  In this note we are concerned with the distribution of Einstein and
non-Einstein nilradicals among all nilpotent Lie groups. A nilpotent Lie group
is called an Einstein, resp. non-Einstein, nilradical if it is a nilpotent Lie
group which does, resp. does not, admit a left-invariant Ricci soliton metric.
  Using techniques from Geometric Invariant Theory, we construct many new
(continuous) families of both kinds of nilpotent Lie groups. Moreover, it is
shown by example that there exist families of non-Einstein nilradicals of
arbitrarily large dimension; the dimension of these families of Lie groups
depends only on the dimension of the underlying Lie groups. In this work our
attention is focused on the class of two-step nilpotent Lie groups.
