Broadening of the superconducting transition by fluctuations in three-dimensional metals at high magnetic fields

The Bragg-chain model of the two-dimensional (2D) vortex state at high magnetic field [V. N. Zhuravlev and T. Maniv, Phys. Rev. B 60, 4277 (1999)] is extended to an array of coupled superconducting (SC) layers. Application to ${\mathrm{MgB}}_2$ and ${\mathrm{YNi}}_2{\mathrm{B}}_2\mathrm{C}$ yields good quantitative agreement with high-field magnetization measurements, indicating that the smeared transitions observed in these materials are, at least in great part, due to SC fluctuations. Similar to the situation in a 2D system, the melting of the vortex lattice in strongly coupled SC layers is predicted to occur well below the mean field $H_{c2}$.

Figure 1

(Color online) The spatially averaged mean-squared order parameter (measured in units of the 2D smearing parameter ${\alpha }_{0I}$) ${\Phi }_0\left(x\right)$ as a function of the dimensionless parameter $x=\alpha ∕\sqrt{2\beta {\beta }_a{k}_{B}T}$ (see text) around the mean-field (MF) transition point $x=0$ in the weak- and strong-coupling limits (solid lines). Dashed lines represent the corresponding results calculated from a simple interpolation formula (13). The result of 3D Monte Carlo simulation by Sasik and Stroud (Ref. 25) is shown as bold squares. The dotted straight line represents the result of mean-field theory. Inset: The derivative with respect to $x$ is plotted to emphasize the region where SC fluctuations are strong. Note the gross similarity between the two limiting curves within the main crossover region around the MF $H_{c2}$.

Figure 2

(Color online) Field dependence of the torque signal of a flux-grown ${\mathrm{YNi}}_2{\mathrm{B}}_2\mathrm{C}$ single crystal with the magnetic field rotated by $8^{°}$ from the $c$ axis towards the $a$ axis. The arrows indicate the field-sweep direction. The insets show the oscillating torque signal after background subtraction.

Figure 3

(Color online) (a) Dingle plot of the dHvA signal shown in Fig. 2 close to the SC transition (solid line) and the extrapolation of the corresponding Dingle plot from the normal state (dashed line). (b) Magnetization difference between the up and down sweep of the hysteresis loop shown in Fig. 2. Full triangles show the experimental data, while the solid lines represent best fits as described in the text. Both theoretical curves were obtained for ${\Delta }_0\simeq 7.6\mathrm{meV}$ and $H_{c2}\simeq 6.8\mathrm{T}$.