Magnon dispersion and dynamic spin response in three-dimensional spin models for α-RuCl3

In the search for experimental realizations of bond-anisotropic Kitaev interactions and resulting spin-liquid phases, the layered magnet alpha-RuCl3 is a prime candidate. Its modeling typically involves Heisenberg, Kitaev, and symmetric off-diagonal Gamma interactions on the two-dimensional honeycomb lattice. However, recent neutron-scattering experiments point towards a sizable magnetic interlayer coupling. Here we study three-dimensional exchange models for alpha-RuCl3, for both possible R (3) over bar and C2/m crystal structures. We discuss the symmetry constraints on the interlayer couplings, construct minimal models, and use them to compute the magnetic mode dispersion and the dynamical spin structure factor, in both the zero-field zigzag phase and the paramagnetic high-field phase. Our predictions for the interlayer mode dispersion shall guide future experiments; they also call for a reevaluation of the quantitative model parameters relevant for alpha-RuCl3.