Soft-Phonon and Charge-Density-Wave Formation in Nematic BaNi_{2}As_{2}.

We use diffuse and inelastic x-ray scattering to study the formation of an incommensurate charge-density-wave (I-CDW) in BaNi_{2}As_{2}, a candidate system for charge-driven electronic nematicity. Intense diffuse scattering is observed around the modulation vector of the I-CDW, Q_{I-CDW}. It is already visible at room temperature and collapses into superstructure reflections in the long-range ordered state where a small orthorhombic distortion occurs. A clear dip in the dispersion of a low-energy transverse optical phonon mode is observed around Q_{I-CDW}. The phonon continuously softens upon cooling, ultimately driving the transition to the I-CDW state. The transverse character of the soft-phonon branch elucidates the complex pattern of the I-CDW satellites observed in the current and earlier studies and settles the debated unidirectional nature of the I-CDW. The phonon instability and its reciprocal space position are well captured by our ab initio calculations. These, however, indicate that neither Fermi surface nesting, nor enhanced momentum-dependent electron-phonon coupling can account for the I-CDW formation, demonstrating its unconventional nature.

Observation of the non-linear Meissner effect.

A long-standing theoretical prediction is that in clean, nodal unconventional superconductors the magnetic penetration depth λ, at zero temperature, varies linearly with magnetic field. This non-linear Meissner effect is an equally important manifestation of the nodal state as the well studied linear-in-T dependence of λ, but has never been convincingly experimentally observed. Here we present measurements of the nodal superconductors CeCoIn5 and LaFePO which clearly show this non-linear Meissner effect. We further show how the effect of a small dc magnetic field on λ(T) can be used to distinguish gap nodes from non-nodal deep gap minima. Our measurements of KFe2As2 suggest that this material has such a non-nodal state.

Emerging symmetric strain response and weakening nematic fluctuations in strongly hole-doped iron-based superconductors.

Electronic nematicity is often found in unconventional superconductors, suggesting its relevance for electronic pairing. In the strongly hole-doped iron-based superconductors, the symmetry channel and strength of the nematic fluctuations, as well as the possible presence of long-range nematic order, remain controversial. Here, we address these questions using transport measurements under elastic strain. By decomposing the strain response into the appropriate symmetry channels, we demonstrate the emergence of a giant in-plane symmetric contribution, associated with the growth of both strong electronic correlations and the sensitivity of these correlations to strain. We find weakened remnants of the nematic fluctuations that are present at optimal doping, but no change in the symmetry channel of nematic fluctuations with hole doping. Furthermore, we find no indication of a nematic-ordered state in the AFe2As2 (A = K, Rb, Cs) superconductors. These results revise the current understanding of nematicity in hole-doped iron-based superconductors.

Ferroelasticity, anelasticity and magnetoelastic relaxation in Co-doped iron pnictide: Ba(Fe0.957Co0.043)2As2.

The hypothesis that strain has a permeating influence on ferroelastic, magnetic and superconducting transitions in 122 iron pnictides has been tested by investigating variations of the elastic and anelastic properties of a single crystal of Ba(Fe0.957Co0.043)2As2 by resonant ultrasound spectroscopy as a function of temperature and externally applied magnetic field. Non-linear softening and stiffening of C 66 in the stability fields of both the tetragonal and orthorhombic structures has been found to conform quantitatively to the Landau expansion for a pseudoproper ferroelastic transition which is second order in character. The only exception is that the transition occurs at a temperature (T S ≈ 69 K) ~10 K above the temperature at which C 66 would extrapolate to zero ([Formula: see text] ≈ 59 K). An absence of anomalies associated with antiferromagnetic ordering below T N ≈ 60 K implies that coupling of the magnetic order parameter with shear strain is weak. It is concluded that linear-quadratic coupling between the structural/electronic and antiferromagnetic order parameters is suppressed due to the effects of local heterogeneous strain fields arising from the substitution of Fe by Co. An acoustic loss peak at ~50-55 K is attributed to the influence of mobile ferroelastic twin walls that become pinned by a thermally activated process involving polaronic defects. Softening of C 66 by up to ~6% below the normal-superconducting transition at T c ≈ 13 K demonstrates an effective coupling of the shear strain with the order parameter for the superconducting transition which arises indirectly as a consequence of unfavourable coupling of the superconducting order parameter with the ferroelastic order parameter. Ba(Fe0.957Co0.043)2As2 is representative of 122 pnictides as forming a class of multiferroic superconductors in which elastic strain relaxations underpin almost all aspects of coupling between the structural, magnetic and superconducting order parameters and of dynamic properties of the transformation microstructures they contain.

Strain relaxation behaviour of vortices in a multiferroic superconductor.

