Motivated by the recent wealth of exotic magnetic phases emerging in two-dimensional frustrated lattices, we investigate the origin of possible magnetism in the monolayer family of triangular lattice materials $M{X}_2$ ($M$=V, Mn, Ni and $X$=Cl, Br, I). We first show that consideration of general properties such as filling and hybridization enables to formulate the trends for the most relevant magnetic interaction parameters. In particular, we observe that the effects of spin-orbit coupling (SOC) can be effectively tuned through the ligand elements as the considered $3d$ transition metal ions do not strongly contribute to the anisotropic component of the intersite exchange interaction. Consequently, we find that the corresponding SOC matrix elements differ significantly from the atomic limit. In the next step and by using two ab initio based complementary approaches, we extract realistic effective spin models and find that in the case of heavy ligand elements, SOC effects manifest in anisotropic exchange and single-ion anisotropy only for specific fillings.

We present first-principles results on the magnetoelastic coupling in $\alpha \text{−}{\mathrm{RuCl}}_3$ and uncover a striking dependence of the magnetic coupling constants on strain effects. Different magnetic interactions are found to respond very unequally to variations in the lattice, with the Kitaev interaction being the most sensitive. Exact diagonalization results on our magnetoelastic model reproduce recent measurements of the structural Grüneisen parameter and explain the origin of the negative magnetostriction of $\alpha \text{−}{\mathrm{RuCl}}_3$, disentangling contributions related to different anisotropic interactions and $g$ factors. Uniaxial strain perpendicular to the honeycomb planes is predicted to reorganize the relative coupling strengths, strongly enhancing the Kitaev interaction while simultaneously weakening the other anisotropic exchanges under compression. Uniaxial strain may therefore pose a fruitful route to experimentally tune $\alpha \text{−}{\mathrm{RuCl}}_3$ nearer to the Kitaev limit.

Motivated by reports of metallic behavior in the recently synthesized RuI₃, in contrast to the Mott-insulating nature of the actively discussed α-RuCl₃, as well as RuBr₃, we present a detailed comparative analysis of the electronic and magnetic properties of this family of trihalides. Using a combination of first-principles calculations and effective-model considerations, we conclude that RuI₃, similarly to the other two members, is most probably on the verge of a Mott insulator, but with much smaller magnetic moments and strong magnetic frustration. We predict the ideal pristine crystal of RuI₃ to have a nearly vanishing conventional nearest-neighbor Heisenberg interaction and to be a quantum spin liquid candidate of a possibly different kind than the Kitaev spin liquid. In order to understand the apparent contradiction to the reported resistivity ρ, we analyze the experimental evidence for all three compounds and propose a scenario for the observed metallicity in existing samples of RuI₃. Furthermore, for the Mott insulator RuBr_3, we obtain a magnetic Hamiltonian of a similar form to that in the much-discussed α-RuCl₃ and show that this Hamiltonian is in agreement with experimental evidence in RuBr₃.

The so-called “Kitaev candidate” materials based on $4d^5$ and $5d^5$ metals have recently emerged as magnetic systems displaying strongly anisotropic exchange interactions reminiscent of the Kitaev’s honeycomb model. Recently, these materials have been shown to commonly display a distinct sawtooth angular dependence of the magnetic torque over a wide range of magnetic fields. While higher order chiral spin interactions have been considered as a source of this observation, we show here that bilinear anisotropic interactions and/or $g$ anisotropy are each sufficient to explain the observed torque response, which may be distinguished on the basis of high-field measurements. These findings unify the understanding of magnetic torque experiments in a variety of Kitaev candidate materials.

We report a detailed experimental and theoretical study on the effect of hydrostatic pressure on various structural and magnetic aspects of the layered honeycomb antiferromagent $\alpha \text{−}{\mathrm{RuCl}}_3$. Through measurements of the magnetic susceptibility $\chi$ performed under almost ideal hydrostatic-pressure conditions by using helium as a pressure-transmitting medium, we find that the phase transition to zigzag-type antiferromagnetic order at $T_N$ = 7.3 K can be rapidly suppressed to about 6.1 K at a weak pressure of about 94 MPa. A further suppression of $T_N$ with increasing pressure is impeded, however, due to the occurrence of a pressure-induced structural transition at $p\ge$ 104 MPa, accompanied by a strong dimerization of Ru-Ru bonds, which gives rise to a collapse of the magnetic susceptibility. Whereas the dimerization transition is strongly first order, the magnetic transition under varying pressure and magnetic field also reveals indications for a weakly first-order transition. We assign this observation to a strong magnetoelastic coupling in this system. Measurements of $\chi$ under varying pressure in the paramagnetic regime ($T>T_N$) and before dimerization ($p<$ 100 MPa) reveal a considerable increase of $\chi$ with pressure. These experimental observations are consistent with the results of ab initio density functional theory (DFT) calculations on the pressure-dependent structure of $\alpha \text{−}{\mathrm{RuCl}}_3$ and the corresponding pressure-dependent magnetic model. We find that pressure strengthens the nearest-neighbor Heisenberg $J$ and off-diagonal anisotropic $\mathrm{\Gamma }$ coupling and simultaneously weakens the Kitaev $K$ and anisotropic ${\mathrm{\Gamma }}^{\prime }$ coupling. Comparative susceptibility measurements on a second crystal showing two consecutive magnetic transitions instead of one, indicating the influence of stacking faults, reveal that by the application of different temperature-pressure protocols the effect of these stacking faults can be temporarily overcome.