We succeeded in growing high-quality single crystals of Rh2Ga9 and Ir2Ga9 with the non-centrosymmetric (distorted Co2Al9-type) monoclinic structure by the Ga-self flux method, and carried out the de Haas-van Alphen (dHvA) experiments. The Fermi surface is found to be split into two different Fermi surfaces, reflecting the non-centrosymmetric crystal structure. A magnitude of the antisymmetric spin-orbit interaction or a splitting energy between the two Fermi surfaces are determined to be 56K for dHvA branch α and 45K for branch β in Rh2Ga9, where these dHvA branches correspond to main Fermi surfaces. The present splitting values are compared with 290 and 130 K in Ir2Ga9, respectively. The splitting energy is found to be larger in the Ir-5d conduction electrons than in the Rh-4d conduction electrons. The split dHvA branches in Rh2Ga9 and Ir2Ga9 are also compared with the single dHvA branch in Co2Al9, Rh2Al9, and Ir2Al9 with inversion symmetry in the crystal structure.
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