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...
We measured specific heat and resistivity of heavy fermion CeCoIn5 between the superconducting critical field Hc2 = 5T and 9 T, with field in the [001] direction, and at temperatures down to 50mK. At 5T the data show Non Fermi Liquid behavior down to the lowest temperatures. At field above 8T the data exhibit crossover from the Fermi liquid to a Non Fermi Liquid behavior. We analyzed the scaling properties of the specific heat, and compared both resistivity and the specific heat with the predictions of a spin-fluctuation theory. Our analysis leads us to suggest that the NFL behavior is due to incipient antiferromagnetism (AF) in CeCoIn5 with the quantum critical point in the vicinity of the Hc2. Below Hc2 the AF phase which competes with the paramagnetic ground state is superseded by the superconducting transition.PACS numbers: 74.70. Tx, 71.27.+a, 74.25.Fy, 75.40.Cx When the symmetry of the ground state of a system changes as a function of an external or internal parameter, the system is said to undergo a quantum phase transition. If, in addition, this transition is second order, the system has a Quantum Critical Point (QCP) at the critical value of the parameter. The competition between the nearly degenerate ground states determines the behavior of the system over a range of temperatures and tuning parameter values in the vicinity of QCP. In this region of the phase diagram the properties of the system differ from those on either side of the transition, and often exhibit unusual dependence on the temperature and the tuning parameter. This has made quantum critical phenomena a subject of intense current interest.Study of quantum critical points in heavy fermion systems has been a focus of particular attention (for a recent review see Ref. 1). In these materials the competition typically takes place between a paramagnetic and a magnetically ordered ground states. The unconventional behavior near QCP is manifested in the deviation of the temperature dependence of measured properties from those of metals described by the Landau Fermi Liquid (FL) theory. In that theory the electronic specific heat is linear in temperature, C(T ) = γT , and the resistivity increases quadratically from a residual value, ρ = ρ 0 + AT 2 . In systems tuned to QCP the Sommerfeld coefficient, γ(T ) = C/T , commonly diverges as the temperature goes to zero, and has been variously argued to behave as either log T or T α , with α < 0. Resistivity with an exponent less than two is also ubiquitous in these compounds.Tuning the system through a QCP can be accomplished experimentally by varying sample's composition [2, 3], applying pressure [4], or applying magnetic field [5]. In non-stoichiometric compounds the Kondo disorder, where a range of Kondo temperatures T K appears due to different environments of the f-electron ions, is an important mechanism leading to a Non Fermi Liquid (NFL) behavior [6,7]. In these compounds it is not easy to separate this origin of NFL behavior from the consequences of the proximity to a QCP. Hence the stoichi...
The superconducting phase transition in heavy fermion CeCoIn5 (T(c)=2.3 K in zero field) becomes first order when the magnetic field H parallel [001] is greater than 4.7 T, and the transition temperature is below T0 approximately 0.31T(c). The change from second order at lower fields is reflected in strong sharpening of both specific heat and thermal expansion anomalies associated with the phase transition, a strong magnetocaloric effect, and a steplike change in the sample volume. This effect is due to Pauli limiting in a type-II superconductor, and was predicted theoretically in the mid-1960s.
We have studied the magnetic order inside the superconducting phase of CeCoIn5 for fields along the [1 0 0] crystallographic direction using neutron diffraction. We find a spin-density wave order with an incommensurate modulation Q=(q,q,1/2) and q=0.45(1), which within our experimental uncertainty is indistinguishable from the spin-density wave found for fields applied along [1 -1 0]. The magnetic order is thus modulated along the lines of nodes of the d{x{2}-y{2}} superconducting order parameter, suggesting that it is driven by the electron nesting along the superconducting line nodes. We postulate that the onset of magnetic order leads to reconstruction of the superconducting gap function and a magnetically induced pair density wave.
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