Real-Space Vortex Glass Imaging and the Vortex Phase Diagram of ${\mathrm{SnMo}}_6{\mathbf{S}}_8$

Using scanning tunneling microscopy at 400 mK, we have obtained maps of around 100 vortices in ${\mathrm{SnMo}}_6{\mathrm{S}}_8$ from 2–9 T. The orientational and positional disorder at 5 and 9 T show that these are the first large-scale images of a vortex glass. At higher temperature a magnetization peak effect is observed, whose upper boundary coincides with a lambda anomaly in the specific heat. Our data favor a kinetic glass description of the vortex melting transition, indicating that vortex topological disorder persists at fields and temperatures far below the peak effect in low-$T_c$ superconductors.

Figure 1

Vortex structure in ${\mathrm{SnMo}}_6{\mathrm{S}}_8$ at 400 mK imaged by STM at (a) 2, (b) 5, and (c) 9 T. Right panels: corresponding Delaunay triangulations with nearest neighbors linked by orange lines and topological defects highlighted with orange triangles. (d) Orientational correlation functions of the structures and a schematic of the angles considered for the calculation (see text). (e) Positional correlation functions and fits of the envelope using power-law (blue-dashed line, 2 T) and exponential (orange and purple-dashed lines, 5 and 9 T) decays. The maps were acquired with a $60\mathrm{M}\Omega$ junction using a lock-in technique [11].

Figure 2

(a) Critical current versus field in ${\mathrm{SnMo}}_6{\mathrm{S}}_8$ (solid lines) obtained from magnetization loops at different temperatures. The crossover from individual to collective vortex pinning is identified as a kink in the curves. Dashed lines: visual guides extrapolating the high-field $J_c(H)$. (b) Pinning crossover field $H_x(T)$. An exponential decay $a{e}^{-bT}+c$ extrapolates the fit to $T=0$.

Figure 3

(a) Magnetization hysteresis loops at $T=10–12.5\mathrm{K}$ using a VSM. Inset: Hysteresis loops from 12.5–14 K using the more sensitive SQUID. (b) Total specific heat in ${\mathrm{SnMo}}_6{\mathrm{S}}_8$ from 0–28 T (the sample remains in the normal state at 28 T above 4 K). The superconducting transition temperature $T_{c2}(H)$ is defined at the midpoint of the heat capacity jump. Right inset: Electronic specific heat $C_{\mathrm{elec}}=C(H)/T-C(28\mathrm{T})/T$ for 3.5–14 T. Dashed lines are linear mean-field extrapolations, arrows indicate melting at $T_{\mathrm{VM}}$ (see text). Left inset: 3D-LLL scaling (see text) of $C_{\mathrm{elec}}$ for 3.5–10.5 T.

Figure 4

Vortex phase diagram of ${\mathrm{SnMo}}_6{\mathrm{S}}_8$. Measured data are displayed by points, extrapolated zones with thin lines. Note that the only true thermodynamic phase transition at high fields is represented by the vortex melting line.