  Low-temperature magnetization curves and thermodynamics of a frustrated
spin-1/2 Heisenberg triangular bilayer with the antiferromagnetic intradimer
interaction and either ferromagnetic or antiferromagnetic interdimer
interaction are investigated in a highly frustrated parameter region, where
localized many-magnon eigenstates provide the most dominant contribution to
magnetothermodynamics. Low-energy states of the highly frustrated spin-1/2
Heisenberg triangular bilayer can be accordingly found from a mapping
correspondence with an effective triangular-lattice spin-1/2 Ising model in a
field. A description based on the effective Ising model implies that the
frustrated Heisenberg triangular bilayer with the ferromagnetic interdimer
coupling displays in a zero-temperature magnetization curve discontinuous
magnetization jump, which is reduced upon increasing of temperature until a
continuous field-driven phase transition from the Ising universality class is
reached at a certain critical temperature. The frustrated Heisenberg triangular
bilayer with the antiferromagnetic interdimer coupling contrarily exhibits
multistep magnetization curve with intermediate plateaus at one-third and
two-thirds of the saturation magnetization, whereas discontinuous magnetization
jumps observable at zero temperature change to continuous field-driven phase
transitions from the universality class of three-state Potts model at
sufficiently low temperatures. Exact results and Monte Carlo simulations of the
effective Ising model are confronted with full exact diagonalization data for
the Heisenberg triangular bilayer in order to corroborate these findings.
