Transition Metal Compounds, Daniel I. Khomskii, Cambridge U. Press, 2014. $125.00 (485 pp.). ISBN 978-1-107-02017-7 Buy at Amazon
For the past half century, John Goodenough’s classic text Magnetism and the Chemical Bond (Interscience-Wiley, 1963) has served as an introduction and guide for both experimentalists and theorists who studied transition metal (TM) compounds, which fall into the subclass of strongly correlated electron systems. Daniel Khomskii’s new monograph, Transition Metal Compounds, updates and further develops Goodenough’s ideas while sticking to the original approach; it also focuses on TM oxides and summarizes Khomskii’s long-term activity researching their electric and magnetic properties.
Khomskii is a well-known theoretician; the Kugel–Khomskii Hamiltonian, for example, describes many phenomena observed in TM oxides. However, Transition Metal Compounds is not a monograph for theorists. Rather, it is a compendium of basic ideas and a qualitative review of those oxides’ generic properties.
The field’s main motivating crystallographic picture is of a TM ion enclosed in an octahedron of oxygen ions. Depending on how those octahedrons are packed, the oxide is classified as a perovskite, rutile, corundum, or other crystalline structure. The TM oxide’s widely varied magnetic and electronic properties are determined by the interplay between strong correlation effects in TM ions’ 3d shells and the covalent bonding of the TM-ion and oxygen-ion orbitals.
The book opens with an introduction to the theory of correlated 3d electrons in crystals and isolated atoms. Then the first three chapters present such topics as the interplay between electronic motion and magnetism in Mott–Hubbard insulators (also known as Mott insulators), atomic Hund’s rules, and the crystal-field and ligand-field theory for TM oxides.
Chapter 4 is the key part of the book; there the author adapts the general mechanism of the Mott–Hubbard transition for the TM oxide geometry. The key idea is that covalent bonding in the octahedral structure results in specific charge-transfer contributions to the transition and thus a specific change in the Mott–Hubbard phase diagram. Here’s a note for the more experienced readers: The metal–insulator transition, when controlled by charge transfer, is described by the Zaanen-Sawatzky-Allen phase diagram.
Based on that charge-transfer effect, the author, in chapter 5, describes indirect effective exchange mechanisms and various magnetic structures realized in TM oxides, with special attention to frustrated magnets and spin liquids. That content is followed by discussions in chapter 6 of the orbital and lattice degrees of freedom characteristic of TM ions and in chapter 7 of the various possibilities of charge ordering.
Chapter 8 is devoted to the recently discovered multiferroic materials, which combine ferromagnetism and ferroelectricity. In it, Khomskii discusses those compounds in the context of classical ferroelectrics and magnetoelectrics. The next two chapters are devoted to some applications of the main ideas and mechanisms. Chapter 9 considers doping, in particular how doping influences the properties of Mott–Hubbard insulators and high-Tc superconductors (both cuprates and ferropnictides). The superconductor discussion, however, is too laconic to serve as a sufficient introduction. Chapter 10 covers metal–insulator transitions.
The description of heavy-fermion and mixed-valence systems in chapter 11 is also, I think, too concise to be an adequate introduction. In my opinion, those two systems, because they exist in compounds containing rare-earth metals, are beyond the scope of a monograph devoted largely to TM oxides. Besides, the basic physical mechanism (Kondo screening) that leads to so-called mass enhancement in such systems radically differs from the correlation effects discussed in the other 10 chapters.
The author concludes each chapter with a short summary that repeats the chapter’s main ideas in a concentrated form. Those addenda enhance the pedagogical effect of the monograph and make it a highly useful introduction to the physics of TM oxides for nascent and experienced experimentalists and theoreticians working in that and adjacent fields of strongly correlated systems.
Konstantin Kikoin is a research professor in the department of physics and astronomy at Tel Aviv University in Israel. He is a coauther, with Mikhail Kiselev and Yshai Avishai, of Dynamical Symmetries for Nanostructures (Springer, 2012).
