Quenching of atomiclike properties upon solid-state formation: Quantitative comparison between Co and Ni in ferrites studied by x-ray resonant Raman scattering at the $L_3$ edge

We have measured the spin and orbital coupled multipole moments for the ground state of the divalent Co and Ni ions in the ferrites using the technique of integrated x-ray resonant Raman scattering (IRRS). This method exploits the sum rules characteristic of a second-order process which gives access to moments higher than those obtained from magnetic circular and linear dichroism in x-ray absorption. Moreover, IRRS is complementary to the latter techniques concerning the lower-order moments. The experimentally deduced values for the quadrupole and octupole moments are small in Ni ferrite but large in Co ferrite. Except for the spin moment, this difference between both ions is in contrast with the ground-state values given by the Hund’s rule that gives the same absolute value for both isolated ions. The difference is due to the quenching of the spin-orbit interaction (its first-order contribution vanishes) in the octahedral crystal field for the Ni $d^8$ ion, which does not occur for the Co $d^7$ ion. We compare the experimental results with a cluster calculation that includes crystal field and hybridization effects, which gives the values of the orbital moment, the quadrupole and octupole moments for both ions. The present results show the extent to which the atomiclike properties are retained in the higher-order multipole moments. This can be used to assess the modification of the atomic behavior due to solid-state effects.