  The S = 1/2 Heisenberg antiferromagnet on the two-dimensional pyramid lattice
is studied by the numerical-diagonalization method. This lattice is obtained by
the combination of the Lieb lattice and the square lattice. It is known that
when interaction on the square lattice is increased from the ferrimagnetic
limit of strong interaction on the Lieb lattice, this system shows gradual
decrease and disappearance of spontaneous magnetization in the ground state.
The present study treats the region near the case of the square-lattice
antiferromagnet accompanied by isolated spins by numerical-diagonalization
calculations of finite-size clusters with the maximum size of 39 sites. Our
numerical results suggest the existence of a new phase with small but nonzero
spontaneous magnetization between two zero-spontaneous-magnetization phases.
