On the dynamics of band Jahn-Teller systems with A15-structure

We construct a thermodynamic model for a system of electronic d-bands coupled to the elastic lattice. For the electronic fluctuations a Debye-type of relaxation, for the lattice displacement a modified elastic equation of motion is assumed. As a result a coupling of certain acoustic and relaxational modes is found leading to a soft mode instability. For non-vanishing external fields displacement and dielectric response functions are derived. The special case for wavevector q[110] is worked out explicitly. A comparison between the present phenomenological model and a microscopic multiple-band electron-phonon transport theory, recently given by the author, reveals remarkable agreement between both approaches.     

Studies of the doubly degenerate product Jahn-Teller system

The static product Jahn-Teller (JT) system with two doubly-degenerate electronic open shells coupling to a single e-mode is further studied in the electronic space using the isostationary function method and the energy minimization procedure. These effects are vividly described by the coupling of two electronic vectors that belong to two different E-spaces. The energy levels in the trough positions are also investigated and it is found that the two doubly degenerate electronic levels are generally lifted by the product JT coupling.      

Variational treatment for the dynamical pseudo Jahn-Teller system

We present a variational treatment for the E × e pseudo Jahn-Teller system. Through canonical transformation the electron and phonon states are decoupled. An analytical form is obtained for the ground state energy by scaling transformation. Including both the dynamical displacement of phonon modes and the softening of phonon frequency, this approach yields fairly accurate results for the ground state energy. The energy splitting and Ham's reduction factor are calculated, which also generates fairly good results compared with other perturbation results. We argue that our variational wave function is valid for the weak and intermediate coupling range.     

Magnetic field effects in the cooperative Jahn-Teller system TbVO4

Effects of a magnetic field on the behaviors of TbVO₄ which shows a cooperative Jahn-Teller phase transition have been investigated. The possibility that the system will return to the undistorted phase at low temperatures in a magnetic field is considered. We show that because of the weak coupling of the system to the magnetic field applied along the c-axis, the magnetic field required to see the transition of the crystal back to the undistorted phase is impractically high. Diluting the crystal with nonmagnetic ions is then a plausible approach in the study of this novel behavior of the system. We have also calculated the effects of a magnetic field applied in the basal plane and shown that the crystal would remain distorted for all temperatures except the cases when the field is applied along the crystallographic axes. Finally, we consider the effects of a magnetic field on the temperature behavior of the specific heat and show that the Schottky anomaly which occurs at a very low temperature (～1°K) will be shifted to a higher temperature by applying a magnetic field.     

Semiempirical model for calculating the lattice dynamics of the Jahn-Teller oxide La2CuO4

Calculations of the properties of NiO, CaO, SrO, and La₂NiO₄ crystals are used as a basis for determining empirical pairwise potentials which are employed in calculating the structure, lattice dynamics, and certain properties of La₂CuO₄. The model developed here differs from those proposed before. First, the many-particle Jahn-Teller contributions to the energy and dynamic matrix of the crystal are taken into account. Second, the analytic expressions for the pairwise potentials contain an additional short-range electrostatic screening term. The results are in satisfactory agreement with experimental data. Fiz. Tverd. Tela (St. Petersburg) 39, 1094–1100 (June 1997)     

