Interplay of nonsymmorphic symmetry and spin-orbit coupling in hyperkagome spin liquids: Applications to Na_4Ir_3O_8

摘要

Na_4Ir_3O_8 provides a material platform to study three-dimensional quantum spin liquids in the geometricallyfrustrated hyperkagome lattice of Ir~(4+) ions. In this work, we consider quantum spin liquids on a hyperkagomelattice for generic spin models, focusing on the effects of anisotropic spin interactions. In particular, we classifypossible Z_2 and U(1) spin liquid states, following the projective symmetry group analysis in the slave-fermionrepresentation. There are only three distinct Z_2 spin liquids, together with 2 different U(1) spin liquids.The nonsymmorphic space group symmetry of the hyperkagome lattice plays a vital role in simplifying theclassification, forbidding “π-flux” or “staggered-flux” phases in contrast to symmorphic space groups.We furtherprove that both U(1) states and one Z_2 state among all 3 are symmetry-protected gapless spin liquids, robustagainst any symmetry-preserving perturbations. Motivated by the “spin-freezing” behavior recently observedin Na_4Ir_3O_8 at low temperatures, we further investigate the nearest-neighbor spin model with the dominantHeisenberg interaction subject to all possible anisotropic perturbations from spin-orbit couplings. We find thata U(1) spin liquid ground state with spinon Fermi surfaces is energetically favored over Z_2 states. Among allspin-orbit coupling terms, we show that only the Dzyaloshinskii-Moriya interaction can induce spin anisotropyin the ground state when perturbing from the isotropic Heisenberg limit. Our work paves the way for a systematicstudy of quantum spin liquids in various materials with a hyperkagome crystal structure.