Limited Ferromagnetic Interactions in Monolayers of MPS3 (M = Mn and Ni).

We present a systematic study of the electronic and magnetic properties of two-dimensional ordered alloys, consisting of two representative hosts (MnPS3 and NiPS3) of transition metal phosphorus trichalcogenides doped with 3d elements. For both hosts, our DFT + U calculations are able to qualitatively reproduce the ratios and signs of all experimentally observed magnetic couplings. The relative strength of all antiferromagnetic exchange couplings, both in MnPS3 and in NiPS3, can successfully be explained using an effective direct exchange model: it reveals that the third-neighbor exchange dominates in NiPS3 due to the filling of the t2g subshell, whereas for MnPS3, the first-neighbor exchange prevails, owing to the presence of the t2g magnetism. On the other hand, the nearest neighbor ferromagnetic coupling in NiPS3 can only be explained using a more complex superexchange model and is (also) largely triggered by the absence of the t2g magnetism. For the doped systems, the DFT + U calculations revealed that magnetic impurities do not affect the magnetic ordering observed in the pure phases, and thus, in general in these systems, ferromagnetism may not be easily induced by such a kind of elemental doping. However, unlike for the hosts, the first and second (dopant-host) exchange couplings are of similar order of magnitude. This leads to frustration in the case of antiferromagnetic coupling and may be one of the reasons of the observed lower magnetic ordering temperature of the doped systems.

Ordered states in the Kitaev-Heisenberg model: From 1D chains to 2D honeycomb.

We study the ground state of the 1D Kitaev-Heisenberg (KH) model using the density-matrix renormalization group and Lanczos exact diagonalization methods. We obtain a rich ground-state phase diagram as a function of the ratio between Heisenberg (J = cosϕ) and Kitaev (K = sinϕ) interactions. Depending on the ratio, the system exhibits four long-range ordered states: ferromagnetic-z, ferromagnetic-xy, staggered-xy, Néel-z, and two liquid states: Tomonaga-Luttinger liquid and spiral-xy. The two Kitaev points [Formula: see text] and [Formula: see text] are singular. The ϕ-dependent phase diagram is similar to that for the 2D honeycomb-lattice KH model. Remarkably, all the ordered states of the honeycomb-lattice KH model can be interpreted in terms of the coupled KH chains. We also discuss the magnetic structure of the K-intercalated RuCl3, a potential Kitaev material, in the framework of the 1D KH model. Furthermore, we demonstrate that the low-lying excitations of the 1D KH Hamiltonian can be explained within the combination of the known six-vertex model and spin-wave theory.