Intertwined orders in heavy-fermion superconductor CeCoIn5

We use thermal conductivity to study a unique state in the high field corner of the superconducting phase of CeCoIn₅. The spin-density-wave (SDW) magnetic order in this high field low temperature (HFLT) phase requires superconductivity for its very existence, and both magnetism and superconductivity disappear together at superconducting critical field Hc2. We measured thermal conductivity of CeCoIn₅ in a rotating magnetic field to study the nature of the HFLT phase. Our measurements reveal the presence of an additional order inside the HFLT phase that is intimately intertwined with the superconducting d-wave and the SDW orders, which we identify as a superconducting p-wave pair-density-wave (PDW). CeCoIn₅ displays a hierarchy of interactions within the HFLT phase, where spin-orbit coupling orients the SDW, which then determines orientation of the secondary PDW component.