Since the first successful fabrication in 2004[1],graphene has received tremendous attention due to its extremely simple atomic structure and alluring physical properties.For example,its mass-less low energy excitations have a linear dispersion and thus its transport property is governed by Dirac equation instead of Schrödinger equation.These special electronic structures suppress the intra-valley and inter-valley backscatterings,leading to the half-integer and fractional quantum Hall effect[2]under magnetic field and the relativistic quantum tunneling described by the Klein paradox[3].

The noncollinear spin textures provide promising avenues to stabilize exotic magnetic phases and excitations. They have attracted vast attention in the past decades due to their nontrivial band topology. Distinct from the conventional route of involving the Dzyaloshinskii-Moriya interaction in a honeycomb magnet, the interplay of bond -dependent Kitaev and I' interactions, originating from the spin -orbit coupling and octahedra crystal field in real materials, has demonstrated to be another source to generate noncollinear spin textures with multiple spins in a magnetic unit cell. Notably, earlier works have revealed a triple-meron crystal (TmX) consisting of 18 spins in the frustrated Kitaev- I' model. Aligning with previous efforts, here we attempt to identify that the TmX hosts several peculiar features with the help of the linear spin -wave theory. To begin with, the symmetric anisotropic exchanges are beneficial for the existence of nonreciprocal magnons, which are stabilized by an external magnetic field. Further, within the regime of TmX, successive topological phase transitions occur, accompanied by the changes of Chern number in value and thermal Hall conductivity in sign. In addition, the topological nature of magnons is also verified by the onset of chiral edge modes in a nanoribbon geometry. Our findings pave the way to study topological phenomena of noncollinear spin textures in potential Kitaev materials.

Skyrmions hold great promise in future spintronics applications since they are robust against local deformations. The meron, due to its topological equivalence to a half skyrmion, has been widely found to appear in pairs. Motivated by recent progresses in high-spin Kitaev magnets, here we investigate numerically a classical Kitaev-Γ model with a single-ion anisotropy. An exotic spin texture consisting of three merons is discovered. Such a state features a peculiar property with an odd number of merons in one magnetic unit cell. Therefore, these merons cannot be dissociated from skyrmions as reported in the literature and their origin is briefly discussed. Moreover, we find that these three merons contribute a finite topological number and thus it can induce the topological Hall effect (THE). Experimentally this spin texture can be observed by the Lorentz transmission electron microscopy and the THE can be used to identify the finite topological number. Our work demonstrates that high-spin Kitaev magnets can host robust unconventional spin textures and thus they offer a versatile platform for exploring exotic spin textures as well as their applications in spintronics.

Ken Chen, 2 Qiang Luo, 4 Zongsheng Zhou, 2 Saisai He, 2 Bin Xi, ∗ Chenglong Jia, 2 Hong-Gang Luo, 2, 6 and Jize Zhao 2, † School of Physical Science and Technology & Key Laboratory for Magnetism and Magnetic Materials of the MoE, Lanzhou University, Lanzhou 730000, China Lanzhou Center for Theoretical Physics and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, China. College of Science, Nanjing University of Aeronautics and Astronautis, Nanjing, 211106, China Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada College of Physics Science and Technology, Yangzhou University, Yangzhou 225002, China Beijing Computational Science Research Center, Beijing 100084, China (Dated: February 8, 2022)

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 CrSiTe3. 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 et al., Phys. Rev. Lett. 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 degrees 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 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 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.