Compass-model physics on the hyperhoneycomb lattice in the extreme spin-orbit regime

Abstract

The physics of spin-orbit entangled magnetic moments of $4d$ and $5d$ transition metal ions on a honeycomb lattice has been much explored in search for unconventional magnetic orders or quantum spin liquids expected for compass spin models, where different bonds in the lattice favour different orientations for the magnetic moments. Realizing such physics with rare-earth ions is a promising route to achieve exotic ground states in the extreme spin orbit limit, however this regime has remained experimentally largely unexplored due to major challenges in materials synthesis. Here we report successful synthesis of powders and single crystals of $\beta$-Na$_2$PrO$_3$, with $4f^{1}$ Pr$^{4+}$ $j_\mathrm{eff}\!=\!1/2$ magnetic moments arranged on a hyperhoneycomb lattice with the same threefold coordination as the planar honeycomb. We find a strongly noncollinear magnetic order with highly dispersive gapped excitations that we argue arise from frustration between bond-dependent, anisotropic off-diagonal exchanges, a compass quantum spin model not explored experimentally so far. Our results show that rare-earth ions on threefold coordinated lattices offer a platform for the exploration of quantum compass spin models in the extreme spin orbit regime, with qualitatively distinct physics from that of $4d$ and $5d$ Kitaev materials.