Topological representations of Jahn-Teller distortions

Topological representations (top-reps), which originally were developed to model molecular polyhedral isomerization processes, can be extended to depict the relationships between the polygons and polyhedra involved in Jahn-Teller (JT) distortions. Using this approach, the top-rep of the E ? (b _1g + b _2g) distortion of square planar molecules to rectangle and rhombus isomers becomes a rhombus in which the vertices alternately represent distortions to the rectangle and rhombus isomers. Similarly the top-rep of the E ? e distortion of regular O_h octahedra to elongated D_4h tetragonal bipyramids becomes a triangle in which the vertices represent the three distinct tetragonal bipyramids from a given octahedron and the edge midpoints represent lower symmetry rhombic D_2h intermediates. A regular octahedron can be used as a top-rep for the T ? (e + t ₂) distortions of regular octahedra if the 6 vertices represent distortions to D_4h tetragonal bipyramid isomers, the 8 face midpoints represent distortions to D_3d trigonal antiprism isomers, and the 12 edge midpoints represent lower symmetry rhombic D_2h intermediates. In the case of Jahn-Teller T ? h distortions of regular I_h icosahedra, the corresponding top-rep becomes a regular icosahedron in which the 12 vertices represent distortions to pentagonal D_5d isomers, the 20 face midpoints represent distortions to trigonal D_3d isomers, and the 30 edge midpoints represent D_2h intermediates. A 4-dimensional analogue of the tetrahedron (i.e. the 4-simplex) can be used as a top-rep for the G ? g problem and the H ? g component of the H ? (g + 2h) problem for JT distortions of regular icosahedra. In this case the 5 vertices and the 10 edge midpoints correspond to T_h isomers and D_3d intermediates, respectively.     

Metamagnetism in Jahn-Teller magnets

Metamagnetism is possible in Jahn-Teller magnetic systems, which include giant-magnetoresistance manganites, as a result of both spin-phonon interaction and the influence on spin exchange due to Jahn-Teller ordering of the electron orbits. Fiz. Tverd. Tela (St. Petersburg) 39, 1586–1588 (September 1997)     

Jahn-Teller distortions of icosahedral complexes

Classification of the stable symmetries of Jahn-Teller systems ofI _h parent group is elaborated for triply, fourfold and fivefold degenerate electronic states with integer spin and for fourfold and sixfold degenerate ones with non-integer spin. The results produced by the epikernel principle and by the method of step-by-step descent in symmetry connected with degenerate states splitting are compared. The results obtained on the basis of epikernel principle are incomplete and may even be incorrect.     

Groundstate-calculation for the T-t Jahn-Teller system by an exponential transformation approach

The dynamical T-t Jahn-Teller problem is handled by a canonical exponential transformation exp (- S) H exp (S). The groundstate wavefunction of the diagonal part of H is given in the transformed and original space. Its expectation value for the total Hamiltonian is shown to agree with the exact numerical groundstate results up to intermediate coupling strengths. For strong coupling values the dominant k power still seems to be given correctly. However, in this limiting case exact results can be derived by a second transformation. Both types of transformations lead in a combined form to very accurate groundstate energies, which can be fitted with respect to the given numerical values.     

Jahn-Teller centers and pseudospin effects

The characteristics of the phenomenon of polar centers exhibiting Jahn-Teller behavior in copper oxides are investigated by the pseudospin approach. The emergence of relaxation pseudospin (dipole-quadrupole) modes and pseudospin-phonon interaction produces a number of anomalies in inelastic neutron scattering. The Jahn-Teller effect in polar centers brings about a change in the character of the tetra-ortho transition in the system La_2−x M_x-CuO₄ as the concentration x is increased. The possibility of the onset of fluctuation domain nanostructures is suggested. Fiz. Tverd. Tela (St. Petersburg) 39, 1948–1955 (November 1997)     

Jahn-Teller effects in paramagnetic crystals

A detailed account is given of the theory of the Jahn-Teller effect in crystals containing (3d)ⁿ paramagnetic impurity ions. The importance of using a complete lattice phonon system is emphasized and full details of a particularly useful multi-mode lattice model are presented. Transformation methods are used to simplify the ion-lattice coupling. Full details of the effective Hamiltonian and associated reduction factors are either derived or reviewed for the T?e, T?t, T?(e+t) and E?e systems in cubic and trigonal e environments. An account of the existing literature concerning various aspects of Jahn-Teller theory is also given. Detailed lists of references to experimental data on (3d)ⁿ systems i which Jahn-Teller effects are thought to occur are also presented. The survey is intended to cover the literature comprehensively from 1970 onwards.     