The elastic and anelastic properties of a single crystal of Co-doped pnictide Ba(Fe0.957Co0.043)2As2 have been determined by resonant ultrasound spectroscopy in the frequency range 10-500 kHz, both as a function of temperature through the normal-superconducting transition (T c ≈ 12.5 K) and as a function of applied magnetic field up to 12.5 T. Correlation with thermal expansion, electrical resistivity, heat capacity, DC and AC magnetic data from crystals taken from the same synthetic batch has revealed the permeating influence of strain on coupling between order parameters for the ferroelastic (Q E) and superconducting (Q SC) transitions and on the freezing/relaxation behaviour of vortices. Elastic softening through T c in zero field can be understood in terms of classical coupling of the order parameter with the shear strain e 6, λe 6 [Formula: see text], which means that there must be a common strain mechanism for coupling of the form λ [Formula: see text] Q E. At fields of ~5 T and above, this softening is masked by Debye-like stiffening and acoustic loss processes due to vortex freezing. The first loss peak may be associated with the establishment of superconductivity on ferroelastic twin walls ahead of the matrix and the second is due to the vortex liquid-vortex glass transition. Strain contrast between vortex cores and the superconducting matrix will contribute significantly to interactions of vortices both with each other and with the underlying crystal structure. These interactions imply that iron-pnictides represent a class of multiferroic superconductors in which strain-mediated coupling occurs between the multiferroic properties (ferroelasticity, antiferromagnetism) and superconductivity.

Spectral Evidence for Emergent Order in Ba_{1-x}Na_{x}Fe_{2}As_{2}.

We report an angle-resolved photoemission spectroscopy study of the iron-based superconductor family, Ba_{1-x}Na_{x}Fe_{2}As_{2}. This system harbors the recently discovered double-Q magnetic order appearing in a reentrant C_{4} phase deep within the underdoped regime of the phase diagram that is otherwise dominated by the coupled nematic phase and collinear antiferromagnetic order. From a detailed temperature-dependence study, we identify the electronic response to the nematic phase in an orbital-dependent band shift that strictly follows the rotational symmetry of the lattice and disappears when the system restores C_{4} symmetry in the low temperature phase. In addition, we report the observation of a distinct electronic reconstruction that cannot be explained by the known electronic orders in the system.

Giant superconducting fluctuations in the compensated semimetal FeSe at the BCS-BEC crossover.

The physics of the crossover between weak-coupling Bardeen-Cooper-Schrieffer (BCS) and strong-coupling Bose-Einstein condensate (BEC) limits gives a unified framework of quantum-bound (superfluid) states of interacting fermions. This crossover has been studied in the ultracold atomic systems, but is extremely difficult to be realized for electrons in solids. Recently, the superconducting semimetal FeSe with a transition temperature Tc=8.5 K has been found to be deep inside the BCS-BEC crossover regime. Here we report experimental signatures of preformed Cooper pairing in FeSe, whose energy scale is comparable to the Fermi energies. In stark contrast to usual superconductors, large non-linear diamagnetism by far exceeding the standard Gaussian superconducting fluctuations is observed below T*∼20 K, providing thermodynamic evidence for prevailing phase fluctuations of superconductivity. Nuclear magnetic resonance and transport data give evidence of pseudogap formation at ∼T*. The multiband superconductivity along with electron-hole compensation in FeSe may highlight a novel aspect of the BCS-BEC crossover physics.

Thermal Conductivity of the Iron-Based Superconductor FeSe: Nodeless Gap with a Strong Two-Band Character.

The thermal conductivity κ of the iron-based superconductor FeSe was measured at temperatures down to 75 mK in magnetic fields up to 17 T. In a zero magnetic field, the electronic residual linear term in the T=0 K limit, κ_{0}/T, is vanishingly small. The application of a magnetic field B causes an exponential increase in κ_{0}/T initially. Those two observations show that there are no zero-energy quasiparticles that carry heat and therefore no nodes in the superconducting gap of FeSe. The full field dependence of κ_{0}/T has the classic two-step shape of a two-band superconductor: a first rise at very low field, with a characteristic field B^{⋆}≪B_{c2}, and then a second rise up to the upper critical field B_{c2}. This shows that the superconducting gap is very small (but finite) on one of the pockets in the Fermi surface of FeSe. We estimate that the minimum value of the gap, Δ_{min}, is an order of magnitude smaller than the maximum value, Δ_{max}.

Magnetostriction and Magnetostructural Domains in Antiferromagnetic YBa2Cu3O6.

