  Exotic state of matter could coexist with conventional orders such that the
gauge fields and fractionalized excitations could prevail in a seemingly
ordered state. We explore the Coulombic antiferromagnet in the spin-1/2
pyrochlores with dipole-octupole doublets. This fractionalized
antiferromagnetic state carries both antiferromagnetic order and emergent
quantum electrodynamics with the gapless gauge photon and fractionalized
quasiparticles. We explain the characteristic physical properties including the
thermodynamics and the dynamics of this exotic state. This includes for example
the anomalously large $T^3$ specific heat and the broad spinon continuum in the
inelastic neutron scattering. We discuss the experimental and material's
relevance and expect this work to inspire interests in the search of exotic
physics among the ordered magnets.
