# Magnetization processes of zigzag states on the honeycomb lattice: Identifying spin models for $\alpha$-RuCl$_3$ and Na$_2$IrO$_3$

## TL;DR

This paper investigates the magnetization processes of extended Heisenberg-Kitaev models on the honeycomb lattice, revealing how different parameter sets influence zigzag states and explaining experimental anisotropic responses in $ ext{RuCl}_3$.

## Contribution

It identifies three distinct mechanisms stabilizing zigzag states and links off-diagonal interactions to anisotropic magnetization responses in $ ext{RuCl}_3$.

## Key findings

- Three mechanisms stabilize zigzag states with different parameter sets.
- Off-diagonal interaction $ extGamma_1 > 0$ explains anisotropic field responses.
- High-field state with finite transversal magnetization predicted for $ ext{RuCl}_3$.

## Abstract

We study the field-induced magnetization processes of extended Heisenberg-Kitaev models on the honeycomb lattice, taking into account off-diagonal and longer-range exchange interactions, using a combination of Monte-Carlo simulations, classical energy minimization, and spin-wave theory. We consider a number of different parameter sets, previously proposed to describe the magnetic behavior of $\alpha$-RuCl$_3$ and Na$_2$IrO$_3$ with their antiferromagnetic zigzag ground states. By classifying these parameter sets, we reveal the existence of three distinct mechanisms to stabilize zigzag states, which differ in the sign of the nearest-neighbor Kitaev interaction, the role of longer-range interactions, and the magnitude of the off-diagonal $\Gamma_1$ interaction. While experimentally hardly distinguishable at zero field, we find that the three different scenarios lead to significantly different magnetization processes in applied magnetic fields. In particular, we show that a sizable off-diagonal interaction $\Gamma_1 > 0$ naturally explains the strongly anisotropic field responses observed in $\alpha$-RuCl$_3$ without the need for a strong anisotropy in the effective $g$ tensor. Moreover, for a generic field direction, it leads to a high-field state with a finite transversal magnetization, which should be observable in $\alpha$-RuCl$_3$.