Minimal models of $\alpha$-Li$_2$IrO$_3$: On the range of the interactions, ground state properties, and magnetization processes

Abstract

In recent years, a lot of effort has been devoted to the quest for experimental realizations of Kitaev interactions in spin systems. Recently, many materials have been synthesized which seem to realize extended Kitaev models, where Kitaev interactions are supplemented by Heisenberg and other bond dependent terms. The crystal and electronic structure of these materials renders the determination of a minimal model a non trivial pursuit. In this work, we will concentrate on one of these particular materials, $\alpha$-Li$_2$IrO$_3$, for which various minimal models have been proposed. Employing large scale Monte Carlo simulations we show how the number of prospective models can be reduced. We study in detail six models with different range of the interactions, and show how only two of those reproduce the most recent experimental results for this material. We obtain two possible minimal models, one of them with nearest neighbour interactions, while the other includes interactions up to third neighbours. Furthermore, we show that strong bond anisotropies and further neighbour interactions are crucial to stabilize the tilted counterotating spirals found in $\alpha$-Li$_2$IrO$_3$. We further clarify the picture, and distinguish these two models by studying the magnetization processes. We predict the magnetization behaviour of these models, and propose future experimental directions.