The spin-half Heisenberg antiferromagnet on the square-kagom\'e lattice: Ground state and low-lying excitations

We discuss the ground state and the low-lying excitations of the spin-half Heisenberg antiferromagnet on the two-dimensional square-kagome lattice. This magnetic system belongs to the class of highly frustrated spin systems with an infinite non-trivial degeneracy of the classical ground state as it is known also for the Heisenberg antiferromagnet on the kagome and on the star lattice. The quantum ground state of the spin-half system is a quantum paramagnet likely with a finite spin gap and with a large number of non-magnetic excitations within this gap. The magnetization versus field curve shows plateaux as well as a macroscopic magnetization jump to saturation due to independent localized magnon states.