Abnormal magnetic moment with orbital degree of freedom

We investigate the effect from the competition between spin-orbit coupling (SOC) and exchange interaction on the magnetic moment of 3d transition metal system with orbital degree of freedom. The ground state of d ⁷ configuration in almost perfect O_h symmetry of Ba₃CoSb₂O₉ possessing orbital degree of freedom is analyzed through X-ray absorption spectroscopy (XAS) on Co L_2,3 edges. Abnormally reduced magnetic moment is derived by full multiplet cluster model calculation based on the spectrum. The XAS shows that the microscopic states of the Ba₃CoSb₂O₉ and CoO are similar, but the calculation shows that the competing spin-orbit coupling and exchange interaction T_N ~ 3.8 K and 300 K respectively, result the ground state ordered moment ~ 1.93 µ_B/Co²⁺ and conventional MM ~ 3.25 µ_B/Co²⁺ as reported. In this context, the general behavior of the MM of d ⁷ system beginning from the MM of Ba₃CoSb₂O₉ with increasing T_N will be presented, and furthermore the MM variation of d ² system, especially of V₂O₃ case will be discussed.