We develop a theory of the coexistence of superconductivity (SC) and
antiferromagnetism (AFM) in CeCoIn5. We show that in Pauli-limited nodal
superconductors the nesting of the quasi-particle pockets induced by Zeeman
pair-breaking leads to incommensurate AFM with the moment normal to the field.
We compute the phase diagram and find a first order transition to the normal
state at low temperatures, absence of normal state AFM, and coexistence of SC
and AFM at high fields, in agreement with experiments. We also predict the
existence of a new double-Q magnetic phase
