Strong spin-orbit coupling (SOC) can lead to many novel physical phenomena, especially the multipolar moment (MPM) order in 4d and 5d transition metal compounds. The quadrupole and octuple moment order parameters will lead to physical phenomena, such as magnetic dielectric coupling effects, quantum magnetic phase transitions, and nonlinear Hall effects, that cannot be explained by traditional dipole moments. Our group are interested in uncovering the MPM order in materials including the cubic lattices with pyrochlore structures (such as Eu2Ir2O7, Cd2Re2O7) and honeycomb hexagonal lattices (such as RuCl3), Na2IrO3 and Li2IrO3), and their detective signals in the experiments.