Spin–Orbit-Entangled Electronic Phases in 4d and 5d Transition-Metal Compounds

Complex oxides with $4d$ and $5d$ transition-metal ions recently emerged as a new paradigm in correlated electron physics, due to the interplay between spin-orbit coupling and electron interactions. For $4d$ and $5d$ ions, the spin-orbit coupling, ζ, can be as large as 0.2-0.4 eV, which is comparable with and often exceeds other relevant parameters such as Hund's coupling JH, noncubic crystal field splitting Δ, and the electron hopping amplitude t. This gives rise to a variety of spin-orbit-entangled degrees of freedom and, crucially, non-trivial interactions between them that depend on the d-electron configuration, the chemical bonding, and the lattice geometry. Exotic electronic phases often emerge, including spin-orbit assisted Mott insulators, quantum spin liquids, excitonic magnetism, multipolar orderings and correlated topological semimetals. This paper provides a selective overview of some of the most interesting spin-orbit-entangled phases that arise in $4d$ and $5d$ transition-metal compounds.