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 H(c2), 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 parallel [110] and H parallel [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 parallel [001], with the FFLO state occupying a smaller part of the phase diagram.     

Possible Fulde-Ferrell-Larkin-Ovchinnikov inhomogeneous superconducting state in CeCoIn5

We present specific heat and thermal conductivity of the heavy fermion superconductor CeCoIn5 in the vicinity of the superconducting critical fieldH _c2, measured with magnetic field in the plane of this quasi-2D compound and at temperatures down to 50 mK. The superconducting phase diagram and the first order nature of the superconducting phase transition at high fields close to a critical fieldH _c2 indicate the importance of the Pauli limiting effect in CeCoIn₅. In the same range of magnetic field we observe a second specific heat anomaly within the superconducting state, and interpret it as a signature of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) inhomogeneous superconducting state. In addition, the thermal conductivity data as a function of field display a kink at a fieldH _k below the superconducting critical field, which closely coincides with the low temperature anomaly in specific heat tentatively identified with the appearance of the FFLO superconducting state. The enhancement of thermal conductivity within the FFLO state calls for further theoretical investigations of the real space structure of the order parameter (and in particular, the structure of vortices) and of the thermal transport within the inhomogeneous FFLO state.     

First-order superconducting phase transition in CeCoIn5

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.     

Texture in the superconducting order parameter of CeCoIn5 revealed by nuclear magnetic resonance

We present a 115In NMR study of the quasi-two-dimensional heavy-fermion superconductor CeCoIn5 believed to host a Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state. In the vicinity of the upper critical field and with a magnetic field applied parallel to the ab plane, the NMR spectrum exhibits a dramatic change below T*(H) which well coincides with the position of reported anomalies in specific heat and ultrasound velocity. We argue that our results provide the first microscopic evidence for the occurrence of a spatially modulated superconducting order parameter expected in a FFLO state. The NMR spectrum also implies an anomalous electronic structure of vortex cores.     

Exploring the fragile antiferromagnetic superconducting phase in CeCoIn5

CeCoIn5 is a heavy fermion type-II superconductor showing clear signs of Pauli-limited superconductivity. A variety of measurements give evidence for a transition at high magnetic fields inside the superconducting state, when the field is applied either parallel to or perpendicular to the c axis. When the field is perpendicular to the c axis, antiferromagnetic order develops on the high-field side of the transition. This order remains as the field is rotated out of the basal plane, but the associated moment eventually disappears above 17°, indicating that anomalies seen with the field parallel to the c axis are not related to this magnetic order. We discuss the implications of this finding.     

Magnetic-field-induced lattice anomaly inside the superconducting state of CeCoIn5: anisotropic evidence of the possible Fulde-Ferrell-Larkin-Ovchinnikov state

We report high magnetic field linear magnetostriction experiments on CeCoIn5 single crystals. Two features are remarkable: (i) a sharp discontinuity in all the crystallographic axes associated with the upper superconducting critical field B(c2) that becomes less pronounced as the temperature increases and (ii) a distinctive second orderlike feature observed only along the c axis in the high field (10 T < or approximately B< or = B(c2)) low temperature (T < or approximately 0.35 K) region. This second order transition is observed only when the magnetic field lies within 20 degrees of the ab planes and there is no signature of it above B(c2), which raises questions regarding its interpretation as a field induced magnetically ordered phase. Good agreement with previous results suggests that this anomaly is related to the transition to a possible Fulde-Ferrel-Larkin-Ovchinnikov superconducting state.     

Fulde-Ferrell-Larkin-Ovchinnikov state in a perpendicular field of quasi-two-dimensional CeCoIn5

A Fulde-Ferrell-Larkin-Ovchinnkov (FFLO) state was previously reported in the quasi-2D heavy fermion CeCoIn5 when a magnetic field was applied parallel to the ab plane. Here, we conduct 115In NMR studies of this material in a perpendicular field, and provide strong evidence for FFLO in this case as well. Although the topology of the phase transition lines in the H-T phase diagram is identical for both configurations, there are several remarkable differences between them. Compared to H parallelab, the FFLO phase for H perpendicularab is confined in a much narrower region at the low-T-high-H corner in the H-T plane, and the critical field separating the FFLO and non-FFLO superconducting states almost ceases to have a temperature dependence. Moreover, directing H perpendicularab results in a notable change in the quasiparticle excitation spectrum within the planar node associated with the FFLO transition.     

