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A method is developed to calculate the ligand field (LF) parameters and the multiplet spectra of local magnetic centers with open $d$- and $f$-shells in solids in a parameter-free way. This method proceeds from density functional theory and employs Wannier projections of nonmagnetic band structures onto local $d$- or $f$-orbitals. Energies of multiplets and optical, as well as X-ray spectra are determined by exact numerical diagonalization of a local Hamiltonian describing Coulomb, LF, and spin-orbit interactions. The method is tested for several 3$d$- and 5$f$-compounds for which the LF parameters and multiplet spectra are experimentally well known. In this way, we obtain good agreement with experiment for La$_2$NiO$_4$, CaCuO$_2$, Li$_2$CuO$_2$, ZnO:Co, and UO$_2$., Comment: 18 pages, 8 figures

The elasticity at high pressure of solid hydrogen in hexagonal close-packed (hcp) phase I has been examined experimentally by laser acoustics technique in a diamond anvil cell, up to 55 GPa at 296 K, and theoretically using pair and three-body semiempirical potentials, up to 160 GPa. In the experiments on ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$, the compressional sound velocity has been measured; the Poisson's ratio has been determined by combining these data with the previously reported equation of state. At room temperature, the difference between the adiabatic and isothermal processes vanishes above 25 GPa but cannot be neglected at lower pressure. Theoretically, all five elastic constants of hcp hydrogen have been calculated, and various derived elastic quantities are presented. The elastic anisotropy of hcp hydrogen was found to be significant, with $\mathrm{\ensuremath{\Delta}}P\ensuremath{\approx}1.2,\phantom{\rule{0.16em}{0ex}}\mathrm{\ensuremath{\Delta}}{S}_{1}\ensuremath{\approx}1.7$, and $\mathrm{\ensuremath{\Delta}}{S}_{2}\ensuremath{\approx}1$. Calculations suggest the Poisson's ratio to decrease with pressure reaching a minimum value of 0.28 at 145 GPa. In the experiment, the Poisson's ratio is also found to decrease with pressure. Theoretical calculations show that the inclusion of zero-point vibrations on the elastic properties of ${\mathrm{H}}_{2}$ does not result in any drastic changes of the behavior of the elastic quantities.

We study the repulsive Hubbard model both analytically and numerically on a family of highly frustrated lattices which have one-electron states localized on isolated trapping cells. We construct and count exact many-electron ground states for a wide range of electron densities and obtain closed-form expressions for the low-temperature thermodynamic quantities. Furthermore, we find that saturated ferromagnetism is obtained only for sufficiently high electron densities and large Hubbard repulsion $U$ while there is no finite average moment in the ground states at lower densities., 8 pages, 7 figures, accepted for publication in Phys. Rev. B

We show that resonant quantum tunneling of the magnetization, until now observed only in zero-dimensional (0D) cluster systems, occurs in the molecular Ising spin chain $[(CH_3)_3NH]CoCl_3\cdot 2H_2O$, which orders as a canted 3D-antiferromagnet at $T_C=4.15 K$. We present three features that prove unambigously the existence of resonant quantum tunneling below $0.3 K$ ($T_C/12$): Temperature independent relaxation of the magnetization, speeding up of the relaxation at a well defined field ($1025 Oe$) and increase of the magnetization each time this field is crossed during a succession of minor hysteresis loops. A mechanism is proposed to describe the behavior based on a simple model of 0D domain wall nucleation., Comment: 5 pages, 6 figures revised version