Ferrimagnetic ordering and spin entropy of field-dependent intermediate spins in Na0.82CoO2

The peculiar field-dependent magnetism of Na0.82CoO2 has been investigated through an analysis of its DC and AC spin susceptibilities. To account for the easily activated narrow b2g-a1g gap of the crystal field for Co in the cobalt oxide layer, the spin-state transition of Co3+ (3d6) between the low spin (LS) state b2g^2-a1g^0 of S=0 and the intermediate spin (IS) state b2g^1-a1g^1 of S=1 is thus seen as thermally activated and exhibits a Boltzmann distribution. The IS state of Co3+ within each sqrt(13a) hexagonal superlattice formed by the S=1/2 state of the Co4+ ions appears randomly within each supercell and shows significant temperature and field dependence. The magnetic field is found to assist in pinning down the thermally activated state of Co3+ and swings the Boltzmann distribution weight toward a higher fraction of the IS state. The field dependence of the in-plane magnetic moment from the added number of S=1 spins is used to explain the origin of A-type antiferromagnetic (AF) ordering, particularly that the ferromagnetic (FM)-like behavior below TN at low field is actually a ferrimagnetic IS spin ordering of Co3+.