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The interplay among anisotropic magnetic terms, such as the bond-dependent Kitaev interactions and single-ion anisotropy, plays a key role in stabilizing the finite-temperature ferromagnetism in the two-dimensional compound $rm{CrSiTe_3}$. While the Heisenberg interaction is predominant in this material, a recent work shows that it is rather sensitive to the compressive strain, leading to a variety of phases, possibly including a sought-after Kitaev quantum spin liquid [C. Xu, textit{et. al.}, Phys. Rev. Lett. textbf{124}, 087205 (2020)]. To further understand these states, we establish the quantum phase diagram of a related bond-directional spin-$3/2$ model by the density-matrix renormalization group method. As the Heisenberg coupling varies from ferromagnetic to antiferromagnetic, three magnetically ordered phases, i.e., a ferromagnetic phase, a $120^circ$ phase and an antiferromagnetic phase, appear consecutively. All the phases are separated by first-order phase transitions, as revealed by the kinks in the ground-state energy and the jumps in the magnetic order parameters. However, no positive evidence of the quantum spin liquid state is found and possible reasons are discussed briefly.
The competition between spin-orbit coupling, bandwidth ($W$) and electron-electron interaction ($U$) makes iridates highly susceptible to small external perturbations, which can trigger the onset of novel types of electronic and magnetic states. Here
The global phase diagram of a doped Kitaev-Heisenberg model is studied using an SU(2) slave-boson mean-field method. Near the Kitaev limit, p-wave superconducting states which break the time-reversal symmetry are stabilized as reported by You {it et
High-resolution thermal expansion and magnetostriction measurements were performed on single crystals of $alpha$-RuCl$_3$ in magnetic fields applied parallel to the Ru-Ru bonds. The length changes were measured in the direction perpendicular to the h
We study the half-filled Hubbard model on the triangular lattice with spin-dependent Kitaev-like hopping. Using the variational cluster approach, we identify five phases: a metallic phase, a non-coplanar chiral magnetic order, a $120^circ$ magnetic o
A central question on Kitaev materials is the effects of additional couplings on the Kitaev model which is proposed to be a candidate for realizing topological quantum computations. However, two spatial dimension typically suffers the difficulty of l