  We study the evolution of the low-temperature field-induced magnetic defects
observed under an applied magnetic field in a series of frustrated amorphous
ferromagnets (Fe$_{1-x}$Mn$_{x}$)$_{75}$P$_{16}$B$_{3}$Al$_{3}$ (a-FeMn).
Combining small-angle neutron scattering and Monte Carlo simulations, we show
that the morphology of these defects resemble that of quasi-bidimensional spin
vortices. They are observed in the reentrant spin-glass (RSG) phase, up to the
critical concentration $x_{\rm C} \approx 0.36$ which separates the RSG and
"true" spin glass (SG) within the low temperature part of the magnetic phase
diagram of a-FeMn. These vortices systematically decrease in size with
increasing magnetic field or decreasing the average exchange interaction, and
they finally disappear in the SG sample ($x = 0.41$), being replaced by
field-induced correlations over finite length scales. We argue that the study
of these nanoscopic defects could be used to probe the nature of the critical
line between the RSG and SG phases.
