  The temperature dependence of the relaxation dynamics in the bilayer thin
film heterostructure composed of multiferroic BiFeO$_{3}$ (BFO) and
superconducting YBa$_{2}$Cu$_{3}$O$_{7}$ (YBCO) grown on a (001) SrTiO$_{3}$
substrate is studied by a time-resolved pump-probe technique, and compared with
that of pure YBCO thin film grown under the same growth conditions. The
superconductivity of YBCO is found to be retained in the heterostructure. We
observe a speeding up of the YBCO recombination dynamics in the superconducting
state of the heterostructure, and attribute it to the presence of weak
ferromagnetism at the BFO/YBCO interface as observed in magnetization data. An
extension of the Rothwarf-Taylor model is used to fit the ultrafast dynamics of
BFO/YBCO, that models an increased quasiparticle occupation of the
ferromagnetic interfacial layer in the superconducting state of YBCO.
