Direct Observation of the Flux-Line Vortex Glass Phase in a Type II Superconductor

The order of the vortex state in ${\mathrm{La}}_{1.9}{\mathrm{Sr}}_{0.1}{\mathrm{CuO}}_4$ is probed using muon-spin rotation and small-angle neutron scattering. A transition from a Bragg glass to a vortex glass is observed, where the latter is composed of disordered vortex lines. In the vicinity of the transition the microscopic behavior reflects a delicate interplay of thermally induced and pinning-induced disorder.

Figure 1

(a) Temperature-dependent probability distributions of the internal field, $p(B)$, due to the presence of the flux lines at applied fields of (a) 80 Oe and (b) 6 kOe. (c) Field distributions derived from Monte Carlo simulations of the vortex state at 6 kOe (see text) for the case of: (i) an ideal vortex lattice ; (ii) a VG phase with a transverse correlation length of about six lattice spacings. The latter also includes a small contribution due to the effects of thermal narrowing (as observed experimentally). All curves in the figure are normalized at the mode of the distribution to allow easy comparison of the shapes.

Figure 2

(a) The variation with field of the linewidth $\sigma$ at selected temperatures. The initial reduction with increasing field corresponds to the field dependent influence on the field distribution of both thermal fluctuations and increasing elastic vortex interactions. Above $B_{\mathrm{cr}}\sim 1\mathrm{kOe}$, the width dramatically rises due to the onset of static disorder in the VG phase. Note that the high-field dependence has almost disappeared by a temperature of 23 K, and disappears completely at the irreversibility line (see Fig. 4).

Figure 3

(a) A small angle neutron diffraction pattern showing the existence of an ordered vortex phase at low fields (150 Oe) and temperature (6.2 K). The intensity of this pattern rapidly falls as the field is increased towards the VG phase (see text). (b) The feature in the magnetization at 16.5 K is associated with the crossover to the VG state, measured on a small piece taken from the $\mu \mathrm{SR}$ sample. The inset shows a complete hysteresis loop.

Figure 4

The magnetic phase diagram derived from the changes observed in the $\mu \mathrm{SR}$ field distributions. $B_{\mathrm{cr}}(T)$ indicates the onset of the broadening at high field, which is significant only below $\sim 25\mathrm{K}$, and should be considered as an upper limit for the BG-VG transition (see text). This uncertainty in the exact position of the transition is represented schematically by the shading below the line $B_{\mathrm{cr}}(T)$. $B_{\mathrm{irr}}(T)$ indicates the irreversibility line as determined by bulk measurements of the field-cooled–zero-field-cooled (FC-ZFC) magnetisation using a SQUID magnetometer. The position of the feature in the magnetisation curves $B_{\mathrm{on}}(T)$ is also plotted [see Fig. 3b].