Explorations of the order-disorder transformation in vortex matter in single crystals of tetragonal structured (c/a $\sim$3) borocarbide superconductors, $YNi_2B_2C$ and $LuNi_2B_2C$, reveal that vortex arrays experience different effective pinning in different crystallographic directions. We surmise that correlation exists between the large anisotropy in effective pinning/disorder and the differences in the (local) symmetry transition from rhombohedral to (quasi) square vortex lattice(VL). For field along high symmetry directions, like, c-axis and ab-basal plane, the VL symmetry is close to square and the ordered state spans a large field interval. When the field is turned away from the c-axis towards ab-plane, at intermediate angles, the region of ordered state shrinks, in response to enhancement in effective pinning. At such intermediate angles the symmetry of the VL would be far from ideal triangular or square.
The symmetry of superconductivity in borocarbides LuNi2B2C and YNi2B2C is an outstanding issue. Here an anisotropic s- wave order parameter (or s+g model) is proposed for these borocarbides. In spite of the dominant s- wave component the proposed superconducting order parameter has nodes and gives rise to the H^(1/2) dependent specific heat in the vortex state (the Volovik effect). This model predicts the fourfold symmetry both in the angular dependent thermal conductivity and in the excess Dingle temperature in the vortex state, which should be readily accessible experimentally.
We present magnetization measurements in single crystals of the tetragonal $YNi_2B_2C$ compound, which exhibit the phenomenon of peak effect as well as the second magnetization peak anomaly for H $>$ 0.5T (H $||$ c). At the lower field (50mT $<$ H $<$ 200mT), we have observed the presence of flux jumps, which seem to relate to a structural change in the local symmetry of the flux line lattice (a first order re-orientation transition across a local field in some parts of the sample, in the range of 100mT to 150mT). These flux jumps are also observed in a single crystal of $LuNi_2B_2C$ for H $||…
The recently discovered intermetallic superconductor MgB2 appears to have a highly anisotopic upper critical field with Hc2(max)/Hc2(min} = γ> 5. In order to determine the temperature dependence of both Hc2(max) and Hc2(min) we propose a method of extracting the superconducting anisotropy from the magnetization M(H,T) of randomly oriented powder samples. The method is based on two features in dM/dT the onset of diamagnetism at Tc(max), that is commonly associated with Hc2, and a kink in dM/dT at a lower temperature Tc(min). Results for LuNi2B2C and YNi2B2C powders are in agreement with anisotr…
Recent experiments on single crystals of YNi$_2$B$_2$C have revealed the presence of point nodes in the superconducting energy gap Delta(k} at k = (1,0,0), (0,1,0), (-1,0,0), and (0,-1,0). In this paper we investigate the effects of impurity scattering on the quasiparticle spectrum in the vortex state of s+g-wave superconductors, which is found to be strongly modified in the presence of disorder. In particular, a gap in the quasiparticle energy spectrum is found to open even for infinitesimal impurity scattering, giving rise to exponentially activated thermodynamic response functions, such as …
The Hall effect in LuNi_2B_2C and YNi_2B_2C borocarbides has been investigated in normal and superconducting mixed states. The Hall resistivity rho_{xy} for both compounds is negative in the normal as well as in the mixed state and has no sign reversal below T_c typical for high-T_c superconductors. In the mixed state the behavior of both systems is quite similar. The scaling relation rho_{xy}\simρ_{xx}^β(ρ_{xx} is the longitudinal resistivity) was found with β=2.0 and 2.1 for annealed Lu- and Y-based compounds, respectively. The scaling exponent βdecreases with increasing degree of disorder a…
We have measured the low temperature heat capacity Cp and microwave surface impedance Zs in the vortex state of YNi_2B_2C. In contrast to conventional s-wave superconductors, Cp shows a nearly \sqrt H-dependence. This \sqrt H-dependence persists even after the introduction of the columnar defects which change the electronic structure of the vortex core regime dramatically and strongly disturb the regular vortex lattice. On the other hand, flux flow resistivity obtained from Zs is nearly proportional to H. Taken together, these results indicate that the vortex state of YNi_2B_2C is fundamentall…
The magnetic field distribution in the vortex state of YNi2B2C has been probed by muon spin rotation (muSR). The analysis based on the London model with nonlocal corrections shows that the vortex lattice has changed from hexagonal to square with increasing magnetic field H. At low fields the vortex core radius, rho_v(H), decreases with increasing H much steeper than what is expected from the sqrt(H) behavior of the Sommerfeld constant gamma(H), strongly suggesting that the anomaly in gamma(H) primarily arises from the quasiparticle excitations outside the vortex cores.
