Interplay of nonsymmorphic symmetry and spin-orbit coupling in hyperkagome spin liquids: Applications to Na4Ir3O8

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 Z 2 and U(1) spin liquid states, following the projective symmetry group analysis in the slave-fermion representation. There are only three distinct Z 2 spin liquids, together with 2 different U(1) spin liquids. The nonsymmorphic space group symmetry of hyperkagome lattice plays a vital role in simplifying the classification, forbidding "π-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.

Classical and quantum order in hyperkagome antiferromagnets

“…Note that similar PSG classification for fermionic states has been done by Huang et al in Ref. [44], where time-reversal symmetry is considered as well. In this paper, we will not involve timereversal symmetry and consider space group symmetry P 4 1 32 only, such that time-reversal symmetry breaking states are allowed indeed.…”

“…Other algebra relations involving screw rotation S 4 , C 2 and C 3 rotations can be found Appendix B as well as detailed calculations. The algebra is straightforward and is similar to that used in fermionic PSG calculation on hyperkagome lattice 44 . Additionally, for bosonic states, there exists a convenient gauge choice by which all the gauge rotations G U (iµ) are independent of the unit cell index i.…”

Magnetic Order with Fractionalized Excitations in Pyrochlore Magnets with Strong Spin-Orbit Coupling

“…We apply the complex fermion mean field theory 27–30 to the nearest neighbor S = 1/2 Hamiltonianon the pyrochlore lattice, which in general contains four independent exchange parameters J 1 , J 2 , J 3 , and J 4 (defined in the global coordinates) 31 . We list Gaulin 31 and Coldea 20 parametrizations of Yb 2 Ti 2 O 7 , which are obtained from spin wave analysis of the inelastic neutron scattering data at high magnetic fields, in Table 1.…”

Spinon Magnetic Resonance of Quantum Spin Liquids

“…All of these are very generic conditions which are satisfied by essentially every model of spin liquids of U (1) and Z 2 type (but not by spin-conserving SU (2) ones). The restriction to low symmetry spin liquids is not really a handicap as it turned out that the number of possible spin liquids with reduced U (1) and Z 2 vastly outnumbers that of SU (2) symmetric ones [30,34,35]. In particular, the SMR should be present in the celebrated Kitaev's honeycomb model [11], as was emphasized in dynamic structure calculations of [36][37][38][39].…”