  Ferrimagnets containing several partially compensated magnetic sublattices
are considered the most promising materials for all-optical data storage and
for ultrafast communications based on spin waves. There are two magnetic phases
of the ferrimagnets: collinear and non-collinear ones. Up to now spin dynamics
in ferrimagnets has been studied mostly in the collinear state without paying
much attention to the kind of the magnetic phase. Here we investigate laser
induced ultrafast spin dynamics in a rare-earth iron garnet film in the
noncollinear phase as well. We identify a crucial influence of the magnetic
phase on the excited spin modes which allowed us to discover several prominent
effects previously overlooked. In particular, the non-collinearity makes the
quasi-antiferromagnetic mode sensitive to the external magnetic field and
brings its frequency close to the frequency of the quasiferromagnetic mode. The
latter maximizes near the magnetization compensation point and vanishes towards
the collinear phase. Spectacularly, at the phase transition the
quasiferromagnetic mode becomes soft and its amplitude significantly increases
reaching 7{\deg}. This opens new opportunities for the ultrafast control of
spins in ferrimagnets for nonthermal data storage and data processing.
