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The effects of a spin-orbit interaction on transition-metal ions of (4d)^3-and (5d)^3 -based oxides in which three electrons occupy t_{2g} orbitals arestudied. The amplitude of the magnetic moment of d electrons on the 5d and 4dorbitals is estimated by numerical diagonalization. It is found that themagnetic moment is reduced by the spin-orbit interaction. It is suggested that(4d)^3- and (5d)^3 -based oxides are located in the middle of the L-S and J-Jcoupling schemes.

Effect of Spin-Orbit Interaction on (4d)^3- and (5d)^3 -Based Transition-Metal Oxides