Nuclear Magnetic Resonance of Paramagnetic Co₃O₄. II. Theory of the NMR Shift

Abstract

Theoretical study is made of the nuclear magnetic resonance shift of a Co³⁺ ion at the B site in Co₃O₄. The temperature-independent part of the shift is attributed to the chemical shift of the Co³⁺ ion. From its analysis it is concluded that the Co³⁺ e_g orbital is radially expanded relative to the d orbital of the free ion and that the e_g electron spends about 30% of its time on the surrounding oxygens. The temperature-dependent shift is explained by the transferred hyperfine interaction between the Co²⁺ magnetic moment and the Co³⁺ nuclear spin which arises from the 0.2% mixing of the Co³⁺ 4s orbital into the oxygen 2s and p_σ orbitals. It is shown that the shift due to the mixing of the Co³⁺ e_g orbital is opposite to the observed one and ten times smaller than it. Finally superexchange mechanisms in Co₃O₄ are examined. It is concluded that 2% fractional spin density in the Co³⁺ e_g orbital mainly contributes to the superexchange.