Perturbing the superconducting planes in CeCoIn5 by Sn substitution

In contrast to substitution on the Co or Ce site, Sn substitution has a remarkably strong effect on superconductivity in CeCoIn5-xSnx, with Tc-->0 beyond only 3.6% Sn. Instead of being randomly distributed on in-plane and out-of-plane In sites, extended x-ray absorption fine structure measurements show the Sn atoms preferentially substitute within the Ce-In plane. This result highlights the importance of the In1 site to impurity scattering and clearly demonstrates the two-dimensional nature of superconductivity in CeCoIn5.     

Evidence for a new magnetic field scale in CeCoIn5

The Nernst coefficient of displays two distinct anomalies in magnetic field. The feature detected at Hk approximately 23 T is similar to what is observed in CeRu2Si2 at Hm = 7.8 T where a metamagnetic transition occurs. In CeCoIn5, new frequencies are observed in de Haas-van Alphen oscillations when the field exceeds 23 T where the Dingle temperature decreases by about 30%. Based on the Nernst coefficient anomalies, the magnetic phase diagram of CeCoIn5 is revised.     

Pressure dependence of the Fulde-Ferrell-Larkin-Ovchinnikov state in CeCoIn5

Pressure studies of the thermodynamics of CeCoIn5 under magnetic fields H parallel to c and H parallel to ab have been made up to P = 1.34 GPa. We recorded the signature of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state for all pressures when H parallel to ab. Also remarkably, the FFLO regime suddenly expands for P = 1.34 GPa. With the help of a microscopic theory for d-wave superconductivity, we have extracted the gyromagnetic ratio g and the Fermi velocities nu(a) and nu(c). Our study is the first evidence for the existence of the FFLO state away from the influence of the antiferromagnetic fluctuations. We find a close parallel between the T-P phase diagram of CeCoIn5 and the T-x phase diagram of the high-Tc cuprates, where x is the hole concentration.     

Field dependence of the ground state in the exotic superconductor CeCoIn5: a nuclear magnetic resonance investigation

We report 115In nuclear magnetic resonance (NMR) measurements in CeCoIn5 at low temperature (T approximately 70 mK) as a function of the magnetic field (H0) from 2 to 13.5 T applied perpendicular to the c axis. A NMR line shift reveals that below 10 T the spin susceptibility increases as sqrt[H0]. We associate this with an increase of the density of states due to the Zeeman and Doppler-shifted quasiparticles extended outside the vortex cores in a d-wave superconductor. Above 10 T a new superconducting state is stabilized, possibly the modulated phase predicted by Fulde, Ferrell, Larkin, and Ovchinnikov. This phase is clearly identified by a strong and linear increase of the NMR shift with the field, before a jump at the first order transition to the normal state.     

Deposition of superconducting CeCoIn5 thin films by co-sputtering and evaporation

Thin superconducting films of CeCoIn₅ were prepared in situ by simultaneous thermal evaporation of indium and dc magnetic field assisted sputtering of planar metallic Ce and Co targets. To achieve an effective sputtering of the magnetic Co target a special geometry with two facing planar targets (Ce and Co) and magnetic field perpendicular to the targets was used. The stoichiometric (0 0 1)-oriented CeCoIn₅ films were grown on r-cut sapphire substrates with a high-rate of 100 nm/min. The temperature dependence of the electrical resistivity revealed the characteristic heavy-fermion behavior and a superconducting transition at about 2 K in agreement with the literature data for CeCoIn₅ bulk material and thin films.     

