Exotic magnetic phenomena in strongly correlated electron systems

Abstract

Magnetism is an ancient and long historical field with abundant phenomena. Studying magnetic order can help gain a deeper understanding of the nature and physical mechanisms underlying these phenomena. The popular studies related to this include Mott insulators, superconductivity, spin liquids, topological insulators, etc. This thesis investigates the magnetism properties on the 2D model triangle lattice and 3D model pyrochlore lattice.\\

For the pyrochlore lattice, we discussed the anti-ferromagnet compounds $R_2$\ce{Ir2O7} and anti ferromagnetic compounds \ce{Lu2V2O7}, in which the magnetism are provided by rare-earth element $R$ and vanadium V. The Heisenberg interaction, Dzyaloshinskii-Moriya (DM) interaction and pseudo-dipole (PD) interaction is considered, varying in a reasonable range and leading to the change of classical spin configuration. The compound $R_2$\ce{Ir2O7} is constructed by composite pyrochlore lattice. The conduction electron provided by iridium is coupling in Kondo-like effect form with the local momentum provided by $R$. For the magnetic subsystem, the spin ice spin configuration is broken. Under strong Kondo-like interactions, the magnetic order of the magnetic system transitions to ferromagnetic order. For the conduction subsystem, we calculated the topological number of the crossing node around the Fermi face. Varying the interaction between two subsystem, the Weyl nodes undergo a process of emergence and disappearance.\\

As for the pyrochlore compound \ce{Lu2V2O7}, the experimental result of neutron scattering and thermal hall conductivity support the Hamiltonian containing Heisenberg exchange and DM exchange. We consider the existence of PD exchange. This exchange cause the canting for the spin configuration comparing to the ferromagnetic order. The spin wave spectrum is not changed dramatically. Further, this exchange takes an obvious contribution for thermal hall conductivity under weak external field, fitting the experimental result well on 20 K.\\

The zero-temperature linear spin wave theory is also applied on triangle-based lattice \ce{KErSe2}. The XXZ exchange and anisotropic interactions are considered, where the Hamiltonian is described by 4 independent parameters. A set of parameter is determined, which is satisfied with the stripe order ground state and dispersion on high symmetry point in Brillouin zone. Further, the numerical simulation of heat capacity support the spin interaction model well. \\

On the final part, we focus on the recent experimental result of superconducting van der Waals material \ce{4Hb}-\ce{TaS2}. This is the platform achieving the $\mathbb{Z}_2$ spin liquid. The recent observation of spontaneous vortex generation in \ce{4Hb}-\ce{TaS2} as a result of vison-vortex nucleation. We propose a nucleation process between the superconducting vortex lattice and the vison crystal. We proposed that the spinion is provided by the layer \ce{1T}-\ce{TaS2}, and the Hamiltonian contains the pairing term, with symmetry. The vison is remaining while the temperature rising process, which is the kernal mechanism of magnetic memory. Further, the corresponding exam is proposed to identify the difference of $\mathbb{Z}_2$ spin liquid and chiral spin liquid.\\