  We investigated the electronic structure of layered Mn oxide Bi3Mn4O12(NO3)
with a Mn honeycomb lattice by x-ray absorption spectroscopy. The valence of Mn
was determined to be 4+ with a small charge-transfer energy. We estimated the
values of superexchange interactions up to the fourth nearest neighbors (J1,
J2, J3, and J4) by unrestricted Hartree-Fock calculations and a perturbation
method. We found that the absolute values of J1 through J4 are similar with
positive (antiferromagnetic) J1 and J4, and negative (ferromagnetic) J2 and J3,
due to Mn-O-O-Mn pathways activated by the smallness of charge-transfer energy.
The negative J3 provides magnetic frustration in the honeycomb lattice to
prevent long-range ordering.