The nature of five-quadrant magnetic isotherms for is different from that for in a single crystal of YNi2B2C, pointing towards an anisotropic behaviour of the flux line lattice (FLL). For, a well defined peak effect (PE) and second magnetization peak (SMP) can be observed and the loop is open prior to the PE. However, for, the loop is closed and one can observe only the PE. We have investigated the history dependence of magnetization hysteresis data for by recording minor hysteresis loops. The observed history dependence in across different anomalous regions are rationalized on the basis of su…
We present an inelastic neutron scattering study of phonon lineshapes in the vortex state of the type-II superconductor YNi$_2$B$_2$C. In a previous study [Phys. Rev. Lett. \textbf{101}, 237002 (2008)] it was shown that certain phonons exhibit a clear signature of the superconducting gap $2Δ$ on entering the superconducting state. Our interest was to find out whether or not the lineshape of such phonons reflects the inhomogeneous nature of the vortex state induced by a magnetic field smaller than the upper critical field $B_{c2}$ .We found that this is indeed the case because the observed phon…
By use of ultrasound studies we resolved magneto-acoustic quantum oscillation deep into the mixed state of the multiband nonmagnetic superconductor YNi2B2C. Below the upper critical field, only a very weak additional damping appears that can be well explained by the field inhomogeneity caused by the flux-line lattice in the mixed state. This is clear evidence for no or a vanishingly small gap for one of the bands, namely, the spheroidal alpha band. This contrasts de Haas--van Alphen data obtained by use of torque magnetometry for the same sample, with a rapidly vanishing oscillation signal in …
Quasiparticle transport in the vortex state of an s-wave superconductor at T -> 0 was investigated by measuring the thermal conductivity of LuNi_2B_2C down to 70 mK in a magnetic field perpendicular to the heat current. In zero field, there is no electronic conduction, as expected for a superconducting gap without nodes. However, as soon as vortices enter the sample quasiparticles are seen to conduct remarkably well, even better than they would in a typical d-wave superconductor. This is in stark conflict with the widely held view that quasiparticle states in s-wave superconductors just above …
We present magnetic field dependence of the critical current density from dc-magnetization measurements concerning the anisotropic behavior of flux line lattice (FLL) in a single crystal of YNi_2B_2C. The peak effect (PE) phenomenon is observed for all crystallographic orientations, but the second magnetization peak (SMP) anomaly is observed only for H//a. Our study reveals that the FLL obtained when H//[100] is better ordered within the basal plane. However, the FLL for H// c is found to be even more ordered than that for H//[110]. The perfect square symmetry of the FLL for H//c is perhaps re…
Evolution of the vortex lattice, the rhombus-square transition included, for LuNi_2B_2C in the field along the c crystal axis, is tracked by the decoration technique pushed up to the record high (for this method) field of 1480 Oe. Decoration images are analyzed with the help of the Fourier transform, which indicates disordered structures in small fields of a few Oe. In fields H < 200 Oe the coexisting domains of different structures are observed. A technique based on the Fourier transform is employed to see the domains separately. The transition to the square lattice is recorded near 900 Oe. T…
We report on the measurements of the superconducting order parameter in the nonmagnetic borocarbides LuNi$_2$B$_2$C and YNi$_2$B$_2$C. Andreev conductance spectra are obtained from nanoscale metallic junctions on single crystal surfaces prepared along three major crystallographic orientations: [001], [110], and [100]. The gap values extracted by the single-gap Blonder-Tinkham-Klapwijk model follow the BCS predictions as a function of temperature and magnetic field and exhibit a small anisotropy. These observations are robust and reproducible among all the measurements on two different sets of …
