  We combine two aspects of magnetic frustration, multiferroicity and emergent
quasi-particles in spin liquids, by studying magneto-electric monopoles. Spin
ice offers to couple these emergent topological defects to external fields, and
to each other, in unusual ways, making possible to lift the degeneracy
underpinning the spin liquid and to potentially stabilize novel forms of charge
crystals, opening the path to a "magnetic crystallography". In developing the
general phase diagram including nearest-neighbour coupling, Zeeman energy,
electric and magnetic dipolar interactions, we uncover the emergence of a
bi-layered crystal of singly-charged monopoles, whose stability, remarkably, is
strengthened by an external [110] magnetic field. Our theory is able to account
for the ordering process of Tb2Ti2O7 in large field for reasonably small
electric energy scales.
