  In this work we investigate the magnetic field dependence of Ag octahedra
rotation (tilt) and B2g symmetric stretching modes frequency at different
temperatures. Our field-dependent Raman investigation at 10K is interpreted by
an ionic displacive nature of the magnetically induced ferroelectric phase
transition. The frequency change of the Ag tilt is in agreement with the
stabilization of the Mn-Gd spin arrangement, yielding the necessary conditions
for the onset of ferroelectricity on the basis of the inverse
Dzyaloshinskii-Moriya interaction. The role of the Jahn-Teller cooperative
interaction is also evidenced by the change of the B2g mode frequency at the
ferroelectric phase transition. This frequency change allows estimating the
shift of the oxygen position at the ferroelectric phase transition and the
corresponding spontaneous polarization of 480 {\mu}C/m2, which agrees with
earlier reported values in single crystals. Our study also confirms the
existence of a large magnetic hysteresis at the lowest temperatures, which is a
manifestation of magnetrostiction.
