Spin-orbital Entangled Molecular $j_{\mathrm{eff}}$ States in Lacunar Spinel Compounds

Abstract

The entanglement of the spin and orbital degrees of freedom through the spin-orbit coupling has been actively studied in condensed matter physics. In several iridium-oxide systems, the spin-orbital entangled state, identified by the effective angular momentum $j_{\mathrm{eff}}$, can host novel quantum phases with the help of electron correlations. Here, we show that a series of lacunar spinel compounds, Ga$M_4{X}_8$ ($M$ = Nb, Mo, Ta, and W and $X$ = S, Se, and Te), gives rise to a $\text{molecular}$ $j_{\mathrm{eff}}$ state as a new spin-orbital composite on which the low energy effective Hamiltonian is based. A wide range of electron correlations is accessible by tuning the bandwidth under external and/or chemical pressure, enabling us to investigate the interesting cooperation between spin-orbit coupling and electron correlations. As illustrative examples, a two-dimensional topological insulating phase and an anisotropic spin Hamiltonian are investigated in the weak and strong coupling regimes, respectively. Our finding can provide an ideal platform for exploring $j_{\mathrm{eff}}$ physics and the resulting emergent phenomena.

17 pages and 4 figures, and with supplementary information (14 pages, 6 figures, and 5 tables). Details of the DFT+U results on the magnetism are included in the supplementary material

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Cited by in corpus (42)

• The Chemistry of Quantum Spin Liquids
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• Featureless adaptive optimization accelerates functional electronic materials design
• Emergent orbitals in the cluster Mott insulator on a breathing Kagome lattice
• Assessing exchange-correlation functional performance in the chalcogenide lacunar spinels GaM${}_4$Q${}_8$ (M = Mo, V, Nb, Ta; Q = S, Se)
• Multiflavor Mott insulators in quantum materials and ultracold atoms
• Structural evolution and skyrmionic phase diagram of the lacunar spinel GaMo${}_4$Se${}_8$
• Alleviating the Sign Problem in Quantum Monte Carlo Simulations of Spin-Orbit-Coupled Multi-Orbital Hubbard Models
• Topological d+s wave superconductors in a multi-orbital quadratic band touching system
• Mapping Skyrmion Stability in Uniaxial Lacunar Spinel Magnets from First-Principles
• Stability of Néel-type skyrmion lattice against oblique magnetic fields in GaV${}_4$S${}_8$ and GaV${}_4$Se${}_8$
• Molecular Mott state in the deficient spinel GaV${}_4$S${}_8$
• Architecture of nanoscale ferroelectric domains in GaMo4S8
• Possible quadrupole order in tetragonal Ba2CdReO6 and chemical trend in the ground states of 5d1 double perovskites
• Lattice dynamics and electronic excitations in a large family of lacunar spinels with a breathing pyrochlore lattice structure
• Structural, magnetic, electric, dielectric, and thermodynamic properties of multiferroic GeV4S8
• Theoretical evidence of spin-orbital-entangled $J_{\mathbf{eff}}$=1/2 state in the 3$d$ transition metal oxide CuAl${}_2$O${}_4$
• Frustrated Magnetism in Mott Insulating (V${}_{1-x}$Cr${}_x$)${}_2$O${}_3$
• Magnetic molecular orbitals in MnSi
• Magnetic phase transitions and spin density distribution in the molecular multiferroic GaV${}_4$S${}_8$ system
• Quasimolecular $J_{\mathrm{tet}}$=3/2 moments in the cluster Mott insulator GaTa${}_4$Se${}_8$
• Terahertz Dielectric Analysis and Spin-Phonon Coupling in Multiferroic GeV${}_4$S${}_8$
• Calculating branching ratio and spin-orbit coupling from first-principles: A formalism and its application to iridates
• Magnetoentropic mapping and computational modeling of cycloids and skyrmions in the lacunar spinels GaV${}_4$S${}_8$ and GaV${}_4$Se${}_8$
• Antipolar transitions in GaNb${}_4$Se${}_8$ and GaTa${}_4$Se${}_8$
• Charge density functional plus $U$ calculation of lacunar spinel GaM${}_4$Se${}_8$ (M = Nb, Mo, Ta, and W)
• Crystal and Electronic Structure of GaTa${}_4$Se${}_8$ From First-Principle Calculations
• Clusterization transition between cluster Mott insulators on a breathing Kagomé lattice
• Resonating holes vs molecular spin-orbit coupled states in group-5 lacunar spinels
• Cluster rearrangement by chiral charge order in lacunar spinel GaNb${}_4$Se${}_8$
• Bond Ordering and Molecular Spin-Orbital Fluctuations in the Cluster Mott Insulator GaTa${}_4$Se${}_8$
• Strong tuning of magnetism and electronic structure by spin orientation
• Novel $J_{\mathrm{eff}}$=3/2 Metallic Phase and Unconventional Superconductivity in GaTa${}_4$Se${}_8$
• Charge ordering in Ir dimers in the ground state of Ba${}_5$AlIr${}_2$O${}_{11}$
• Entropy and specific heat of the infinite-dimensional three-orbital Hubbard model
• Spin dynamics in the skyrmion-host lacunar spinel GaV4S8
• Jahn-Teller driven quadrupolar ordering and spin-orbital dimer formation in GaNb${}_4$Se${}_8$
• Quasimolecular electronic structure of the trimer iridate Ba${}_4$NbIr${}_3$O${}_{12}$
• Optical, dielectric, and magnetoelectric properties of ferroelectric and antiferroelectric lacunar spinels
• Electronic Self-Organization in the β-Pyrochlore Oxide CsW2O6