D. I. Khomskiǐ

The field of multiferroics has greatly expanded in the last few years, particularly with the discovery of so many different types of multiferroic materials. This review organizes these materials according to the microscopic origin of their properties and explores how we can expect to find similar multiferroic behavior in systems that we have been studying all along.

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.

The electronic structure of the perovskite ${\mathrm{LaCoO}}_{3}$ for different spin states of Co ions was calculated in the local-density approximation LDA+U approach. The ground state is found to be a nonmagnetic insulator with Co ions in a low-spin state. Somewhat higher in energy, we find two intermediate-spin states followed by a high-spin state at significantly higher energy. The calculations show that Co 3d states of ${\mathit{t}}_{2\mathit{g}}$ symmetry form narrow bands which could easily localize, while ${\mathit{e}}_{\mathit{g}}$ orbitals, due to their strong hybridization with the oxygen 2p states, form a broad \ensuremath{\sigma}* band. With temperature variation which is simulated by a corresponding change of the lattice parameters, a transition from the low- to intermediate-spin state occurs. This intermediate-spin (occupation ${\mathit{t}}_{2\mathit{g}}^{5}$${\mathit{e}}_{\mathit{g}}^{1}$) can develop an orbital ordering which can account for the nonmetallic nature of ${\mathrm{LaCoO}}_{3}$ at 90 KT500 K. Possible explanations of the magnetic behavior and gradual insulator-metal transition are suggested. \textcopyright{} 1996 The American Physical Society.

Describing all aspects of the physics of transition metal compounds, this book provides a comprehensive overview of this unique and diverse class of solids. Beginning with the basic concepts of the physics of strongly correlated electron systems, the structure of transition metal ions, and the behaviours of transition metal ions in crystals, it goes on to cover more advanced topics such as metal-insulator transitions, orbital ordering, and novel phenomena such as multiferroics, systems with oxygen holes, and high-Tc superconductivity. Each chapter concludes with a summary of key facts and concepts, presenting all the most important information in a consistent and concise manner. Set within a modern conceptual framework, and providing a complete treatment of the fundamental factors and mechanisms that determine the properties of transition metal compounds, this is an invaluable resource for graduate students, researchers and industrial practitioners in solid state physics and chemistry, materials science, and inorganic chemistry.