Spin-orbit-entangled electronic phases in 4$d$ and 5$d$ transition-metal compounds

TL;DR

This paper reviews the emergence of exotic spin-orbit-entangled electronic phases in 4d and 5d transition-metal oxides, highlighting the interplay of strong spin-orbit coupling with electron interactions that leads to novel quantum states.

Contribution

It provides a selective overview of the most interesting spin-orbit-entangled phases in 4d and 5d transition-metal compounds, emphasizing recent discoveries and theoretical insights.

Findings

Identification of spin-orbit-assisted Mott insulators

Discovery of quantum spin liquids and topological semimetals

Observation of multipolar orderings and excitonic magnetism

Abstract

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, $\zeta$, 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 $J_{\rm H}$, noncubic crystal field splitting $\Delta$, 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.