Jahn-Teller magnets

A wide class of materials with different crystal and electronic structures from quasi-two-dimensional unconventional superconductors (cuprates, nickelates, ferropnictides/chalcogenides, ruthenate SrRuO$_4$), 3D systems as manganites RMnO$_3$, ferrates (CaSr)FeO$_3$, nickelates RNiO$_3$, to silver oxide AgO are based on Jahn-Teller $3d$ and $4d$ ions. These unusual materials called Jahn-Teller (JT) magnets are characterized by an extremely rich variety of phase states from non-magnetic and magnetic insulators to unusual metallic and superconducting states. The unconventional properties of the JT-magnets can be related to the instability of their highly symmetric Jahn-Teller "progenitors" with the ground orbital $E$-state to charge transfer with anti-Jahn-Teller $d$-$d$ disproportionation and the formation of a system of effective local composite spin-singlet or spin-triplet, electronic or hole $S$-type bosons moving in a non-magnetic or magnetic lattice. We consider specific features of the anti-JT-disproportionation reaction, properties of the electron-hole dimers, possible phase states of JT-magnets, effective Hamiltonians for single- and two-band JT-magnets, and present a short overview of physical properties for actual JT-magnets.