Counter-rotating spiral order in three-dimensional iridates: Signature of hidden symmetry in the Kitaev- Γ model

Abstract

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, counterrotating 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 Γ interaction on the hyperhoneycomb lattice using exact diagonalization. We first show that a 12-site unitary transformation unveils a Heisenberg model with hidden SU(2) symmetry when K = Γ. The magnetic ordering in the transformed basis then generically maps to the counter-rotating noncoplanar spiral order of the original spin. The moment direction depends on perturbations away from the SU(2) point. When K and Γ are negative, a positive Heisenberg interaction favors the (110)-direction reported in the neutron scattering measurement on β-Li2IrO3. Our findings offer a relevant set of microscopic parameters, which in turn guides a way to approach possible Kitaev spin liquids. arXiv:1806.04688v2 [cond-mat.str-el]

Extent of frustration in the classical Kitaev-$Γ$ model via bond anisotropy

“…This pattern is refered to as a counterrotating spiral as the moments alternate as ABC along one site sublattice and ACB along the other, forming two FM dimers serving as inversion centers. This pattern has appeared in previous models of hyperhoneycomb materials [55][56][57][58] suggesting a relation between the 12 and 6 + 18 phases to the so-called K states of Ref. [57].…”

Nonsymmorphic-Symmetry-Protected Topological Magnons in Three-Dimensional Kitaev Materials

“…1 (a)] [17]. This model not only reproduces the known zero-field ground state, incommensurate noncoplanar spiral [14,17,31,32], but also the recently discovered field-induced canted zig-zag order [33,34] under a sufficiently strong magnetic field alongb-axis (S z direction), H h = −h j S z j . Based on first principle calculations [37], the experimentally relevant set of parameters for β-Li 2 IrO 3 is (J, K, Γ) = (0.063, −1, −0.33) in energy unit |K| = 1 [38].…”

“…In this paper, we theoretically study the symmetryprotected topological nodal magnons in three dimensional Kitaev materials, whose properties can be tuned by changing the underlying magnetic order. It has been known that the novel bond-dependent exchange interactions lead to the highly unusual counter-rotating incommensurate spiral order in β-Li 2 IrO 3 [14,17,31,32], where the spin-orbit coupled j eff = 1/2 local moments of Ir 4+ are located on the three-dimensional hyperhoneycomb lattice. Upon the application of an external magnetic field along theb-axis, a recent experiment has found the phase transition to a canted zig-zag order [ Fig.…”

Field evolution of low-energy excitations in the hyperhoneycomb magnet β−Li2IrO3

“…The size of the magnon gap may serve as a useful experimental constraint for the microscopic parametrization of β-Li 2 IrO 3 within the framework of the JK model [35][36][37], where J, K, and stand for the isotropic (Heisenberg) exchange, Kitaev exchange, and off-diagonal anisotropy, respectively. According to linear spin-wave calculations by Ducatman et al [26], gapless spectra are expected along the lines J = 0 and K = , but only in the latter case the gapless state is caused by symmetry, and the gap vanishes identically.…”