Interplay of non-symmorphic symmetry and spin-orbit coupling in hyperkagome spin liquids: Applications to Na${}_4$Ir${}_3$O${}_8$

Abstract

Na${}_4$Ir${}_3$O${}_8$ provides a material platform to study three-dimensional quantum spin liquids in the geometrically frustrated hyperkagome lattice of Ir${}^{4+}$ ions. In this work, we consider quantum spin liquids on hyperkagome lattice for generic spin models, focusing on the effects of anisotropic spin interactions. In particular, we classify possible ${\mathbb{Z}}_2$ and $U(1)$ spin liquid states, following the projective symmetry group analysis in the slave-fermion representation. There are only three distinct ${\mathbb{Z}}_2$ spin liquids, together with 2 different $U(1)$ spin liquids. The non-symmorphic space group symmetry of hyperkagome lattice plays a vital role in simplifying the classification, forbidding "$\pi$-flux" or "staggered-flux" phases in contrast to symmorphic space groups. We further prove that both $U(1)$ states and one $Z_2$ state among all 3 are symmetry-protected gapless spin liquids, robust against any symmetry-preserving perturbations. Motivated by the "spin-freezing" behavior recently observed in Na${}_4$Ir${}_3$O${}_8$ at low temperatures, we further investigate the nearest-neighbor spin model with dominant Heisenberg interaction subject to all possible anisotropic perturbations from spin-orbit couplings. We found a $U(1)$ spin liquid ground state with spinon fermi surfaces is energetically favored over $Z_2$ states. Among all spin-orbit coupling terms, we show that only Dzyaloshinskii-Moriya (DM) interaction can induce spin anisotropy in the ground state when perturbing from the isotropic Heisenberg limit. Our work paves the way for a systematic study of quantum spin liquids in various materials with a hyperkagome crystal structure.

arXiv comment27 pages, 9 figures, reference updated

References in corpus (38)

• Anyons in an exactly solved model and beyond
• Quantum Spin Liquid States
• Quantum Orders and Symmetric Spin Liquids
• Spin-Liquid State in the S = 1/2 Hyperkagome Antiferromagnet Na4Ir3O8
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Filling constraints for spin-orbit coupled insulators in symmorphic and non-symmorphic crystals
• Topological Order and Absence of Band Insulators at Integer Filling in Non-Symmorphic Crystals
• Doping a spin-orbit Mott Insulator: Topological Superconductivity from the Kitaev-Heisenberg Model and possible application to (Na2/Li2)IrO3
• Z2-topology in nonsymmorphic crystalline insulators: Mobius twist in surface states
• Kitaev-Heisenberg models for iridates on the triangular, hyperkagome, kagome, fcc, and pyrochlore lattices
• Classification of gapless Z2 spin liquids in three-dimensional Kitaev models
• Spin-orbit effects in Na${}_4$Ir${}_3$O${}_8$, a hyper-kagomé lattice antiferromagnet
• Symmetry fractionalization and twist defects
• Gapless spin liquids on the three dimensional hyper-kagome lattice of Na${}_4$Ir${}_3$O${}_8$
• Topological Insulators from Group Cohomology
• Topological spin liquid on the hyper-kagome lattice of Na_4Ir_3O_8
• Triplet and Singlet Excitations in the Valence Bond Crystal Phase of Kagome Lattice Heisenberg Model
• Na4Ir3O8 as a 3D spin liquid with fermionic spinons
• Magnetic properties and heat capacity of the three-dimensional frustrated S=1/2 antiferromagnet PbCuTe2O6
• Spin Liquid State in the 3D Frustrated Antiferromagnet PbCuTe2O6: NMR and muSR Studies
• Classical antiferromagnet on a hyperkagome lattice
• SU(2) Slave Fermion Solution of the Kitaev Honeycomb Lattice Model
• Short-range correlations in the magnetic ground state of Na4Ir3O8
• Competing magnetic orders and spin liquids in two- and three-dimensional kagome systems: A pseudo-fermion functional renormalization group perspective
• Spin liquid close to a quantum critical point in Na${}_4$Ir${}_3$O${}_8$
• Frozen State and Spin Liquid Physics in Na4Ir3O8: an NMR study
• Quantum spin liquids in the absence of spin-rotation symmetry: application to Herbertsmithite
• Projective studies of spin nematics in a quantum frustrated ferromagnet
• Anomalous enhancement of Wilson ratio in a quantum spin liquid with strong spin-orbital entanglement: the case of Na4Ir3O8
• Majorana spin liquids and projective realization of SU(2) spin symmetry
• Classification of spin liquids on the square lattice with strong spin-orbit coupling
• High temperature series expansion study of the Heisenberg antiferromagnet on the hyperkagome lattice: Comparison with Na${}_4$Ir${}_3$O${}_8$
• Spin Hamiltonian of Hyperkagome Na4Ir3O8
• Space group constraints on weak indices in topological insulators
• Nature of Possible Magnetic Phases in Frustrated Hyperkagome Iridate
• Generic model for hyperkagome iridate in the local moment regime
• Fractionalizing glide reflections in two-dimensional Z2 topologically ordered phases

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