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Register a new userPlaquette order in classical spin liquid stabilized by strong off-diagonal exchange
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We report a new classical spin liquid in which the collective flux degrees of freedom break the translation symmetry of the honeycomb lattice. This exotic phase exists in frustrated spin-orbit magnets where a dominant off-diagonal exchange, the so-called $Gamma$ term, results in a macroscopic ground-state degeneracy at the classical level. We demonstrate that the system undergoes a phase transition driven by thermal order-by-disorder at a critical temperature $T_c approx 0.04 |Gamma|$. At first sight, this transition reduces an emergent spherical spin-symmetry to a cubic one: spins point predominantly toward the cubic axes at $T < T_c$. However, this seems to simply restore the cubic symmetry of the $Gamma$ model, and the non-coplanar spins remain disordered below $T_c$. We show that the phase transition actually corresponds to plaquette ordering of hexagonal fluxes and the cubic symmetry is indeed broken, a scenario that is further confirmed by our extensive Monte Carlo simulations.
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We show that the off-diagonal exchange anisotropy drives Mott insulators with strong spin-orbit coupling to a classical spin liquid regime, characterized by an infinite number of ground states and Ising variables living on closed or open strings. Depending on the sign of the anisotropy, quantum fluctuations either fail to lift the degeneracy down to very low temperatures, or select non-collinear magnetic states with unconventional spin correlations. The results apply to all 2D and 3D tri-coordinated materials with bond-directional anisotropy, and provide a consistent interpretation of the suppression of the x-ray magnetic circular dichroism signal reported recently for $beta$-Li$_2$IrO$_3$ under pressure.
Iridate oxides on a honeycomb lattice are considered promising candidates for realization of quantum spin liquid states. We investigate the magnetic couplings in a structural model for a honeycomb iridate K$_2$IrO$_3$, with $C_3$ point group symmetry at the Ir sites, which is an end member of the recently synthesized iridate family K$_x$Ir$_y$O$_2$. Using textit{ab-initio} quantum chemical methods, we elucidate the subtle relationship between the real space symmetry and magnetic anisotropy and show that the higher point group symmetry leads to high frustration with strong magnetic anisotropy driven by the unusually large off-diagonal exchange couplings ($Gamma$s) as opposed to other spin-liquid candidates considered so far. Consequently, large quantum fluctuations imply lack of magnetic ordering consistent with the experiments. Exact diagonalization calculations for the fully anisotropic $K$-$J$-$Gamma$ Hamiltonian reveal the importance of the off-diagonal anisotropic exchange couplings in stabilizing a spin liquid state and highlight an alternative route to stabilize spin liquid states for ferromagnetic $K$.
Both the Jahn-Teller distortion of Cu$^{2+}$O$_6$ octahedra and magnetic ordering are absent in hexagonal Ba$_3$CuSb$_2$O$_9$ suggesting a Cu 3$d$ spin-orbital liquid state. Here, by means of resonant x-ray scattering and absorption experiment, we show that oxygen 2$p$ holes play crucial role in stabilizing this spin-orbital liquid state. These oxygen holes appear due to the reaction Sb$^{5+}$$rightarrow$Sb$^{3+}$ $+$ two oxygen holes, with these holes being able to attach to Cu ions. The hexagonal phase with oxygen 2$p$ holes exhibits also a novel charge-orbital dynamics which is absent in the orthorhombic phase of Ba$_3$CuSb$_2$O$_9$ with Jahn-Teller distortion and Cu 3$d$ orbital order. The present work opens up a new avenue towards spin-charge-orbital entangled liquid state in transition-metal oxides with small or negative charge transfer energy.
Resonant x-ray diffraction experiments were performed for the metallic iridium oxide IrO$_{2}$. We observed anisotropic tensor of susceptibility (ATS) scattering, the spectrum of which shows a sharp contrast between the $L_{3}$ and $L_{2}$ edges. At the $L_{3}$ edge, resonance excitations were clearly observed from the core 2$p$ orbitals to both the 5$d$ $t_{2g}$ and $e_{g}$ orbitals. In contrast, the resonance mode associated with 5$d$ $t_{2g}$ orbitals was indiscernible at the $L_{2}$ edge. This contrasting behavior indicates that Ir 5$d$ $t_{2g}$ orbitals are fairly close to the $J_{rm eff}$ = 1/2 state due to the strong spin--orbit coupling in 5$d$ transition metal ions, as in the Mott insulator Sr$_{2}$IrO$_{4}$. Our results clearly demonstrate that ATS scattering is a useful probe for investigating complex orbital states in a metallic state. Such states induce novel phenomena such as the spin Hall effect.
We present a large-scale density matrix renormalization group (DMRG) study of the spin-$1$ SU(3) bilinear-biquadratic model on the square lattice, which was shown to host a nematic spin liquid state in recent DMRG calculations. We report that this spin liquid appears to strongly compete with a three-sublattice magnetic order. To further study the competition between the two states, and the reason of the emergent nematic spin liquid, we included an additional next-nearest-neighbor SU(3) symmetric interactions along one of the two plaquette diagonal directions. This allows to tune the square-lattice model to the triangular-lattice model. By computing spin correlation functions and various order parameters, we find that the three-sublattice order may develop at infinitesimal additional new coupling, at least within the precision of our study. Compared with the previous findings that the nematic spin liquid is stable in extended parameter regions with additional couplings that respect the lattice symmetries of the square lattice, we argue that here the diagonal couplings, which frustrate the bipartite-lattice structure, rapidly suppress the two-sublattice fluctuations and the three-sublattice order thus wins. This numerical result is consistent with the conjecture that the nematic spin liquid emerges from the competition between two- and three-sublattice fluctuations.
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