  There are two interpretations offered for the different structural and
magnetic properties of the mixed valence homo-metallic ludwigites, Co3O2BO3 and
Fe3O2BO3. One of them associates the physical behavior to charge ordering
processes among the cations, as is well known in simpler oxides. The other
attributes the effects to local pairwise magnetic interactions. Recently first
principles calculations in the iron ludwigite have shown that the structural
cation dimerization is due to the formation of strong magnetic dyads supporting
the second model. Here we confirm the dominance of magnetic interactions to
explain the absence of dimerization in the cobalt compound. Density functional
non-collinear spin calculations are carried out on Co3O2BO3 to determine its
low temperature magnetic order. Low spin is found on tri-valent cobalt sites,
thus preventing the formation of the ferromagnetic dyad, the mechanism which
favors dimerization in Fe3O2BO3. We conclude that the difference between high
spin Fe3+ and low spin Co3+ pairwise interactions is responsible for the
observed differences between the two compounds. The pairwise magnetic
interactions also explain the difference between the existence of low
temperature bulk AF state in the Fe ludwigite and its absence in the Co
material.
