Figure 8

(a) The dominant exchange interaction paths \(J_{1}\), \(J_{2}\) and \(J_{3}\) for the Mn spins in the layered compound BMTO. \(J_{1}\) represents the in-plane nearest neighbor (5.81 Å) exchange interaction, while \(J_{2}\) and \(J_{3}\) correspond to out-of-plane nearest and next-nearest interactions with Mn-Mn separations at 5.81 Å and 8.22 Å, respectively. The \(J_{1}\) forms a triangular lattice in the plane. To estimate the strengths of the \(J_{i}\)’s, several total energy calculations were carried out on four spin arrangements, defined as FM, AFM1, AFM2, and AFM3 (b–e).