Search

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 nontrivial pursuit. In this work, we will concentrate on one of these particular materials, $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$, 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 a different range of 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 neighbor interactions, while the other includes interactions up to third neighbors. Furthermore, we show that strong bond anisotropies and further neighbor interactions are crucial to stabilize the tilted counterrotating spirals found in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Li}}_{2}{\mathrm{IrO}}_{3}$. We further clarify the picture and distinguish these two models by studying the magnetization processes. We predict the magnetization behavior of these models and propose future experimental directions.

We develop a generalized pseudo-fermion functional renormalization group (PFFRG) approach that can be applied to arbitrary Heisenberg models with spins ranging from the quantum case $S=1/2$ to the classical limit $S\rightarrow\infty$. Within this framework, spins of magnitude $S$ are realized by implementing $M=2S$ copies of spin-1/2 degrees of freedom on each lattice site. We confirm that even without explicitly projecting onto the highest spin sector of the Hilbert space, ground states tend to select the largest possible local spin magnitude. This justifies the average treatment of the pseudo fermion constraint in previous spin-1/2 PFFRG studies. We apply this method to the antiferromagnetic $J_1$-$J_2$ honeycomb Heisenberg model with nearest neighbor $J_1>0$ and second neighbor $J_2>0$ interactions. Mapping out the phase diagram in the $J_2/J_1$-$S$ plane we find that upon increasing $S$ quantum fluctuations are rapidly decreasing. In particular, already at $S=1$ we find no indication for a magnetically disordered phase. In the limit $S\rightarrow\infty$, the known phase diagram of the classical system is exactly reproduced. More generally, we prove that for $S\rightarrow\infty$ the PFFRG approach is identical to the Luttinger-Tisza method., 14 pages, 13 figures