This review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration," "broken replica symmetry," "broken ergodicity," etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed include site-disorder models, phenomenological theories for the frozen phase and its excitations, phase diagrams in which spin glass order and ferromagnetism or antiferromagnetism compete, the Ne\'el model of superparamagnetism and related approaches, and possible connections between spin glasses and other topics in the theory of disordered condensed-matter systems.

Spin glasses: Experimental facts, theoretical concepts, and open questions

The properties of magnetic insulators containing orbitally degenerate transition metal ions (Jahn-Teller ions) are discussed. The Jahn-Teller effect in these insulators causes structural phase transitions, lowers the lattice symmetry, and gives rise to an orbital ordering. Various interactions responsible for these effects are discussed: the electron-lattice, quadrupole-quadrupole, and exchange interactions. The mutual effects of the orbital ordering and the magnetic properties of corresponding compounds are discussed. The exchange interaction in the cases of twofold and threefold orbital degeneracy is discussed. The effect of a magnetic field on the orbital and magnetic structure and the temperature dependence of the exchange interaction are studied. The properties of several representative compounds containing Jahn-Teller ions are discussed.

https://iopscience.iop.org/article/10.1070/PU1982v025n04ABEH004537/pdf

The Jahn-Teller effect and magnetism: transition metal compounds

The different physical aspects of glass transitions are reviewed and models aiming at their explanation are described. The following three main aspects are distinguished: the degree of stability of supercooled liquids with respect to crystallisation; the variation of physical properties of supercooled liquids in metastable equilibrium above the glass transition; the arrest of structural relaxation at the glass transition. The physical significance of computer simulations of glass transitions in simple liquids and the question of a hidden phase transition underlying an observed glass transition are examined critically. In relation to the stability problem, the geometrical constraints operative in typical disordered structures, such as random sphere packings and random covalent networks, are also discussed. A general survey of glass transition phenomena and concepts is presented in an introductory section.

https://iopscience.iop.org/article/10.1088/0034-4885/49/2/002/pdf

Models of the glass transition

The software program SPuDS has been developed to predict the crystal structures of perovskites, including those distorted by tilting of the octahedra. The user inputs the composition and SPuDS calculates the optimal structure in ten different Glazer tilt systems. This is performed by distorting the structure to minimize the global instability index, while maintaining rigid octahedra. The location of the A-site cation is chosen so as to maximize the symmetry of its coordination environment. In its current form SPuDS can handle up to four different A-site cations in the same structure, but only one octahedral ion. Structures predicted by SPuDS are compared with a number of previously determined structures to illustrate the accuracy of this approach. SPuDS is also used to examine the prospects for synthesizing new compounds in tilt systems with multiple A-site coordination geometries (a(+)a(+)a(+), a(0)b(+)b(+), a(0)b(-)c(+)).

/pdf/prediction-of-the-crystal-structures-of-perovskites-using-39c9mj2y0l.pdf

Prediction of the crystal structures of perovskites using the software program SPuDS.

The review dwells on the problems of high-temperature superconductivity. Ideas encouraging the search for high-temperature superconductivity are elucidated. The way from cubical alloys, containing niobium, to laminated copper-containing oxides with the perovskite-type structure is shown. Properties of new laminated oxide superconductors are described.

Perovskite‐Type Oxides—the New Approach to High—Tc Superconductivity

We discuss the phase diagram of the Kondo lattice: we generalize to the lattice a method proposed by Yoshimori and Sakurai for the single-impurity Kondo problem; this method transforms the Kondo exchange interaction into a fictitious $s\ensuremath{-}f$ hybridization, and gives a resonance of width ${T}_{K}$ at the Fermi level. We study the Kondo phase and compare its energy with the energy of the magnetic phase. The Kondo state is stable when the exchange interaction is larger than a critical value; this state is insulating when the conduction band is half filled.

Phase diagram of the Kondo lattice

Volume collapse in the Kondo lattice

The density of states of yttrium compounds YM2 (M = Fe, Co, Ni) is calculated within a tight-binding scheme. Using the Stoner model, conclusions are drawn about their magnetic and electronic properties. In YCo2, we show that one has to introduce paramagnon effects in order to explain the electronic properties. The additional d-f interaction introduced by rare-earth atoms (R) in RM2 is treated with a Hartree-Fock approximation. Little change is obtained in iron and nickel compounds. Conversely, in RCo 2 compounds, the exchange field due to the rare-earth atoms can produce collective metamagnetism as described by Wohlfarth and Rhodes [1] and cobalt becomes magnetic. This effect stems from the position of the Fermi level of these compounds in a steep decrease of the density of states. Curie temperature, order of the transition and effect of an external magnetic field are studied following this method. Other consequences are drawn from the model.

https://hal.archives-ouvertes.fr/jpa-00209160/document

Density of states and magnetic properties of the rare-earth compounds RFe2, RCO2 and RNi2

The gamma - alpha transition and the related volume collapse are explained within a compressible Kondo lattice where the variation of mod J mod /D with volume is taken into account. The authors show that, contrary to the promotion model, the Kondo contribution is sufficient to induce a first-order transition at low temperature from a magnetic to a Kondo phase. The alpha phase is then characterised by an extremely high Kondo temperature. The calculations are also made at zero and finite temperatures and the existence of a critical point is demonstrated. Finally, they propose a generalisation to the effect of a chemical pressure. Applications are made to Ce, CeAl2 and Ce1-xThx.

/pdf/the-g-a-transition-in-cerium-compounds-4zup5dwe3p.pdf

M. Cyrot

Papers

Phase diagram of the Kondo lattice

Volume collapse in the Kondo lattice

Density of states and magnetic properties of the rare-earth compounds RFe2, RCO2 and RNi2

The γ-α transition in cerium compounds

Preparation and structure of the compounds SrVO3 and Sr2VO4