narrow oxygen bands contribute to the magnetism with spin-minority polarization., Comment: 11 pages, 5 figures plus supplement 8 pages, 4 figures

We report electronic band structure calculations for Sr$_{4}$Ru$_{3}$O$_{10}$ that displays both ferromagnetic and metamagnetic behavior. The density functional calculations find the ground state to be ferromagnetic in agreement with the experiment and we find that the inclusion of Coulomb Hubbard interaction U applied to the Ru 4d states has dramatic effects on the Fermi surface, which reveal the role of Coulomb interactions and correlated many-body physics. The minority spin bands are mainly empty with Fermi surfaces in the outer areas of the Brillouin zone away from the $\Gamma$ point with bands that disperse steeply upward. The majority spin bands are full or nearly fully occupied and form narrow bands near the Fermi energy around the $\Gamma$ point, which could be the electronic origin of the metamagnetism. The results are in qualitative agreement with recent angle resolved photoemission spectroscopy (ARPES) experiments and show the need for a combined theoretical study and experimental ARPES investigation with better energy resolution to reveal the nature of the narrow bands close to the Fermi-level, which is critical for understanding the exotic magnetic properties observed in this material.

We present an analytical model for the theoretical analysis of spin dynamics and spontaneous symmetry breaking in a spinor Bose-Einstein condensate (BEC). This allows for an excellent intuitive understanding of the processes and provides good quantitative agreement with experimental results in Phys. Rev. Lett. 105, 135302 (2010). It is shown that the dynamics of a spinor BEC initially prepared in an unstable Zeeman state mF=0 (|0>) can be understood by approximating the effective trapping potential for the state |+-1> with a cylindrical box potential. The resonances in the creation efficiency of these atom pairs can be traced back to excitation modes of this confinement. The understanding of these excitation modes allows for a detailed characterization of the symmetry breaking mechanism, showing how a twofold spontaneous breaking of spatial and spin symmetry can occur. In addition a detailed account of the experimental methods for the preparation and analysis of spinor quantum gases is given., Comment: 12 pages, 14 figures

Parametric amplification of quantum fluctuations constitutes a fundamental mechanism for spontaneous symmetry breaking. In our experiments, a spinor condensate acts as a parametric amplifier of spin modes, resulting in a twofold spontaneous breaking of spatial and spin symmetry in the amplified clouds. Our experiments permit a precise analysis of the amplification in specific spatial Bessel-like modes, allowing for the detailed understanding of the double symmetry breaking. On resonances that create vortex-antivortex superpositions, we show that the cylindrical spatial symmetry is spontaneously broken, but phase squeezing prevents spin-symmetry breaking. If, however, nondegenerate spin modes contribute to the amplification, quantum interferences lead to spin-dependent density profiles and hence spontaneously-formed patterns in the longitudinal magnetization., Comment: 5 pages, 4 figures

Spin-changing collisions may lead under proper conditions to the parametric amplification of matter waves in spinor Bose-Einstein condensates. Magnetic dipole-dipole interactions, although typically very weak in alkaline atoms, are shown to play a very relevant role in the amplification process. We show that these interactions may lead to a strong dependence of the amplification dynamics on the angle between the trap axis and the magnetic-field orientation. We analyze as well the important role played by magnetic-field gradients, which modify also strongly the amplification process. Magnetic-field gradients must be hence carefully controlled in future experiments, in order to observe clearly the effects of the dipolar interactions in the amplification dynamics.

Parametric amplification of vacuum fluctuations is crucial in modern quantum optics, enabling the creation of squeezing and entanglement. We demonstrate the parametric amplification of vacuum fluctuations for matter waves using a spinor F=2 Rb-87 condensate. Interatomic interactions lead to correlated pair creation in the m_F= +/- 1 states from an initial unstable m_F=0 condensate, which acts as a vacuum for m_F unequal 0. Although this pair creation from a pure m_F=0 condensate is ideally triggered by vacuum fluctuations, unavoidable spurious initial m_F= +/- 1 atoms induce a classical seed which may become the dominant triggering mechanism. We show that pair creation is insensitive to a classical seed for sufficiently large magnetic fields, demonstrating the dominant role of vacuum fluctuations. The presented system thus provides a direct path towards the generation of non-classical states of matter on the basis of spinor condensates., Comment: 5 pages, 4 figures

We analyze the spinor dynamics of a Rb-87 F=2 condensate initially prepared in the m_F=0 Zeeman sublevel. We show that this dynamics, characterized by the creation of correlated atomic pairs in m_F=+/-1, presents an intriguing multi-resonant magnetic field dependence induced by the trap inhomogeneity. This dependence is directly linked to the most unstable Bogoliubov spin excitations of the initial m_F = 0 condensate, showing that, in general, even a qualitative understanding of the pair creation efficiency in a spinor condensate requires a careful consideration of the confinement., Comment: 5 pages, 4 figures