Spin-orbit coupling in octamers in a spinel sulfide CuIr${}_2$S${}_4$: Competition between spin-singlet and quadrupolar states, and its relevance to remnant paramagnetism

Abstract

We theoretically investigate magnetic properties in the low-temperature phase with the formation of eight-site clusters, octamers, in the spinel compound CuIr${}_2$S${}_4$. The octamer state was considered to be a spin-singlet state induced by a Peieirls instability through the strong anisotropy of $d$ orbitals, the so-called orbital Peierls state. We reexamine this picture by taking into account the spin-orbit coupling which was ignored in the previous study. We derive a low-energy effective model between $j_{\mathrm{eff}}=1/2$ quasispins on Ir${}^{4+}$ cations in an octamer from the multiorbital Hubbard model with the strong spin-orbit coupling by performing the perturbation expansion from the strong correlation limit. The effective Hamiltonian is in the form of the Kitaev-Heisenberg model but with an additional interaction, a symmetric off-diagonal exchange interaction originating from the perturbation process including both d-d and d-p-d hopping. Analyzing the effective Hamiltonian on two sites and the octamer by the exact diagonalization, we find that there is a competition between a spin-singlet state and a quadrupolar state. The former singlet state is a conventional one, adiabatically connected to the orbital-Peierls state. On the other hand, the latter quadrupolar state is stabilized by the additional interaction, which consists of a linear combination of different total spin momenta along the spin quantization axis. In the competing region, the model exhibits paramagnetic behavior with a renormalized small effective moment at low temperature. This peculiar remnant paramagnetism is not obtained in the Kitaev-Heisenberg model without the additional interaction. Our results renew the picture of the octamer state and provide a scenario for the intrinsic paramagnetic behavior recently observed in a muon spin rotation experiment [K. M. Kojima et al., Phys. Rev. Lett. 112, 087203 (2014)].

arXiv comment13 pages, 12 figures

References in corpus (16)

• Anyons in an exactly solved model and beyond
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Novel Jeff = 1/2 Mott State Induced by Relativistic Spin-Orbit Coupling in Sr2IrO4
• Kitaev-Heisenberg Model on Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_2$IrO${}_3$
• Generic spin model for the honeycomb iridates beyond the Kitaev limit
• Spin waves and revised crystal structure of honeycomb iridate Na2IrO3
• Direct evidence of a zigzag spin chain structure in the honeycomb lattice: A neutron and x-ray diffraction investigation on single crystal $\mathrm{N}{\mathrm{a}}_2\mathrm{Ir}{\mathrm{O}}_3$
• Long range magnetic ordering in Na${}_2$IrO${}_3$
• Nematic order in square lattice frustrated ferromagnets
• Orbitally-driven Peierls state in spinels
• Possible proximity of the Mott insulating Iridate Na2IrO3 to a topological phase: Phase diagram of the Heisenberg-Kitaev model in a magnetic field
• Spin singlet formation in MgTi${}_2$O${}_4$: evidence of a helical dimerization pattern
• Finite-temperature phase diagram of the Heisenberg-Kitaev model
• Ab initio analysis of the tight-binding parameters and magnetic interactions in Na2IrO3
• Optical study of the metal-insulator transition in CuIr${}_2$S${}_4$ crystals
• Magnetic frustration in iridium spinel compound CuIr${}_2$S${}_4$

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• Field-angle dependence of thermal Hall conductivity in magnetically ordered Kitaev-Heisenberg system
• The Valence Transition Model of Pseudogap, Charge-Order and Superconductivity in Electron- and Hole-Doped Copper Oxides
• Reexamination of the charge-ordered dimer pattern in the spinel compound CuIr2S4 using single-crystal synchrotron x-ray diffraction
• Superconductivity on the verge of metal-insulator transition in Cu${}_{1-x}$Zn${}_x$Ir${}_2$S${}_4$ probed by $\mu$SR