The anisotropic g factors g_{∥} and g_{⊥} of La_2Ni_{0.5}Li_{0.5}O_4 are theoretically investigated using the perturbation formulae of the g factors for a low spin (S=1/2) 3d^7 ion in tetragonally elongated octahedra. The studied Ni^{3+} (3d^7) center arises from the original Ni^{2+} capturing one hole by Li^{+} doping. The positive anisotropy Δ g (= g_{⊥}-g_{∥}) can be ascribed to the lowest ^2 A_{1g} state due to the obvious (about 0.14 Å) tetragonal elongation of the oxygen octahedron around the Ni^{3+} site via the Jahn-Teller effect, and the effective magnetic moment is also interpreted in a uniform way. The calculated results show good agreement with the experimental data, and the imperfection of the previous studies based on various adjusted tetragonal energy splittings without correlating to the local structure of the magnetic center is thus overcome in this work.
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