  An interplay of spin-orbit coupling and intrinsic magnetism is known to give
rise to the quantum anomalous Hall and topological magnetoelectric effects
under certain conditions. Their realization could open access to low power
consumption electronics as well as many fundamental phenomena like image
magnetic monopoles, Majorana fermions and others. Unfortunately, being realized
very recently, these effects are only accessible at extremely low temperatures
and the lack of appropriate materials that would enable the temperature
increase is a most severe challenge. Here, we propose a novel material platform
with unique combination of properties making it perfectly suitable for the
realization of both effects at elevated temperatures. The key element of the
computational material design is an extension of a topological insulator (TI)
surface by a thin film of ferromagnetic insulator, which is both structurally
and compositionally compatible with the TI. Following this proposal we suggest
a variety of specific systems and discuss their numerous advantages, in
particular wide band gaps with the Fermi level located in the gap.