We use high-resolution neutron Larmor diffraction and capacitative dilatometry to investigate spontaneous and forced magnetostriction in undoped, antiferromagnetic YBa_{2}Cu_{3}O_{6.0}, the parent compound of a prominent family of high-temperature superconductors. Upon cooling below the Néel temperature T_{N}=420 K, Larmor diffraction reveals the formation of magnetostructural domains of characteristic size ∼240 nm. In the antiferromagnetic state, dilatometry reveals a minute (4×10^{-6}) orthorhombic distortion of the crystal lattice in external magnetic fields. We attribute these observations to exchange striction and spin-orbit coupling induced magnetostriction, respectively, and show that they have an important influence on the thermal and charge transport properties of undoped and lightly doped cuprates.

Superconductivity-induced re-entrance of the orthorhombic distortion in Ba1-xKxFe2As2.

Detailed knowledge of the phase diagram and the nature of the competing magnetic and superconducting phases is imperative for a deeper understanding of the physics of iron-based superconductivity. Magnetism in the iron-based superconductors is usually a stripe-type spin-density-wave, which breaks the tetragonal symmetry of the lattice, and is known to compete strongly with superconductivity. Recently, it was found that in some systems an additional spin-density-wave transition occurs, which restores this tetragonal symmetry, however, its interaction with superconductivity remains unclear. Here, using thermodynamic measurements on Ba1-xKxFe2As2 single crystals, we show that the spin-density-wave phase of tetragonal symmetry competes much stronger with superconductivity than the stripe-type spin-density-wave phase, which results in a novel re-entrance of the latter at or slightly below the superconducting transition.

Infrared Study of the Spin Reorientation Transition and Its Reversal in the Superconducting State in Underdoped Ba(1-x)K(x)Fe(2)As(2).

With infrared spectroscopy we investigated the spin-reorientation transition from an orthorhombic antiferromagnetic (o-AF) to a tetragonal AF (t-AF) phase and the reentrance of the o-AF phase in the superconducting state of underdoped Ba(1-x)K(x)Fe(2)As(2). In agreement with the predicted transition from a single-Q to a double-Q AF structure, we found that a distinct spin density wave develops in the t-AF phase. The pair breaking peak of this spin density wave acquires much more low-energy spectral weight than the one in the o-AF state which indicates that it competes more strongly with superconductivity. We also observed additional phonon modes in the t-AF phase which likely arise from a Brillouin-zone folding that is induced by the double-Q magnetic structure with two Fe sublattices exhibiting different magnitudes of the magnetic moment.

Dichotomy between the Hole and Electron Behavior in Multiband Superconductor FeSe Probed by Ultrahigh Magnetic Fields.

Magnetoresistivity ρ(xx) and Hall resistivity ρ(xy) in ultrahigh magnetic fields up to 88 T are measured down to 0.15 K to clarify the multiband electronic structure in high-quality single crystals of superconducting FeSe. At low temperatures and high fields we observe quantum oscillations in both resistivity and the Hall effect, confirming the multiband Fermi surface with small volumes. We propose a novel approach to identify from magnetotransport measurements the sign of the charge carriers corresponding to a particular cyclotron orbit in a compensated metal. The observed significant differences in the relative amplitudes of the quantum oscillations between the ρ(xx) and ρ(xy) components, together with the positive sign of the high-field ρ(xy), reveal that the largest pocket should correspond to the hole band. The low-field magnetotransport data in the normal state suggest that, in addition to one hole and one almost compensated electron band, the orthorhombic phase of FeSe exhibits an additional tiny electron pocket with a high mobility.

Origin of the tetragonal-to-orthorhombic phase transition in FeSe: a combined thermodynamic and NMR study of nematicity.

The nature of the tetragonal-to-orthorhombic structural transition at T_{s}≈90 K in single crystalline FeSe is studied using shear-modulus, heat-capacity, magnetization, and nuclear magnetic resonance measurements. The transition is shown to be accompanied by a large shear-modulus softening, which is practically identical to that of underdoped Ba(Fe,Co)_{2}As_{2}, suggesting a very similar strength of the electron-lattice coupling. On the other hand, a spin-fluctuation contribution to the spin-lattice relaxation rate is only observed below T_{s}. This indicates that the structural, or "nematic," phase transition in FeSe is not driven by magnetic fluctuations.

Nematic susceptibility of hole-doped and electron-doped BaFe2As2 iron-based superconductors from shear modulus measurements.

The nematic susceptibility, χφ, of hole-doped Ba(1-x)K(x)Fe2As2 and electron-doped Ba(Fe(1-x)Co(x))2As2 iron-based superconductors is obtained from measurements of the elastic shear modulus using a three-point bending setup in a capacitance dilatometer. Nematic fluctuations, although weakened by doping, extend over the whole superconducting dome in both systems, suggesting their close tie to superconductivity. Evidence for quantum critical behavior of χφ is, surprisingly, only found for Ba(Fe(1-x)Co(x))2As2 and not for Ba(1-x)K(x)Fe2As2--the system with the higher maximal Tc value.