Jahn-Teller effect at exciton self-trapping

In the adiabatic approximation two limiting cases of exciton self-trapping have been considered for a degenerate atomic term creating the bands of Frenkel excitons, which interact with all crystal deformations admitted by symmetry: a case of a large radius excitation on the self-trapping barrier and a small-radius case. In the first case wave functions and deformations have been found which correspond to the barrier, in the second case the adiabatic surface of self-trapping excitons have been obtained. It is shown that the interaction with non-totally symmetric deformations leads to a lowering of the crystal point symmetry in a state corresponding to the lowest self-trapping barrier, that is the manifestation of the Jahn-Teller effect applied to a self-trapping exciton.     

Extended perturbation formulae for Jahn-Teller molecules

The effect of the Jahn-Teller interaction on a symmetric top molecule with a threefold axis of symmetry in a ^2S + 1E state has been investigated by perturbation theory. Contributions up to sixth order are included. Explicit formulae for various quantities have been derived on the assumption that there is only one Jahn-Teller active mode of vibration; both linear and quadratic Jahn-Teller interactions are considered. The quantities concerned are (i) the vibronic energy levels, (ii) the orbital quenching factor d_t, (iii) the correction to the A-rotational constant, (iv) the correction to the spin-spin dipolar coupling term, and (v) the correction to the spin-rotation coupling constant ε_aa. Because the perturbation expansion converges slowly, the results are only applicable to molecules subject to a weak Jahn-Teller effect. There are several examples of this type of molecule which have been studied experimentally.     

Jahn-Teller antiferroelectric ordering in praseodymium hydroxide

Electric and magnetic susceptibility experiments on Pr(OH)₃ show one- and three-dimensional ordering of Pr electric dipoles similar to that observed in PrC1₃. The smaller unit cell of Pr(OH)₃ leads to substantially stronger Pr-Pr interactions and to a phase transition at 1.25 K compared with 0.4 K in PrC1₃.     

IR-spectroscopy of crystals containing Jahn-Teller impurity centers

Using a novel IR-technique, the low-temperature spectra of CdTe, ZnTe and Cd_0.95Mn_0.05Te crystals, doped by Jahn-Teller Co²⁺ impurity ions, were studied in the spectral range from 1 to 400 μm. The absorption spectrum regions and the energy positions of ZPL, corresponding to the transitions ⁴A₂(⁴F)→⁴T₁(P), ⁴T₁(F), ⁴T₂(F) and ²G were detected. The parameters of the spin-orbit interaction λ, the crystal field parameter D_q, the parameters of electron-electron interaction B and C were obtained. It was found, that Jahn-Teller interaction differently affects the parameter λ for ⁴A₂(F)→⁴T₁(F) and ⁴T₂(F) transitions and, consequently, the energy positions of ZPL. The electron-vibronic spectra were compared with phonon spectra.     

狭义相对论动力学的逻辑体系

阐述了物理逻辑体系的构成,依据马赫动力学逻辑体系的基本思想,给出了狭义相对论动力学的一个严格的逻辑体系.其中给出了一般情况(包括高速和低速情况)下质量和力的操作型定义,并对马赫提出的力的定义———“质量与加速度的乘积”进行了批评和修正.对另外一些相关问题,如牛顿第二定律的实验检验也作了讨论.     

Inverse Jahn-Teller transition in bimetallic oxalates

Because of the competition between the spin-orbit coupling and the Jahn-Teller (JT) energies in Fe(II)Fe(III) bimetallic oxalates, we theoretically predict that an undistorted phase with C3 symmetry about each Fe site may be recovered at low temperatures. Both lower and upper JT transitions bracketing the ferrimagnetic transition temperature Tc are predicted for compounds that exhibit magnetic compensation. Comparisons with recent measurements and first-principles calculations provide strong evidence for the inverse JT transition below Tc.     

The Jahn-Teller effect in manganic acetylacetonate

The infra-red spectra of the tris-acetylacetonates of chromium, managanese, iron and aluminium have been measured as far as 400 cm^-1. The nature of the bands due to vibrations involving motion of the oxygen atoms relative to the metal is consistent with the operation of the Jahn-Teller mechanism in the manganic compound.