Possible Fulde-Ferrell-Larkin-Ovchinnikov Superconducting State inCeCoIn5

Abstract

We report specific heat measurements of the heavy fermion superconductor CeCoIn5 in the vicinity of the superconducting critical field Hc2, with magnetic field 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 field above 10 T for H [110] and H [100]. In the same range of magnetic field 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) One is the interaction of the spin of the electron with magnetic field 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-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 H c2 which suppresses superconductivity. This effect is called Pauli limiting, with the characteristic Pauli field H P determining the upper bound of H c2 [3]. Another effect of magnetic field 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 A number of conventional superconductors were proposed as candidates for observation of the FFLO state, due to their high orbital critical field H c20 and, therefore, relatively strong Pauli limiting effect, in the early and mid-sixties. Experimental searches, however, yielded null results [5,6,7,8]. The failure to observe the FFLO state was attributed to high spin-orbit scattering rate in these compounds [9]. In the last decade the FFLO state was suggested to exist in heavy fermion UPd 2 Al 3 (Ref. [10] and CeRu 2 (Ref.[11]), based on thermal expansion and magnetization data, respectively. Subsequent research identified the magnetization feature in CeRu 2 as due to flux motion [12], and the region of the suggested FFLO state in UPd 2 Al 3 was shown to be inconsistent with theoretical models [13]. Most notably, multiple phase transitions that can be associated with the FFLO state have not been observed with a single measurement technique.Heavy-fermion superconductor CeCoIn 5 satisfies all requirements of theory for the formation of the FFLO state. It is very clean, with an electronic mean free path on the order of microns in the superconducting state, which significantly exceeds the superconducting correlation length [14]. Its Maki parameter α ≈ 3.5 is twice the minimum required for the format...

Multiple phase transitions in Pauli-limited iron-based superconductors

“…T C is reported as 2.3 K and 3.5 K for CeCoIn 5 and KFe 2 As 2 respectively, while in both cases T + can be approximated as 0.31 T C [8,19]. In CeCoIn 5 the specific heat displays an additional anomaly within the superconducting state at a temperature ∼ 300 mK (∼ 0.12 T C ) [7]. These experimental results are interpreted as evidence for the existence of the FFLO phase.…”

“…in multiband superconductors like IBSC [33][34][35][36] or MgB 2 [37,38]. Specific heat measurements have been also successfully used to investigate the FFLO phase in heavy-fermion systems [7,8,11] and organic superconductors [14], where the peaks, deep in the superconducting state in the LTHM regime, have been interpreted as phase transitions from BCS to FFLO state.…”

“…Only in the last decade systems have appeared in which we expect an experimental verification of this phase, such as heavy-fermion superconductors [6] (e.g. CeCoIn 5 [7][8][9][10][11]) or organic superconductors (e.g. [14][15][16][17][18]).…”

Emerging evidence for FFLO states in layered organic superconductors (Review Article)

“…These claims, however, later had to be revised or are inconclusive (see [7] for an overview). For the heavyfermion compound CeCoIn 5 , clear thermodynamic evidence for a field-induced phase inside the superconducting state was found [21,22]. This phase, however, does not show the features expected from the FFLO prediction, but rather an antiferromagnetically ordered state [23,24].…”

Superconductivity and Non-Fermi-Liquid Behavior in the Heavy-Fermion Compound CeCo1−xNixIn5

“…[7][8][9] In magnetic fields, the spin degrees of freedom are significantly coupled with the stability of the SC order; a strong Pauli paramagnetic effect gives rise to a first-order transition at the SC upper critical field H c2 below 0.7 K, 7,[10][11][12] and the SC phase coexistent with AFM spin modulation evolves just below H c2 at very low temperatures. [13][14][15][16][17][18] Furthermore, the existence of the AFM-QCP at ∼ H c2 is strongly suggested from the observations of the NFL behavior in the paramagnetic phase above H c2 , including the − ln T divergence in specific heat divided by temperature, the T -linear dependence in magnetization, and electrical resistivity. 10,19,20) In fact, the long-range AFM orders are generated by substituting the ions for the elements in CeCoIn 5 , such as Nd for Ce, 21,22) Rh for Co, [23][24][25][26] and Cd, Hg, and Zn for In.…”