  The ground state and zero-temperature magnetization process of the spin-1/2
Ising-Heisenberg model on two-dimensional triangles-in-triangles lattices is
exactly calculated using eigenstates of the smallest commuting spin clusters.
Our ground-state analysis of the investigated classical--quantum spin model
reveals three unconventional dimerized or trimerized quantum ground states
besides two classical ground states. It is demonstrated that the spin
frustration is responsible for a variety of magnetization scenarios with up to
three or four intermediate magnetization plateaus of either quantum or
classical nature. The exact analytical results for the Ising-Heisenberg model
are confronted with the corresponding results for the purely quantum Heisenberg
model, which were obtained by numerical exact diagonalizations based on the
Lanczos algorithm for finite-size spin clusters of 24 and 21 sites,
respectively. It is shown that the zero-temperature magnetization process of
both models is quite reminiscent and hence, one may obtain some insight into
the ground states of the quantum Heisenberg model from the rigorous results for
the Ising-Heisenberg model even though exact ground states for the
Ising-Heisenberg model do not represent true ground states for the pure quantum
Heisenberg model.
