Zeeman effect in dynamic Jahn-Teller impurities (original) (raw)
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Dynamic and Static Jahn-Teller Effect in Impurities: Determination of the Tunneling Splitting
Vibronic Interactions and the Jahn-Teller Effect, 2011
In this paper we review the concepts of dynamic and static Jahn-Teller (JT) effects and study their influence in the electron paramagnetic resonance (EPR) spectra of transition metal impurities in wide gap insulators. We show that the key quantities involved in this problem are the tunneling splitting, usually denoted 3Γ, and the splitting, δ, between ∼3z 2 − r 2 and ∼x 2 − y 2 energy levels due to the random strain field which is present in every real crystal. It is pointed out that in the E ⊗ e JT problem the kinetic energy of nuclei involved in the ground state plays a key role for understanding the actual value of 3Γ and thus the existence of dynamic JT effect. The results of ab initio calculations on a variety of JT systems show that 3Γ values span a much larger range than previously suggested. In particular, we find that 3Γ = 235 cm −1 for MgO:Cu 2+ while 3Γ = 10 −4 cm −1 for KCl:Ag 2+. We also show that the dynamic JT effect can only appear for such large values of 3Γ as those found in MgO:Cu 2+ since usual strain fields lead to δ values of the order of 10 cm −1 that would otherwise localize the system in only one of the JT wells. The present results explain satisfactorily why the JT effect for Cu 2+ and Ag 2+ impurities in MgO is dynamic while static for Ag 2+-doped CaO and alkali chlorides. The origin of such a difference is discussed in detail.
Geometric phase effect at N -fold electronic degeneracies in Jahn-Teller systems
International Journal of Quantum Chemistry, 2004
The geometric phase effect at arbitrary integral N-fold electronic degeneracies is investigated in Jahn-Teller systems. It is shown to be a property inherent to inversion of the adiabatic electronic wave vectors in the N-dimensional electronic wave-vector space. The relationship between the geometric phase and mixing angles has also been established.
Journal of Molecular Structure, 2007
In this (partly review) paper several important situations are analyzed in which molecular systems are distorted, but there are no apparent degeneracies or close in energy states to justify their origin as due to the Jahn-Teller effect (JTE) or pseudo JTE (PJTE). It is shown that in all these cases above the JTE are ''hidden'' in the excited states of the undistorted configuration even when the energy gap to these states is very large, and the involvement of these states in the vibronic coupling explains the JT origin of the distortions. This confirms the general validity of the JTE as the only source of instabilities and distortions of high-symmetry configurations of polyatomic systems. For the example of the ozone molecule, which has no degenerate ground state, neither in the distorted (obtuse-triangular), nor in the undistorted (regular triangular) configurations, and there are no low-lying excited states, the distortion is shown to emerge from the JTE in the excited E state situated at 8.3eVabovethegroundstate.TheJTstabilizationenergyismorethan8.3 eV above the ground state. The JT stabilization energy is more than 8.3eVabovethegroundstate.TheJTstabilizationenergyismorethan9 eV which makes the distorted configuration the lowest in energy.
Theory of the Jahn-Teller-Kondo effect
Physical review. B, Condensed matter, 1988
There is a Kondo effect associated with ions such as Cu + which have an orbital doublet in a cubic field. The ground state is a Jahn-Teller-Kondo singlet which can have a characteristic energy 10 cm '. This large energy might stabilize the pseudocubic site recently observed in YBa2Cu307. Mehran eral. ' have observed electron spin resonance (ESR) signals, associated with Cu +, from single-crystal, single-phase, samples of YBazCu307 which exhibit a pseudocubic site symmetry and are unique in the ESR literature. The signal does not come from an impurity phase. These are high-quality single crystals, but unannealed, and exhibit no appreciable diamagnetic response above-60 K; however"other than in this final treatment, the samples are identical to similar crystals with a narrow-90-K transition, but which do not exhibit an ESR signal. The absence of a signal from the annealed samples suggests that the Cu moments are somehow "compensated" in this final stage of preparation. Within experimental error, below 100 K, the magnetic ground state of the Cuz+ observed via ESR refiects cubic symmetry. Above this temperature the ground state remains close to, but not exactly, cubic while at all temperatures the partially resolved hyperfine structure exhibits an-20% anisotropy. These latter two facts indicate that the local site symmetry of the Cu is far from cubic. Somewhat similar signals for dielectrics are associated with the dynamic Jahn-Teller "vibronic" singlet. z However, there are no Cu sites in the high-T', materials which have (even close to) the cubic coordination which is essential for a classical Jahn-Teller effect.
