The unconventional magnetic orderings found in Kitaev spin liquid candidates suggest frustration of spin interactions and raise a possibility of nearby spin liquid phases. In particular, counter-rotating spiral ordering in three-dimensional (3D) iridates is striking, and understanding the microscopic mechanism of such ordering may provide routes to 3D Kitaev spin liquids. We study a minimal 3D model including Kitaev $K$ and a symmetric off-diagonal bond-dependent $\mathrm{\ensuremath{\Gamma}}$ interaction on the hyperhoneycomb lattice by using exact diagonalization (ED). An ED cluster was chosen to satisfy a hidden SU(2) symmetry when $K=\mathrm{\ensuremath{\Gamma}}$ via a 12-site unitary transformation. The magnetic ordering in the transformed basis then generically maps to the counter-rotating noncoplanar spiral order of the original spin when the moment is pinned along a certain direction. When $K$ and $\mathrm{\ensuremath{\Gamma}}$ are negative, a small positive Heisenberg interaction favors the (1,1,0) direction consistent with the reported spiral order in $\ensuremath{\beta}\ensuremath{-}{\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$. Two other ordered phases close to the spiral order and spin liquids are identified. Our findings offer a relevant set of microscopic parameters, which in turn guides a way to approach possible Kitaev spin liquids.The unconventional magnetic orderings found in Kitaev spin liquid candidates suggest frustration of spin interactions and raise a possibility of nearby spin liquid phases. In particular, counter-rotating spiral ordering in three-dimensional (3D) iridates is striking, and understanding the microscopic mechanism of such ordering may provide routes to 3D Kitaev spin liquids. We study a minimal 3D model including Kitaev $K$ and a symmetric off-diagonal bond-dependent $\mathrm{\ensuremath{\Gamma}}$ interaction on the hyperhoneycomb lattice by using exact diagonalization (ED). An ED cluster was chosen to satisfy a hidden SU(2) symmetry when $K=\mathrm{\ensuremath{\Gamma}}$ via a 12-site unitary transformation. The magnetic ordering in the transformed basis then generically maps to the counter-rotating noncoplanar spiral order of the original spin when the moment is pinned along a certain direction. When $K$ and $\mathrm{\ensuremath{\Gamma}}$ are negative, a small positive Heisenberg interaction favors the (1,1,0) direction consistent with the reported spiral order in $\ensuremath{\beta}\ensuremath{-}{\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$. Two other ordered phases close to the spiral order and spin liquids are identified. Our findings offer a relevant set of microscopic parameters, which in turn guides a way to approach possible Kitaev spin liquids.

arXiv:1806.04688Physical review. B./Physical review. BSep 4, 201821 citations

Concept and realization of Kitaev quantum spin liquids

H. Takagi, T. Takayama, George Jackeli +2 more

arXiv:1903.08081Nature Reviews PhysicsMar 25, 2019813 citations

K

and a symmetric off-diagonal bond-dependent $\mathrm{\ensuremath{\Gamma}}$ interaction on the hyperhoneycomb lattice by using exact diagonalization (ED). An ED cluster was chosen to satisfy a hidden SU(2) symmetry when $K=\mathrm{\ensuremath{\Gamma}}$ via a 12-site unitary transformation. The magnetic ordering in the transformed basis then generically maps to the counter-rotating noncoplanar spiral order of the original spin when the moment is pinned along a certain direction. When

K

and $\mathrm{\ensuremath{\Gamma}}$ are negative, a small positive Heisenberg interaction favors the (1,1,0) direction consistent with the reported spiral order in $\ensuremath{\beta}\ensuremath{-}{\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$. Two other ordered phases close to the spiral order and spin liquids are identified. Our findings offer a relevant set of microscopic parameters, which in turn guides a way to approach possible Kitaev spin liquids.