  Hexagonal Sr0.6Ba0.4MnO3 (SBMO) follows P63/mmc symmetry where MnO6 octahedra
are both face-shared (Mn2O9 bi-octahedra) and corner-shared via oxygen anion.
It undergoes ferroelectric (FE) and antiferromagnetic (AFM) orderings close to
the room temperature. Magnetic properties appear to be governed by intricate
exchange interactions among Mn4+ ions within and in adjacent Mn2O9
bi-octahedra, contingent upon the local structural changes. Calculations based
on our model spin-Hamiltonian reveal that the dominant linear AFM fluctuations
between the Mn4+ ions of two oxygen-linked bi-octahedra result in short range
correlations, manifest as a smooth drop in magnetization below 325 K.
Competition between spin-exchange and local-strain is reckoned as responsible
for the atypical magneto-electricity, obtained near the room temperature.