Feedback spin resonance in superconducting CeCu2Si2 and CeCoIn5

We show that the recently observed spin resonance modes in heavy-fermion superconductors CeCoIn5 and CeCu2Si2 are magnetic excitons originating from superconducting quasiparticles. The wave vector Q of the resonance state leads to a powerful criterion for the symmetry and node positions of the unconventional gap function. The detailed analysis of the superconducting feedback on magnetic excitations reveals that the symmetry of the superconducting gap corresponds to a singlet d_{x;{2}-y;{2}} state symmetry in both compounds. In particular this resolves the long-standing ambiguity of the gap symmetry in CeCoIn5. We demonstrate that in both superconductors the resonance peak shows a significant dispersion away from Q which can be checked experimentally. Our analysis reveals the similar origin of the resonance peaks in the two heavy-fermion superconductors and in layered cuprates.     

Reversible tuning of the heavy-fermion ground state in CeCoIn5

Cadmium doping the heavy-fermion superconductor CeCoIn(5) at the percent level acts as an electronic tuning agent, sensitively shifting the balance between superconductivity and antiferromagnetism and opening new ambient-pressure phase space in the study of heavy-fermion ground states.     

On the density fluctuations of the superconducting state

The fluctuations of the number of particles in a subvolumeΩ′≦Ω in the superconducting state are investigated in the framework of the strong coupling limit of the BCS-theory. It is shown for values ofΩ′?Ω these fluctuations are proportional to the subvolumeΩ′ and agree for theseΩ′-values with the density fluctuations of the quasivacuum state.     

Effect of interconfigurational fluctuations on superconducting magnetic alloys

A theory which includes impurity-atom correlation and many electron structure at the outset and gives rise to interconfigurational excitation energy resonances close to the Fermi energy is applied to effects of Ce impurities on the superconducting transition temperature of La and La_1?xTh_x, as functions of pressure and x respectively, and on the normal state resistivity of La as a function of pressure.     

Spin fluctuations and the superconducting state in doped insulators

We propose a model of electron pairing via spin fluctuations in doped insulators. The bare states for the superconducting condensate correspond to impurity bands in the original band gap of the undoped material. We obtain a complete set of equations for the superconducting state. We show that fermion pairing in impurity bands of extended states is possible, and thus so is superconductivity, if localized spin-0 bosons are produced. The latter are necessarily accompanied by localized spin-1 bosons, which are responsible for the relationship between singlet and triplet pairing channels of quasiparticles. Zh. éksp. Teor. Fiz. 114, 1765–1784 (November 1998)     

Evolution of paramagnetic quasiparticle excitations emerged in the high-field superconducting phase of CeCoIn5

We present (115)In NMR measurements in a novel thermodynamic phase of CeCoIn(5) in a high magnetic field, where exotic superconductivity exists with the incommensurate spin-density wave order. We show that the NMR spectra in this phase provide direct evidence for the emergence of the spatially distributed normal quasiparticle regions. The quantitative analysis for the field evolution of the paramagnetic magnetization and newly emerged low-energy quasiparticle density of states is consistent with the nodal plane formation, which is characterized by an order parameter in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. The NMR spectra also suggest that the spatially uniform spin-density wave is induced in the FFLO phase.     

Multiple superconducting phases in heavy fermion compounds PrOs4Sb12 and CeCoIn5

In recently discovered heavy fermion compounds, quasi-two-dimensional CeCoIn₅ and skutterudite PrOs₄Sb₁₂, multiple superconducting phases with different symmetries manifest themselves belowT _c. The angle-resolved magnetothermal transport measurements revealed that in PrOs₄Sb₁₂ a novel change in the symmetry of the superconducting gap function occurs deep inside the superconducting state. The ultrasound velocity measurements revealed that in CeCoIn5 the Fulde-Ferrel-Larkin-Ovchinikov (FFLO) phase, in which the order parameter is spatially modulated and has planar nodes aligned perpendicular to the vortices, appears at low temperature and high field. These results open up a new realm for the study of the superconductivity with multiple phases.