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, $z
eta$, can be as large as 0.2-0.4 eV, which is comparable with and often exceeds other relevant parameters such as Hunds 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.
We study the exchange interactions and resulting magnetic phases in the honeycomb cobaltates. For a broad range of trigonal crystal fields acting on Co2+ ions, the low-energy pseudospin-1/2 Hamiltonian is dominated by bond-dependent Ising couplings t
hat constitute the Kitaev model. The non-Kitaev terms nearly vanish at small values of trigonal field Delta, resulting in spin liquid ground state. Considering Na3Co2SbO6 as an example, we find that this compound is proximate to a Kitaev spin liquid phase, and can be driven into it by slightly reducing Delta by sim 20 meV, e.g., via strain or pressure control. We argue that due to the more localized nature of the magnetic electrons in 3d compounds, cobaltates offer the most promising search area for Kitaev model physics.
The concept of the entanglement between spin and orbital degrees of freedom plays a crucial role in understanding various phases and exotic ground states in a broad class of materials, including orbitally ordered materials and spin liquids. We invest
igate how the spin-orbital entanglement in a Mott insulator depends on the value of the spin-orbit coupling of the relativistic origin. To this end, we numerically diagonalize a 1D spin-orbital model with the Kugel-Khomskii exchange interactions between spins and orbitals on different sites supplemented by the on-site spin-orbit coupling. In the regime of small spin-orbit coupling w.r.t. the spin-orbital exchange, the ground state to a large extent resembles the one obtained in the limit of vanishing spin-orbit coupling. On the other hand, for large spin-orbit coupling the ground state can, depending on the model parameters, either still show negligible spin-orbital entanglement, or can evolve to a highly spin-orbitally entangled phase with completely distinct properties that are described by an effective XXZ model. The presented results suggest that: (i) the spin-orbital entanglement may be induced by large on-site spin-orbit coupling, as found in the 5d transition metal oxides, such as the iridates; (ii) for Mott insulators with weak spin-orbit coupling of Ising-type, such as e.g. the alkali hyperoxides, the effects of the spin-orbit coupling on the ground state can, in the first order of perturbation theory, be neglected.
A hypothetical layered oxide La_2NiMO_6 where NiO_2 and MO_2 planes alternate along the c-axis of ABO_3 perovskite lattice is considered theoretically. Here, M denotes a trivalent cation Al, Ga,... such that MO_2 planes are insulating and suppress th
e c-axis charge transfer. We predict that correlated e_g electrons in the NiO_2 planes develop a planar x^2-y^2 orbital order driven by the reduced dimensionality and further supported by epitaxial strain from the substrate. Low energy electronic states can be mapped to a single-band t-t-J model, suggesting favorable conditions for high-T_c superconductivity.
We derive and study a spin one-half Hamiltonian on a honeycomb lattice describing the exchange interactions between Ir$^{4+}$ ions in a family of layered iridates $A_2$IrO$_3$ ($A$=Li,Na). Depending on the microscopic parameters, the Hamiltonian inte
rpolates between the Heisenberg and exactly solvable Kitaev models. Exact diagonalization and a complementary spin-wave analysis reveal the presence of an extended spin-liquid phase near the Kitaev limit and a conventional Neel state close to the Heisenberg limit. The two phases are separated by an unusual stripy antiferromagnetic state, which is the exact ground state of the model at the midpoint between two limits.