Evidence of strong correlations and coherence-incoherence crossover in the iron pnictide superconductor KFe2As2.

Using resistivity, heat-capacity, thermal-expansion, and susceptibility measurements we study the normal-state behavior of KFe2As2. Both the Sommerfeld coefficient (γ≈103 mJ mol(-1) K(-2)) and the Pauli susceptibility (χ≈4×10(-4)) are strongly enhanced, which confirm the existence of heavy quasiparticles inferred from previous de Haas-van Alphen and angle-resolved photoemission spectroscopy experiments. We discuss this large enhancement using a Gutzwiller slave-boson mean-field calculation, which shows the proximity of KFe2As2 to an orbital-selective Mott transition. The temperature dependence of the magnetic susceptibility and the thermal expansion provide strong experimental evidence for the existence of a coherence-incoherence crossover, similar to what is found in heavy fermion and ruthenate compounds, due to Hund's coupling between orbitals.

Enhancement of the critical temperature of HgBa2CuO(4+δ) by applying uniaxial and hydrostatic pressure: implications for a universal trend in cuprate superconductors.

It is well known that the superconducting transition temperature (T(c)) of cuprate superconductors can be enhanced by varying certain structural and electronic parameters, such as the flatness of the CuO2 planes or their doping level. We determine the uniaxial and hydrostatic pressure derivatives of T(c) in the structurally simple tetragonal compound HgBa2CuO(4+δ) near optimal doping. Our results provide experimental evidence for two further methods to enhance T(c): (i) reducing the area of the CuO2 planes, and (ii) increasing the separation of the CuO2 planar groups. T(c) is found to couple much more strongly to the ratio c/a of the lattice constants than to the unit cell volume. A comparison with prior results for structurally more complicated cuprates reveals a general trend of uniaxial pressure derivatives with T(c).

Magnetic structure of the kagome mixed compound (Co(0.5)Ni(0.5))(3)V(2)O(8).

We report the magnetic structure of (Co(0.5)Ni(0.5))(3)V(2)O(8) (CNVO) deduced by single crystal neutron diffraction. This compound exhibits features which differ from that of its parent compounds, which are absolutely collinear along the a axis for Co(3)V(2)O(8) (CVO) or exhibit magnetic moments predominantly in the a-b plane with small components along c in the case of Ni(3)V(2)O(8) (NVO). The averaged magnetic moments of the statistically distributed Ni(2+) and Co(2+) ions in CNVO are oriented in the a-c plane and form loops of quasiferromagnetically coupled spins. These loops are connected along the a axis and separated along the c axis by cross-tie spins forming a quasiferromagnetic wave with the upper part of the respective neighbouring loops. The magnetic moments are sinusoidally modulated by the propagation vector k = (0.49,0,0) with an average amplitude of 1.59(1) µ(B) for a magnetic ion on a cross-tie site and 1.60(1) µ(B) for the spine site. In addition to neutron diffraction, specific heat and magnetization data, which confirm that the only magnetic phase transition above 1.8 K is the onset of antiferromagnetic order at T(N) = 7.4(1) K, are presented.

Importance of in-plane anisotropy in the quasi-two-dimensional antiferromagnet BaNi2V2O8.

The phase diagram of the quasi-two-dimensional antiferromagnet BaNi(2)V(2)O(8) is studied by specific heat, thermal expansion, magnetostriction, and magnetization for magnetic fields applied perpendicular to c. At micro(o)H* approximately 1.5 T, a crossover to a high-field state, where T(N)(H) increases linearly, arises from a competition of intrinsic and field-induced in-plane anisotropies. The pressure dependences of T(N) and H* are interpreted using the picture of a pressure-induced in-plane anisotropy. Even at zero field and ambient pressure, in-plane anisotropy cannot be neglected, which implies deviations from pure Berezinskii-Kosterlitz-Thouless behavior.

Magnetic-field-induced finite-size effect in the nigh-temperature superconductor YBa2Cu3O(7-delta): a comparison with rotating superfluid 4He.

The effect of strong magnetic fields (11 T) on superconductivity in YBa2Cu3O(7-delta) is investigated using high-resolution thermal expansion. We show that the field-induced broadening of the superconducting transition is due to a finite-size effect resulting from the field-induced vortex-vortex length scale. The physics of this broadening has recently been elucidated for the closely related case of rotating superfluid 4He [Phys. Rev. B 60, 12 373 (1999)]]. Our results imply that the primary effect of magnetic fields of the order of 10 T is to destroy the phase coherence; the pairing, on the other hand, appears to be quite insensitive to these fields.