Multiwell potentials of endohedral complexes of icosahedral symmetry

We examine multiwell potentials that correspond to the displacements of off-center ions in complexes with icosahedral symmetry (dodecahedrons, icosahedrons, fullerenes, etc.) along symmetry directions (toward vertices, midpoints of edges, and centers of faces). An expression is derived for an effective Hamiltonian, which describes the behavior of endohedral complexes with off-center ions placed in external electric fields of arbitrary strength and orientation. We find the eigenvalues of this Hamiltonian and calculate the intensities of the lines of all possible transitions between tunneling levels. We also predict and analyze the spectra of paraelectric resonances in the absence of an external static electric field (zero-field resonances) and in the presence of such a field. Finally, we provide recommendations for detecting these effects and discuss the specific features of the effects and the possibility of studying them. Zh. éksp. Teor. Fiz. 114, 222–238 (July 1998)     

Group representations and multinomial combinatorics of the icosahedral symmetry

The icosahedral symmetry is one of the most intriguing symmetries, as it not only presents a challenge but it appears in many fullerenes and high energetic materials such as the dodecahedral N₂₀. We have considered the combinatorics of all irreducible representations of the icosahedral symmetry for a number of multinomial partitions for vertex, face and edge colourings in this work. We have constructed the combinatorial tables for all irreducible representations for various multinomial partitions of colourings for the vertices, edge and faces of the icosahedron. These techniques should have important applications to enumerations and spectroscopy of fullerenes and high-energy materials such as N₂₀.     

Nuclear magnetic resonance in icosahedral Al-Pd-Mn alloys

²⁷Al and⁵⁵Mn nuclear magnetic resonance shift,K, and²⁷Al spin lattice relaxation time,T ₁, have been measured for the six-dimensional face-centered icosahedral quasicrystals, Al_75-x Pd₁₅Mn_10+x withx=0, 2 and7. The Al₇₅Pd₁₅Mn₁₀ quasicrystal exhibits a temperature independent Knight shiftK and(T ₁ T)^–1=0.022±0.002 (K s)^–1 in a temperature range from room temperature to 5 K because there exist no Mn atoms with local magnetic moment. The replacement of Al with Mn drastically decreases the²⁷AlK, the⁵⁵MnK andT ₁ of²⁷Al, andthe²⁷AlK becomes negative. There is an additional contribution to the spin lattice relaxation time independent of temperature. This is considered to be due to the presence of a localized magnetic moment in the replaced Mn atoms.     

Paraelectric resonance of slightly reduced rutile (TiO2)

Paraelectric resonance experiments on slightly reduced, aluminium doped rutile single crystals are reported. In the region 32–37 GHz at reduced He-temperatures a single resonance line is observed which is ascribed to an orientable electric dipole constituted of a multiply localized electron and an interstitial Ti³⁺ ion.     

EPR of trivalent chromium centers with monoclinic symmetry in SrF2 crystals

Cr³⁺ centers with monoclinic symmetry in SrF₂:Cr crystals are studied by EPR. Based on an analysis of the EPR data and a study of the conditions under which the observed samples were formed, a model is proposed which explains the low symmetry of the magnetic properties in terms of the simultaneous effect on the impurity ion state of interactions with the interstitial F⁻ ion and with normal vibrations of the crystal lattice in a trigonal symmetry. Fiz. Tverd. Tela (St. Petersburg) 39, 302–305 (February 1997)     

Geometrical shape resonances in multicenter systems with icosahedral symmetry: A controllable molecular trap for electrons

Specific shape resonances were studied in systems with the highest point symmetry. The resonances occur in narrow energy intervals and disappear when inner potentials increase. A model system of point scatterers that are placed in the vertexes of an icosahedron and at its center was analyzed. In this system, the geometric resonance lifetime is extremely sensitive to structure changes and may attain 10⁻¹⁰ s, i.e., exceed the rotation period of electrons in atoms by six orders of magnitude. The feasibility of molecular traps that capture elastically scattered electrons and bring them into the resonant state is discussed. The resident time of electrons in these traps can be controlled with external static fields.     

Electron spin resonance of copper pair centers in crystals with perovskite structure

Copper pair centers, which could be of interest for obtaining quantitative information about exchange interactions in superconductors based on cuprate perovskites, are observed in crystals with the perovskite structure by the ESR method. Such centers are investigated in KTaO₃:Cu and K_1−x Li_xTaO₃:Cu crystals. A model consisting of a chain of two equivalent Cu²⁺ ions and three oxygen vacancies, extending along the 〈 100〉 axis, is proposed for the centers. The exchange interaction in the pairs is ferromagnetic. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 12, 890–894 (25 June 1999)     

Electron spin resonance of donor centers in beryllium oxide

The ESR spectra of two deep centers found in irradiated BeO crystals and powders, respectively, are reported and analyzed. They are due to electrons trapped at substitutional boron (B⁺⁺⁺) and fluorine (F^?) ions as concluded from the hf interaction of the unpaired electron with the respective nuclei. The boron center revealed a static, the fluorine center a dynamic Jahn-Teller effect between 77°K and 300°K. In both cases, the unpaired electron was found to be localized in nonaxial orbitals, which is shown to be consistent with the direction of the polar field of the crystal structure. The strong localisation of the electron is contrasted to the behavior of donor electrons in other II–VI compounds, which are highly delocalized.     

Electronic resonance and symmetry in single-molecule inelastic electron tunneling

Two families of exact global solutions to the equations of plasma equilibrium are derived. The solutions model astrophysical jets and solar prominences and provide counterexamples to Parker's hypothesis.