Spin and charge ordering in three-leg ladders in oxyborates

We study the spin ordering within the three-leg ladders present in the oxyborate Fe3O2BO3 consisting of localized classical spins interacting with conduction electrons (one electron per rung). We also consider the competition with antiferromagnetic superexchange interactions to determine the magnetic phase diagram. Besides a ferromagnetic phase we find (i) a phase with ferromagnetic rungs ordered antiferromagnetically and (ii) a zigzag canted spin ordering along the legs. We also determine the induced charge ordering within the different phases and the interplay with lattice instability. Our model is discussed in connection with the lattice dimerization transition observed in this system, emphasizing the role of the magnetic structure.