  A recent inelastic neutron scattering experiment on $\mathrm{Yb}_2
\mathrm{Ti}_2 \mathrm{O}_7$ uncovers an unusual scattering continuum in the
spin excitation spectrum despite the splayed ferromagnetic order in the ground
state. While there exist well defined spin wave excitations at high magnetic
fields, the one magnon modes and the two magnon continuum start to strongly
overlap upon decreasing the field, and eventually they become the scattering
continuum at zero field. Motivated by these observations, we investigate the
possible emergence of a magnetically ordered ground state with fractionalized
excitations in the spin model with the exchange parameters determined from two
previous experiments. Using the fermionic parton mean field theory, we show
that the magnetically ordered state with fractionalized excitations can arise
as a stable mean field ground state in the presence of sufficiently strong
quantum fluctuations. The spin excitation spectrum in such a ground state is
computed and shown to have the scattering continuum. Upon increasing the
magnetic field, the fractionalized magnetically ordered state is suppressed,
and is eventually replaced by the conventional magnetically ordered phase at
high fields, which is consistent with the experimental data. We discuss further
implications of these results to the experiments and possible improvements on
the theoretical analysis.
