We report high magnetic field (H) neutron scattering investigations of
the superconducting phase diagram of the clean heavy fermion
superconductor CeCoIn5. By elastic neutron scattering we studied the
connection between the superconducting and magnetic order parameters
in CeCoIn5. Using small angle neutron scattering we explored the H-
dependence of the vortex lattice structure and the form factor |F|2
throughout the superconducting phase diagram. Superconductivity in
CeCoIn5 has several unconventional aspects to it: The d-wave
superconductivity is in competition with antiferromagnetic order, as
suggested by the presence of a magnetic quantum critical point located
at the upper critical field Hc2 determined by the Pauli effect. For
fields applied in the ab-plane a second superconducting phase has been
identified in CeCoIn5. By elastic neutron scattering we found that
within this phase, CeCoIn5 adopts a multicomponent ground state which
simultaneously carries cooperating magnetic and superconducting
orders. A symmetry analysis of the coupling between the magnetic order
and the superconducting gap function suggests that the superconducting
order parameter of CeCoIn5 has a non-vanishing momentum.
The strong spin effect in CeCoIn5 is also responsible for the unusual field dependence of |F|2 observed with small angle neutron scattering. By applying H along c, as well as in the ab-plane we find that |F|2 increases continuously almost all the way up to Hc2. This finding is in contrast to that normally observed in type-II superconductors, where |F|2 decreases with increasing H. It suggests a departure from the Abrikosov-Ginzburg-Landau paradigm, where the properties of the vortex state can be described by the coherence length ξ and the penetration depth λ.
 A. D. Bianchi et al., Science 319, 177 (2008).
 M. Kenzelmann et al., Science 321, 1652 (2008).