  By analyzing how the Borel regulator classes vanish on various groups related
to $\mathrm{GL}(n,\mathrm{Z})$, we define three series of secondary
characteristic classes for subgroups of automorphism groups of free groups.
  The first case is the $\mathrm{IA}$-automorphism groups and we show that our
classes coincide with higher $\mathrm{FR}$ torsions due to Igusa. The second
case is the mapping class groups and our classes also turn out to be his higher
torsions which are non-zero multiples of the Mumford-Morita-Miller classes of
even indices. Our construction gives new group cocycles for these still
mysterious classes. The third case is the outer automorphism groups of free
groups of specific ranks. Here we give a conjectural geometric meaning to a
series of unstable homology classes called the Morita classes. We expect that
certain unstable secondary classes would detect them.
