Gapless Spin Liquids on the Three-Dimensional Hyperkagome Lattice of ${\mathrm{Na}}_4{\mathrm{Ir}}_3{\mathrm{O}}_8$

Recent experiments indicate that ${\mathrm{Na}}_4{\mathrm{Ir}}_3{\mathrm{O}}_8$, a material in which $s=1/2$ Ir local moments live on a three-dimensional “hyperkagome” lattice of corner-sharing triangles, may have a quantum spin liquid ground state with gapless spin excitations. Using a combination of exact diagonalization, symmetry analysis of fermionic mean field ground states and Gutzwiller projected variational wave functions studies, we propose a quantum spin liquid with spinon Fermi surfaces as a favorable candidate for the ground state of the Heisenberg model on this lattice. We point out implications of this proposal for thermodynamic properties and discuss possible weak instabilities of the spinon Fermi surfaces.

Figure 1

Exact diagonalization (ED) results (solid line) for the inverse uniform magnetic susceptibility $1/\chi$ compared with experiments (open circles). The ED was done on a single unit cell of the hyperkagome lattice (inset) with $J=304\mathrm{K}$ chosen to reproduce the high temperature experimental $1/\chi$.

Figure 2

Energetics of the $Z_2$ family of states parametrized by $\theta$. Points show VMC data and the solid line is the mean field result multiplied by $g_J\approx 3$. The uniform state ($\theta =0$) appears to have the lowest energy in this class of states.

Figure 3

Comparison of the specific heat coefficient $C/T$ and entropy $S(T)$ of the U(1) uniform state with measurements on ${\mathrm{Na}}_4{\mathrm{Ir}}_3{\mathrm{O}}_8$ (after phonon subtraction). The inset compares the phonon subtracted $C/T$ with the ED result for $J=304\mathrm{K}$.