  We report on the depth dependence and technological limits of the phase
transition of the iron rhodium alloy as function of temperature, external
magnetic and electric fields in the FeRh/BaTiO3 multiferroic, determined by
grazing-incidence nuclear resonant scattering measurements. The change of
temperature induces a continuous and homogenous antiferromagnetic /
ferromagnetic phase transition through the entire FeRh layer, except in the
near substrate region. External magnetic field does not affect this mechanism,
but the application of electric field changes it fundamentally (via
piezoelectric strain): the phase transition of the alloy suddenly propagates
from the substrate up to a height, defined by the combination of temperature
and external magnetic field, as soon as the applied electric field reaches ~ 20
kV/m.
