Theory of magnetic phase diagrams in hyperhoneycomb and harmonic-honeycomb iridates

摘要

Motivated by recent experiments, we consider a generic spin model in the j_(eff) = 1/2 basis for the hyperhoneycomb and harmonic-honeycomb iridates. Based on microscopic considerations, the effect of an additional bond-dependent anisotropic spin exchange interaction (Γ) beyond the Heisenberg-Kitaev model is investigated. We obtain the magnetic phase diagrams of the hyperhoneycomb and harmonic-honeycomb (H-1) lattices via a combination of the Luttinger-Tisza approximation, single-Q variational ansatz, and classical Monte Carlo simulated annealing. The resulting phase diagrams on both systems show the existence of incommensurate, noncoplanar spiral magnetic orders as well as other commensurate magnetic orders. The spiral orders show counterpropagating spiral patterns, which may be favorably compared to recent experimental results on both iridates. The parameter regimes of various magnetic orders and ordering wave vectors are quite similar in both systems. We discuss the implications of our work for recent experiments and also compare our results to those of the two-dimensional honeycomb iridate systems.