  A left invariant metric on a nilpotent Lie group is called minimal, if it
minimizes the norm of the Ricci tensor among all left invariant metrics with
the same scalar curvature. Such metrics are unique up to isometry and scaling
and the groups admitting a minimal metric are precisely the nilradicals of
(standard) Einstein solvmanifolds. If $N$ is endowed with an invariant
symplectic, complex or hypercomplex structure, then minimal compatible metrics
are also unique up to isometry and scaling. The aim of this paper is to give
more evidence of the existence of minimal metrics, by presenting several
explicit examples. This also provides many continuous families of symplectic,
complex and hypercomplex nilpotent Lie groups. A list of all known examples of
Einstein solvmanifolds is also given.