The Jahn–Teller effect in systems
Journal of Molecular Structure, 2007
A general consideration is made of the vibronic coupling in a ðh þ u Þ 2 h g Jahn-Teller system, that is to say, a system in which two holes of H u symmetry are coupled to vibrations of h g symmetry. We find that the resulting high-spin states may undergo spontaneous distortion into species exhibiting one of the following four possible symmetries: D 5d , D 3d , D 2h or C 2h. The system may be viewed as a first approximation to a C 2þ 60 ion, but our intention here is to make a general consideration of the model without application to any specific molecular system. Coulombic interactions between holes, which must be important in real systems, are therefore ignored throughout. However, they could be included in the model, if required, using the method described in an earlier work [I.D. Hands, J.L. Dunn, W.A. Diery, C.A. Bates, Phys. Rev. B 73 (2006) 115435]. For each of the different symmetry types, projection operators are used to create symmetry-adapted states (SASs) that give a good account of the states of the system over a wide range of coupling strengths. These SASs are used, in turn, to derive energies for the vibronic states.
Dynamical Jahn‐Teller effect in the first excited
International Journal of Quantum Chemistry, 2019
The Jahn-Teller effect of C 60 anions in the first electronically excited states was theoretically investigated. The orbital vibronic coupling parameters for the t 1g next lowest unoccupied molecular orbitals were derived from the Kohn-Sham orbital levels with hybrid B3LYP functional by using the frozen phonon approach. With the use of these coupling parameters, the vibronic states of the first excited C − 60 were derived by exactly diagonalizing the dynamical Jahn-Teller Hamiltonian. The dynamical Jahn-Teller stabilization energy of the first excited C − 60 is stronger than that of the ground electronic states.
Valence-bond states in dynamical Jahn-Teller molecular systems
Physical Review B, 1997
We discuss a hopping model of electrons between idealized molecular sites with a local orbital degeneracy and a dynamical Jahn-Teller effect, for crystal field environments of sufficiently high symmetry. For the Mott-insulating case ͑one electron per site and large Coulomb repulsions͒, in the simplest twofold degenerate situation, we are led to consider a particular exchange Hamiltonian, describing two isotropic spin-1/2 Heisenberg problems coupled by a quartic term on equivalent bonds. This twin-exchange Hamiltonian applies to a physical regime in which the interorbital singlet is the lowest-energy intermediate state available for hopping. This regime is favored by a relatively strong electron-phonon coupling. Using variational arguments, a largen limit, and exact diagonalization data, we find that the ground state, in the one dimensional case, is a solid valence-bond state. The situation in the two dimensional case is less clear. Finally, the behavior of the system upon hole doping is studied in one dimension. ͓S0163-1829͑97͒00424-4͔
The Jahn–Teller Effect in Chemistry
Bulletin of the Chemical Society of Japan, 2007
A uniform view of electronic degeneracies, resulting from finite point group symmetries, is developed. It relates any n-fold degeneracy to the geometrical structure formed by the set of equidistant points in a space with exactly n dimensions. Jahn-Teller interactions within the degenerate manifold can simply be represented as bond stretchings of this structure. This approach thus can be qualified as the ''chemical perspective'' to the study of vibronic instabilities. The procedure is described for twofold , threefold , four-fold, and five-fold degeneracies. As a result a simple general proof of the Jahn-Teller theorem can be obtained. The electronic degeneracy is connected to the reaction graph of the stable minima on the surrounding Jahn-Teller surface. The findings are illustrated with some structural and dynamic molecular examples.
Jahn-Teller effect in crystals: Optical response function and vibronic states
Physica A: Statistical Mechanics and its Applications, 1982
We present a method for evaluating the optical spectrum of a Jahn-Teller centre in a crystal. We are able to obtain an approximated, but not perturbative, expression for the optical response function of the system in the weak coupling case. All cases of electronic degeneracy are treated together. The general formulae giving the zero-phonon line and the one-and two-phonon bands are obtained in the two cases of Jahn-Teller interaction acting when the electron is in the ground or in an excited level. In particular, the contribution of the vibronic states as peaks in the one-phonon band is explicitly shown.
Physical Review B
The coexistence of distortions of different symmetry due to the quadratic Jahn-Teller interactions in an octahedral complex is revisited. Analytical expressions for the position and energy of the different stationary points are given; afterwards the influence of the spin-orbit coupling is numerically evaluated for the overall system (3 T 1 ϩ 1 T 1), which is encountered in the excited configuration of ns 2 impurities. An evaluation of the magnitude of the Jahn-Teller effect for 6-, 8-, and 12-coordinated complexes is performed according to the angular overlap model. Particular attention is paid to parameter values consistent with the eight-coordinated CsX:Tl ϩ systems (XϭCl, Br, I͒. The coexistence of trigonal minima with tetragonal or orthorhombic ones is found for a rather wide range of parameter values with the minima better pronounced in the singlet state 1 T even for high values of the spin-orbit coupling. ͓S0163-1829͑97͒00521-3͔