  Fractionalised excitations that emerge from a many body system have revealed
rich physics and concepts, from composite fermions in two-dimensional electron
systems, revealed through the fractional quantum Hall effect, to spinons in
antiferromagnetic chains and, more recently, fractionalisation of Dirac
electrons in graphene and magnetic monopoles in spin ice. Even more surprising
is the fragmentation of the degrees of freedom themselves, leading to
coexisting and a priori independent ground states. This puzzling phenomenon was
recently put forward in the context of spin ice, in which the magnetic moment
field can fragment, resulting in a dual ground state consisting of a
fluctuating spin liquid, a so-called Coulomb phase, on top of a magnetic
monopole crystal. Here we show, by means of neutron scattering measurements,
that such fragmentation occurs in the spin ice candidate Nd$_2$Zr$_2$O$_7$. We
observe the spectacular coexistence of an antiferromagnetic order induced by
the monopole crystallisation and a fluctuating state with ferromagnetic
correlations. Experimentally, this fragmentation manifests itself via the
superposition of magnetic Bragg peaks, characteristic of the ordered phase, and
a pinch point pattern, characteristic of the Coulomb phase. These results
highlight the relevance of the fragmentation concept to describe the physics of
systems that are simultaneously ordered and fluctuating.
