Muons as Local Probes of Three-Body Correlations in the Mixed State of Type-II Superconductors

The vortex glass state formed by magnetic flux lines in a type-II superconductor is shown to possess nontrivial three-body correlations. While such correlations are usually difficult to measure in glassy systems, the magnetic fields associated with the flux vortices allow us to probe these via muon-spin rotation measurements of the local field distribution. We show via numerical simulations and analytic calculations that these observations provide detailed microscopic insight into the local order of the vortex glass and more generally validate a theoretical framework for correlations in glassy systems.

Figure 1

The field distribution function $n(B)$ for two values of the applied magnetic field $H$ at $T=5\mathrm{K}$: (a) $H=40\mathrm{mT}$ and (b) $H=0.5\mathrm{T}$. The insets show the same data, plotted over the same range, with the $y$ axis plotted on a logarithmic scale, indicating the errors on the points. The curves are normalized at the mode of the distribution, $B_{pk}$.

Figure 2

The line shape anisotropy ratio $\alpha$ as obtained in (i) experiments at 5 K (black circles), (ii) calculated from Monte Carlo simulations of disordered structures (red crosses), and from (iii) a theoretical description in terms of liquid state theory (blue squares connected by a solid line).

Figure 3

Regimes in $H\mathrm{\text{−}}T$ space associated with a fixed sign of $\alpha =⟨[\Delta B{]}^3{⟩}^{1/3}/⟨[\Delta B{]}^2{⟩}^{1/2}$, and thus of the third moment. The inset shows the schematic phase diagram for this system in $H\mathrm{\text{−}}T$ space, obtained from a combination of muon-spin rotation and magnetic and small angle neutron scattering measurements [6]. The change of sign of $\alpha$ reported here occurs deep within the vortex glass phase shown in the inset (dotted line in inset) and over a fairly short range in field and temperature.

Figure 4

Contours of constant magnetic field strength $B(r)$ computed for (a) a perfect Abrikosov lattice at $B=0.5\mathrm{T}$ and (b) a disordered state with a translational correlation length of about 4 intervortex spacings generated using simulated annealing techniques, with $\gamma /{\gamma }^{\prime }=3$ (see text). In (c) is shown a plot of the structure factor $S(q)$, obtained analytically as described in the text ($q$ is given in units of the inverse mean interparticle spacing).