Related papers: A fundamental requirement for crystal-field parame…
The second moment of the sublevels within the initial state | \alpha SLJ > which constitutes a natural and adequate measure of the crystal-field (CF) effect can be redefined as sigma^{2}=1/(2J+1)\sum_{k} S_{k}^{2} A_{k}^{2}, where…
The variation ranges of the axial B_{k0} crystal-field parameters, for k=2,4,6, of tetragonal including cubic crystal-field Hamiltonians H_{CF} for all possible orientations of the relevant reference frame are studied. The distinguished…
Central quantities in spectroscopy and magnetism of transition ions in crystals are crystal field parameters (CFPs). Nature self-imposed limits on orthorhombic and lower symmetry CFPs, and existence of intrinsically incomparable CFP sets…
The crystal-fields causing $|J>$ electron states splittings of the same second moment $\sigma^{2}$ can produce different total splittings $\Delta E$ magnitudes. Based on the numerical data on crystal-field splittings for the representative…
Any electron eigenstate |\Psi>of the paramagnetic ion open-shell is characterized by the three independent multipole asphericities A_{k}=<\Psi || C^(k)}||\Psi> for k=2,4 and 6 related to the second moments of the relevant crystal-field…
Symmetry adaptation techniques are applied to the determination of the intensity of two-photon absorption transitions, between Stark levels of configurations with opposite parities, for transition ions in finite symmetry environments. The…
The relationship between the energy total splitting $\Delta E$ of the free-ion electron states in the axial crystal-fields and the second moment of that splitting $\sigma^{2}$ is thoroughly investigated. The non-Kramers and Kramers states…
For a prime $p>2$ and a smooth proper $p$-adic formal scheme $X$ over $\mathcal{O}_K$ where $K$ is a $p$-adic field, we study a series of conditions ($\mathrm{Cr}_s$), $s\geq 0$ that partially control the $G_K$-action on the image of the…
The most important recent results in the theory of phase transitions and quantum effects in quantum anharmonic crystals are presented and discussed. In particular, necessary and sufficient conditions for a phase transition to occur at some…
In this paper we provide a detailed convergence analysis for an unconditionally energy stable, second-order accurate convex splitting scheme for the Modified Phase Field Crystal equation, a generalized damped wave equation for which the…
Periodic boundary condition (PBC) is a standard approximation for calculating crystalline materials properties. However, a PBC crystal is not the same as the real macroscopic crystal, therefore, if applied indiscriminately, it can lead to…
We fully support the interpretation of Prof. F. Steglich, reported recently in Phys. Rev. Lett. 91 (2003)156401, that the observed \textit{below} Kondo temperature, Electron Spin Resonance (ESR) in a heavy fermion metal YbRh2Si2 is…
We describe two dimensional models with a metallic Fermi surface which display quantum phase transitions controlled by strongly interacting critical field theories below their upper critical dimension. The primary examples involve…
Models describing one- and two-photon transitions for ions in crystalline environments are unified and extended to the case of parity-allowed and parity- forbidden p-photon transitions. The number of independent parameters for…
We study the effect of changes in the parameters of a two-dimensional potential energy surface on the phase space structures relevant for chemical reaction dynamics. The changes in the potential energy are representative of chemical…
Inorganic crystals are periodic, highly-symmetric arrangements of atoms in three-dimensional space. Their structures are constrained by the symmetry operations of a crystallographic \emph{space group} and restricted to lie in specific…
We report the synthesis of powder and single-crystal samples of the cerium pyrohafnate and their characterization using neutron diffraction, thermogravimetry and X-ray absorption spectroscopy. We evaluate the amount of non-magnetic…
Symmetry adaptation techniques are applied to the determination of intensities of intra-configurational two-photon transitions for transition-metal ions in cubical symmetry. This leads to a simple model giving the polarization dependence of…
Calculated energy levels from recent \emph{ab initio} studies of the electronic structure of SrCl$_{2}$:Yb$^{2+}$ and CsCaBr$_{3}$:Yb$^{2+}$ are fitted with a semi-empirical "crystal-field" Hamiltonian, which acts within the model space…
Magnetic phase transitions between ordered phases are often understood on the basis of semi-classical spin models. Deviations from the classical description due to the quantum nature of the atomic spins as well as quantum fluctuations are…