  The complexity embedded in condensed matter fertilizes the discovery of new
states of matter, enriched by ingredients like frustration. Illustrating
examples in magnetic systems are Kitaev spin liquids, skyrmions phases, or spin
ices. These unconventional ground states support exotic excitations, for
example the magnetic charges in spin ices, also called monopoles. Beyond their
discovery, an important challenge is to be able to control and manipulate them.
Here, we propose a new mechanism to inject monopoles in a spin ice through a
staggered magnetic field. We show theoretically, and demonstrate experimentally
in the Ho$_2$Ir$_2$O$_7$ pyrochlore iridate, that it results in the
stabilization of a monopole crystal, which exhibits magnetic fragmentation. In
this new state of matter, the magnetic moment fragments into an ordered part
and a persistently fluctuating one. Compared to conventional spin ices, the
different nature of the excitations in this fragmented state opens the way to
novel tunable field-induced and dynamical behaviors.
