No Arabic 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 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.
Entanglement of spin and orbital degrees of freedom drives the formation of novel quantum and topological physical states. Discovering new spin-orbit entangled ground states and emergent phases of matter requires both experimentally probing the relevant energy scales and applying suitable theoretical models. Here we report resonant inelastic x-ray scattering measurements of the transition metal oxides Ca$_3$LiOsO$_6$ and Ba$_2$YOsO$_6$. We invoke an intermediate coupling approach that incorporates both spin-orbit coupling and electron-electron interactions on an even footing and reveal the ground state of $5d^3$ based compounds, which has remained elusive in previously applied models, is a novel spin-orbit entangled J=3/2 electronic ground state. This work reveals the hidden diversity of spin-orbit controlled ground states in 5d systems and introduces a new arena in the search for spin-orbit controlled phases of matter.
The $4d$ and $5d$ transition metal oxides have become important members of the emerging quantum materials family due to competition between onsite Coulomb repulsion ($U$) and spin-orbit coupling (SOC). Specifically, the systems with $d^5$ electronic configuration in an octahedral environment are found to be capable of posessing invariant semimetallic state and perturbations can lead to diverse magnetic phases. In this work, by formulating a multi-band Hubbard model and performing SOC tunable DFT+$U$ calculations on a prototype SrIrO$_3$ and extending the analysis to other iso-structural and isovalent compounds, we present eight possible electronic and magnetic configurations in the $U$-SOC phase diagram that can be observed in the family of low-spin $d^5$ perovskites. They include the protected Dirac semimetal state, metal and insulator regimes, collinear and noncollinear spin ordering. The latter is explained through connecting hopping interactions to the rotation and tilting of the octahedra as observed in GdFeO$_3$. Presence of several soft phase boundaries makes the family of $d^5$ perovskites an ideal platform to study electronic and magnetic phase transitions under external stimuli.
Spin-orbit coupling of as large as a half eV for electrons in 5$d$ orbitals often gives rise to the formation of spin-orbital entangled objects, characterized by the effective total angular momentum $J_{eff}$. Of particular interest are the $J_{eff}$ = 3/2 states realized in 5$d^{1}$ transition metal ions surrounded by an anion octahedron. The pure $J_{eff}$ = 3/2 quartet does not have any magnetic dipolar moment (<$M$> = 0) but hosts hidden pseudo-dipolar moments accompanied by charge quadrupoles and magnetic octupoles. Cs$_2$TaCl$_6$ and Rb$_2$TaCl$_6$ are correlated insulators with 5$d^{1}$ Ta$^{4+}$ ions in a regular Cl octahedron. Here we demonstrate that these Ta chlorides have a substantially suppressed effective magnetic dipolar moment of ~ 0.2 ${mu}_B$. Two phase transitions are observed at low temperatures that are not pronounced in the magnetization but accompanied with large electronic entropy of $R$ln4. We ascribe the two transitions to the ordering of hidden multipoles.
We report structural studies of the spin-orbit Mott insulator family K$_x$Ir$_y$O$_2$, with triangular layers of edge-sharing IrO$_6$ octahedra bonded by potassium ions. The potassium content acts as a chemical tuning parameter to control the amount of charge in the Ir-O layers. Unlike the isostructural families with Ir replaced by Co or Rh ($y=1$), which are metallic over a range of potassium compositions $x$, we instead find insulating behaviour with charge neutrality achieved via iridium vacancies, which order in a honeycomb supercell above a critical composition $x_c$. By performing density functional theory calculations we attribute the observed behaviour to a subtle interplay of crystal-field environment, local electronic correlations and strong spin-orbit interaction at the Ir$^{4+}$ sites, making this structural family a candidate to display Kitaev magnetism in the experimentally unexplored regime that interpolates between triangular and honeycomb structures.
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 that 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.