Possible Fulde–Ferrell–Larkin–Ovchinnikov superconducting state in CeCoIn5

We report specific heat measurements of the heavy fermion superconductor CeCoIn5 in the vicinity of the superconducting critical field Hc2, with magnetic fields in the [110], [100], and [001] directions, and at temperatures down to 50 mK. The superconducting phase transition changes from second to first order for fields above 10 T for H k� 110� and H k� 100� . In the same range of magnetic fields, we observe a second specific heat anomaly within the superconducting state. We interpret this anomaly as a signature of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) inhomogeneous superconducting state. We obtain similar results for H k� 001� , with the FFLO state occupying a smaller part of the phase diagram. In the early 1960s, following the success of the BCS theory of superconductivity, Fulde and Ferrell [1] and Larkin and Ovchinnikov [2] developed theories of inhomogeneous superconducting states. At the core of FFLO theory lie competing interactions of a very basic nature. One is the interaction of the spin of the electron with magnetic fields and the other is the energy of the superconducting coupling of electrons into Cooper pairs, or the condensation energy. In the normal state, the electrons are free to lower their total energy by preferentially aligning their spins along the magnetic field, leading to a temperature-independent Pauli susceptibility. For spinsinglet superconductors (both s wave and d wave), the condensate contains an equal number of spin-up and spindown electrons. Therefore, Pauli paramagnetism will always favor the normal state over the spin-singlet superconducting state, and will reduce the superconducting critical field Hc2 which suppresses superconductivity. This effect is called Pauli limiting, with the characteristic Pauli field HP determining the upper bound of Hc2 [3]. Another effect of magnetic fields that leads to the suppression of superconductivity is orbital limiting, or suppression of superconductivity when the kinetic energy of the supercurrent around the normal cores of the superconducting vortices in type II superconductors becomes greater than the superconducting condensation energy. The orbital limiting field H 02 defines Hc2 in the absence of Pauli limiting. The relative strength of Pauli and orbital limiting, the so-called Maki parameter � � H 02 =HP, determines the behavior of the system in high magnetic fields. The prediction of FFLO theory is that for a clean type II superconductor with sufficiently large � (for �> 1:8 in the calculations of Ref. [4]), a new inhomogeneous superconducting FFLO state will appear between the normal and the mixed, or vortex, state below the critical temperature T0 [4]. Within the particular realization of Larkin and Ovchinnikov [2], this state is characterized by the appearance of a periodic array of planes of normal electrons that can take advantage of the Pauli