We present studies of the magnetic field distribution around the vortices in LuNi2B2C. Small-angle neutron scattering measurements of the vortex lattice (VL) in this material were extended to unprecedentedly large values of the scattering vector q, obtained both by using high magnetic fields to decrease the VL spacing and by using higher order reflections. A square VL, oriented with the nearest neighbor direction along the crystalline [110] direction, was observed up to the highest measured field. The first-order VL form factor, |F(q10)|, was found to decrease exponentially with increasing mag…
Recently, Mun et.al. (Phys. Rev. Lett., 76, 2790 (1996)) have published their results on single crystal YNi_2B_2C, claiming that their experimental observations can be explained in terms of formation of Vortex Glass and Lattice melting. Our experiments, carried out on samples obtained from the SAME source, reveal a much richer phase diagram and span wider regions of experimental parameter space than Mun et. al. that encompasses most of their observations. We speculate that this material has anomalous intrinsic properties and the results cannot be explained by simple models about the flux latti…
We have studied the pinning force density Fp of YNi_2B_2C superconductors for various field orientations. We observe anisotropies both between the c-axis and the basal plane and within the plane, that cannot be explained by usual mass anisotropy. For magnetic field $H \parallel c$, the reorientation structural transition in the vortex lattice due to nonlocality, which occurs at a field $H_1 \sim 1kOe$, manifests itself as a kink in Fp(H). When $H \bot c$, Fp is much larger and has a quite different H dependence, indicating that other pinning mechanisms are present. In this case the signature o…
Measurements of the rf penetration depth λ(T,H,θ) are used to study the superconducting order parameter, vortex dynamics in the mixed state and delineate critical fields in the borocarbide superconductor YNi_2B_2C. The lower critical field has an anomalous T dependence, H_{c1}(T)=1.12[1-(T/T_c)] kOe, which is however consistent with independent superfluid density measurements at microwave frequencies. The vortex response is dominated by viscous flux flow, indicative of extremely weak pinning, and is parametrized by a field scale H_{c2,eff}. The angular dependence of the vortex contribution λ(θ…
We have studied the field-orientational dependence of zero-energy density of states (FODOS) for a series of systems with different Fermi surface and superconducting gap structures. Instead of phenomenological Doppler-shift method, we use an approximate analytical solution of Eilenberger equation together with self-consistent determination of order parameter and a variational treatment of vortex lattice. First, we compare zero-energy density of states (ZEDOS) when a magnetic field is applied in the nodal direction ($ν_{node}(0)$) and in the antinodal direction ($ν_{anti}(0)$), by taking account…
Vortex lattice (VL) elastic response is analyzed within nonlocal London model. The squash modulus turns zero at the field $H_{\Box}$ where VL undergoes square-to-rhombus structural transition. In the field region $H>H_{\Box}$ where the square VL is stable, the rotation modulus turns zero at a field $H_r$ indicating instability of the square VL with respect to rotations. The shear modulus depends on the shear direction; the dependence is strong in the vicinity of $H_{\Box}$ where the square VL is soft with respect to the shear along [110]. The $H$ dependences of elastic moduli are evaluated for…
The physics behind the rhombic$\to$square$\to$rhombic flux line lattice transformation in increasing fields is clarified on the basis of Eilenberger theory. We demonstrate that this reentrance observed in LuNi$_2$B$_2$C is due to intrinsic competition between superconducting gap and Fermi surface anisotropies. The calculations reproduce not only it but also predict yet not found lock-in transition to a square lattice with different orientation in higher field. In view of physical origin given, this sequence of transitions is rather generic to occur in four-fold symmetric superconductors.
The microwave complex surface impedance Z_s of Y(Ni_{1-x}Pt_x)_2B_2C was measured at 0.5 K under magnetic fields H up to 7T. In nominally pure YNi_2B_2C, which is a strongly anisotropic s-wave superconductor, the flux flow resistivity ρ_f calculated from Z_s was twice as large as that expected from the conventional normal-state vortex core model. In Pt-doped samples where the gap anisotropy is smeared out, the enhancement of ρ_f is reduced and ρ_f approaches to the conventional behavior. These results indicate that energy dissipation in the vortex core is strongly affected by the anisotropy of…
