Strain-induced topological insulator phase and effective magnetic interactions in Li2IrO3

Abstract

We present an effective tight-binding Hamiltonian for Li${}_{2}$IrO${}_{3}$ based on maximally localized Wannier functions for states near the Fermi level as obtained from first-principles electronic structure calculations. The majority of the Wannier orbitals are positioned on the center site with dominant ${j}_{\mathrm{eff}}=1/2$ character, while relatively small ${j}_{\mathrm{eff}}=3/2$ tails lie on the three nearest-neighbor sites. Interestingly, the spin quantization axis of the ${j}_{\mathrm{eff}}=1/2$ components deviates from the local octahedral axis and points toward the nearest-neighbor Ir direction. In our tight-binding model, there are relatively strong next-nearest- and the third-nearest-neighbor hopping terms within the two-dimensional Ir honeycomb lattice in addition to the relatively small but significant interlayer hopping terms. The ratio between the nearest-neighbor and the third-nearest-neighbor hoppings, which can be controlled by the lattice strain, plays a critical role in determinating the ${Z}_{2}$-invariant character of Li${}_{2}$IrO${}_{3}$. From our tight-binding model, we also derive an effective Hamiltonian and its parameters for the magnetic exchange interactions. Due to the complex spin-dependent next-nearest-neighbor hopping terms, our pseudospin Hamiltonian includes significant next-nearest-neighbor antiferromagnetic Kitaev terms as well as Dzyaloshinskii-Moriya and Heisenberg interactions. From our model Hamiltonian we estimate classical energies of collinear magnetic configurations as functions of the Hund's coupling of the Ir atom, from which zigzag-type magnetic order gives the lowest energy.