dc and ac magnetic properties of thin-walled superconducting niobium cylinders

We report the results of an experimental study of the dc and ac magnetic properties of superconducting Nb thin-walled cylinders in parallel to the axis magnetic fields. The magnetization curves at various temperatures are measured. Surprisingly, at 4.5 K, for magnetic fields much lower than $H_{c1}$, avalanchelike jumps of the magnetization are observed. The position of the jumps is not reproducible and changes from one experiment to another, resembling vortex lattice instabilities usually observed for magnetic fields larger than $H_{c1}$. At temperatures larger than 6.5 K, the measured magnetization curves become smooth. ac response is measured in constant and swept dc magnetic fields. A phenomenological model that describes the ac response of the surface superconducting states is proposed. This model assumes that the observed ac response in dc fields larger than $H_{c2}$ is due to the relaxation of surface superconducting states with nonzero current in the walls to the state with zero current, and the existence of a critical current below which this relaxation is absent.

Figure 1

Sketch of the S2 sample. Here, $L_s=15$ mm, $W_s=3$ mm, and $2D=1.5$ mm are the substrate length, width, and thickness, respectively. Both dc and ac fields were parallel to $z$ axis. Dimensions are not to scale.

Figure 2

SEM images of the 100-nm films deposited at room temperature (top) and at 300${}^{\circ }$C (bottom).

Figure 3

Magnetization curves of the S1 type 240-nm sample at 4.5 and 6.5 K. (Top inset) $M_0\left(T\right)$ at $H_0=20$ Oe. (Bottom inset) Temperature dependence of $H_{c2}$ for this film.

Figure 4

Magnetization curves of S2 sample with thickness 300 nm at 4.5 and 7 K.

Figure 5

Expanded view of magnetization curves in low magnetic fields.

Figure 6

Minor magnetization loops at 4.5 and 6.5 K [(a) and (b), respectively]. The number near the traces designates a maximal field for a given loop. All measurements were done after ZFC. Data for 30 Oe in (a) are shifted for clarity. Minor magnetization loop with maximal $H_0=200$ Oe (c). Arrows show the direction changes of the magnetic field. The symbols in legend of (b) indicate maximal field for each loop.

Figure 7

The magnetic field inside the substrate as a function of the applied magnetic field. The plateau length characterizes the value of the critical current, $J_c$.

Figure 8

(Top) Magnetic moment of the S2 sample with wall thickness 60 nm as a function of the dc magnetic field at temperatures 4.5, 5.5, and 6.5 K. The inset shows the expanded view of ascending branch $M_0\left(H_0\right)$ at low fields. (Bottom) Normalized on the film thickness magnetization curves of two S2 samples with film thicknesses 60 and 300 nm at 4.5 K.

Figure 9

${\chi }_1\left(H_0\right)$ of S2 sample with film thickness 60 nm at 4.5 K measured in PBP mode.

Figure 10

$|{\chi }_3\left(H_0\right)|$ of the cylinder with 60-nm-thick walls at 4.5 K, frequencies 293 and 1465 Hz [(a) and (b), respectively] measured in PBP mode. Lines with “Exp” in the legend correspond to the experimental data, with “Sim” to the simulated data. Inset to (a) shows the part of unpinned SSS as a function of dc fields for two ac amplitudes. The “effective” part of the unpinned SSS increases with ac amplitude (see Discussions).

Figure 11

${\chi }_1\left(H_0\right)$ of the cylinder sample with 60-nm-thick walls at 4.5 K, frequencies 293 and 1465 Hz, ac amplitudes 0.04 and 0.2 Oe, and sweep rate 20 Oe/s.

Figure 12

Field dependence of the $|{\chi }_2|$ and $|{\chi }_3|$ of the S2 samples with 60-nm (top) and 120-nm (bottom) wall thickness at 6.5 K, frequency 293 Hz, ac amplitude 0.04 Oe, and sweep rate 20 Oe/s. Lines with “exp” correspond to experimental data, with “c” to simulated data (see Discussion).

Figure 13

Normalized magnetic field in the wall for shielded (1) and transparent (2) solutions of GL equations. The thickness of the wall $d/\lambda =3,D/d=5\times {10}^3$, the GL parameter $\kappa =1.5$, and the applied magnetic field $H_0/H_{c2}=0.003$. For this set of parameters, the solutions with shielding exist only for $H_0/H_{c2}<4\times {10}^{-3}$.

Figure 14

Normalized order parameter and magnetic field for surface states localized at the inner (1) and outer (2) sides of the wall. The total current in these states equals zero. The thickness of the film $d/\lambda =3$, the Ginzburg-Landau parameter $\kappa =1.5$, and the applied magnetic field $H_0/H_{c2}=1.4$.