  Hexagonal perovskite 15R-BaMnO2.99 with a ratio of cubic to hexagonal layers
of 1/5 in the unit cell is an antiferromagnetic insulator that orders at a
N\'eel temperature TN = 220 K. Here we report structural, magnetic, dielectric
and thermal properties of single crystal BaMnO2.99 and its derivatives
BaMn0.97Li0.03O3 and Ba0.97K0.03MnO3. The central findings of this work are:
(1) these materials possess a usually large, high-temperature magnetoelectric
effect that amplifies the dielectric constant by more than an order of
magnitude near their respective N\'eel temperature; (2) Li and K doping can
readily vary the ratio of cubic to hexagonal layers and cause drastic changes
in dielectric and magnetic properties; in particular, a mere 3% Li substitution
for Mn significantly weakens the magnetic anisotropy and relaxes the lattice;
consequently, the dielectric constant for both the a- and c-axis sharply rises
to 2500 near the N\'eel temperature. This lattice softening is also accompanied
by weak polarization. These findings provide a new paradigm for developing
novel, high-temperature magnetoelectric materials that may eventually
contribute to technology.
