Peak Effect in Polycrystalline Vortex Matter

We report a study of the peak-effect phase diagram of a strongly disordered type-II superconductor V-21 at. %Ti using ac magnetic susceptibility and small-angle neutron scattering (SANS). In this system, the peak effect appears only at fields higher than 3.4 T. The sample is characterized by strong atomic disorder. Vortex states with field-cooled thermal histories show that both deep in the mixed state, as well as close to the peak effect, there exist no long-range orientationally ordered vortex lattices. The SANS scattering radial widths reveal vortex states ordered in the sub-$\mu \mathrm{m}$ scale. We conjecture that the peak effect in this system is a remnant of the Bragg glass disordering transition, but occurs on submicron length scales due to the presence of strong atomic disorder on larger length scales.

Figure 1

Three-dimensional (3D) magnetic field and temperature dependence of the real part of the ac susceptibility $4\pi {\chi }^{\prime }(T)$. Field-cooling scans, performed with $H_{\mathrm{ac}}=58\mathrm{Oe}$ at $f=107\mathrm{Hz}$. The color codes highlight the normal (red) and superconducting phases (blue). Inset: SEM image of a heavily etched sample surface. The visible domains (termed “phase $A$”) contain approximately 20% titanium. The etched grooves surrounding phase $A$ domains show the extent of a second phase (phase $B$), with elevated titanium content.

Figure 2

Phase diagram constructed from the $4\pi {\chi }^{\prime }(T)$ data (shown in Fig. 1). The filled green and empty blue circles correspond to the occurrences of the peak effect and the bulk superconducting transitions below and above the peak effect ($H_{c2}$ and $T_{c2}$, respectively). $H_{c2}$ and $T_{c2}$ are defined to be at the temperature, at which $4\pi {\chi }^{\prime }=-0.001$. The filled green square is extracted from the ultrasonic attenuation $\alpha$ vs $H$ at $T=1.5\mathrm{K}$ scan of Shapira and Neuringer, performed on the same sample [15]. Inset: typical $4\pi {\chi }^{\prime }(T)$ scan for fields at which the peak effect is readily visible ($H=5.5\mathrm{T}$). The points marked in pink and violet are the locations of the peak effect and $T_{c2}$ shown at $H=5.5\mathrm{T}$ in the phase diagram.

Figure 3

(a)–(e) SANS images taken on FC deep in the mixed state of V-Ti, at $T=4.2\mathrm{K}$, $H=0.4\mathrm{T}$, and turning angle (a) $\varphi =0.50°$, (b) $\varphi =0.25°$, (c) $\varphi =0.00°$, (d) $\varphi =-0.25°$, and (e) $\varphi =-0.50°$. The intensity maximum occurs at $Q_r=0.009173\pm 0.000192{\AA }^{-1}$, whereas the expected value for a hexagonal Abrikosov lattice is $Q_r=0.009386{\AA }^{-1}$ [18].

Figure 4

(a)–(b) SANS images taken closer to the peak-effect regime, at $H=3.7\mathrm{T}$, $T=3.6\mathrm{K}$. (a) $\varphi =0.25°$ and (b) $\varphi =0.75°$. (c) Radial averages of the scattered intensity at 0.4 T (black, squares) and 3.7 T (red, circles). At high field the radial width is resolution limited, implying higher degree of translational order at high field.