Unusual Magnetic Behaviors involving Large Spin-Orbit Coupling

Large spin-orbit coupling makes the magnetic eigenstate of the total angular momentum state with an admixed spin state and induces unusual magnetic behaviors. In cooperation with the crystal field, it could introduce the Kramers doublet in the magnetic ion site. Then the magnetism is described with the so-called spin-orbit coupled isospin 1/2, and the system often displays novel quantum magnetism behaviors. On the other hand, the admixed spin states possibly introduce anisotropic spin-spin interactions involving the inter-site hopping. In this talk, I will discuss recent results of spin-orbit coupled isospin quantum magnetism in a geometrical frustrated pyrochlore Ba3Yb2Zn5O11 and a layered Kitaev lattice α-RuCl3. If time is available, I will also briefly discuss giant magnetic anisotropy observed in layered Cr compounds, which has been puzzled for the Cr3+ (t2g3) magnetic ion with L = 0.