The co-operative Jahn-Teller effect is a phase transition which is driven by the interaction between localized orbital electronic states and the crystal lattice. The possible origins, symmetries and properties of the electron-lattice interactions and how they lead to possible hamiltonians for the coupled system are discussed. The relation of these interactions with quadrupolar interactions and magnetostriction is included. The methods of solution of the hamiltonians lead to an understanding of the electronic states, the phonon spectrum and the mixed normal modes. The wide variety of experimental techniques used on this problem are reviewed in detail and the results are compared with theoretical expressions whenever possible. The application of external stress and magnetic field is of particular significance in the case of the rare earth compounds, because they can product effects which are larger than the low-temperature spontaneous effects.

http://iopscience.iop.org/article/10.1088/0034-4885/38/1/001/pdf

Co-operative Jahn-Teller effects

A brief review is first made of systems for which the spin-iIsing model in a transverse field provides a useful description (insulating magnetic systems, order-disorder ferroelectrics, cooperative Jahn-Teller systems and other systems with 'pseudo-spin'- phonon interactions). A perturbation expansion is then developed which provides for all temperatures an approximate description of the model. The perturbation series is classified with respect to the small parameter l/z, where z is the number of spins interacting with a given spin; this generates the molecular-field approximation and the random-phase approxi- mation as the lowest-order description of the thermodynamic functions and correlation functions respectively. The leading-order approximations for the correlation functions, susceptibilities and spectral functions are discussed in detail. The formalism, which is the first application of such techniques to systems with varying magnetization direction, provides a basis for subsequent higher-order calculations of the free energy and correlation functions.

https://iopscience.iop.org/article/10.1088/0022-3719/6/15/009/pdf

Ising model in a transverse field. I. Basic theory

Until recently most interest in interactions between paramagnetic ions has centred upon ions with quenched orbital angular momentum, for which exchange has the isotropic Heisenberg form JS1.S2 and the major anisotropic terms are due to magnetic dipole-dipole interaction. The interactions for ions with unquenched orbital angular momentum are quite different; exchange is anisotropic, and in addition to exchange and magnetic multipole interactions, there are sometimes sizeable anisotropic contributions from electric multipole interactions and virtual phonon exchange. The qualitative theory of these interactions has been developed and is summarized herein, and the problems in making quantitative theories are discussed. A large number of experimental measurements have been made, mainly on rare earth ions, but several on Co2+, using electron paramagnetic resonance pair spectra and other techniques. The experimental methods and the data obtained are described. The difficulties of interpreting the mass of data are discussed, and the successful identification of particular mechanisms is critically explained. So far the only definite example of electric multipole interaction is for Ce3+ ions in LaCl3 and LaBr3. Virtual phonon exchange is highly likely to be the principal nondipolar interaction in UO2, rare-earth ethyl sulphates and Pr3+ in LaCl3. Most measured nondipolar interactions are due to exchange.

http://iopscience.iop.org/article/10.1088/0034-4885/34/1/303/pdf

Interactions between ions with orbital angular momentum in insulators

DyVO4 and TbVO4 undergo a Jahn-Teller induced crystallographic phase change at 14 and 34 K respectively, and elastic constants of these materials behave anomalously at the transition temperature TD. Brillouin scattering measurements on DyVO4 show that the elastic constant (c11 - c12) falls to zero at TD. The electron lattice interaction which drives the transition in this material is predominantly of short range and a cluster theory is used to interpret the measurements. The elastic constant c66 of TbVO4 also has an anomaly. It falls to zero at TD when measured at ultrasonic frequencies but only falls to a finite value when measured at the higher frequencies used in Brillouin scattering. This frequency dependence of the elastic constants is explained using both thermodynamic and microscopic theories.

http://iopscience.iop.org/article/10.1088/0022-3719/5/21/017/pdf

Brillouin scattering, ultrasonic and theoretical studies of acoustic anomalies in crystals showing Jahn-Teller phase transitions

Magnetic susceptibility measurements on LiHoF4 show that this compound undergoes a transition to a ferromagnetic state below Tc=1.53K, with the Ising-like Ho3+ moments oriented along the crystallographic c-axis. Analysis of the shape-dependent Curie-Weiss O indicates that magnetic dipole interaction dominates the ordering process.

http://iopscience.iop.org/article/10.1088/0022-3719/8/23/021/pdf

Ferromagnetism in lithium holmium fluoride-LiHoF4. I. Magnetic measurements

Observation of a magnetically controllable Jahn Teller distortion in dysprosium vanadate at low temperatures.

Absorption spectra of Dy3+ in DyVO4 yield evidence that this material undergoes a crystallographic phase transition near 14 °K and a magnetic phase transition near 3 °K. The former is believed to be due to a Jahn Teller type of distortion which removes an accidental degeneracy in the Dy3+ ground state. At 4.2 °K and below the effects associated with the magnetic transition have been studied in detail. Zeeman spectra in high fields show the ground state to be anisotropic, with ga = 19, gb ≤ 1, gc ≈ 0.5 (a and b correspond to the original a, a' of the tetragonal cell).

https://hal.archives-ouvertes.fr/jpa-00214403/document

R. L. White

Papers

Observation of a magnetically controllable Jahn Teller distortion in dysprosium vanadate at low temperatures.

Spectroscopic properties of dysprosium vanadate