Observation of intermediate mixed state in high-purity cavity-grade Nb by magneto-optical imaging

Suppression of the occurrence of remanent vortices is necessary to improve the quality factor of superconducting resonators. In particular, the flux-expulsion dynamics in Nb during cooling has become of major interest to researchers focusing on superconducting cavities. To study the vortex states and their behavior in high-purity cavity-grade Nb, we used a magneto-optical imaging technique to perform real-space observations of the magnetic field distributions during the field-cooling and field-scanning processes. In the field-cooling process, the distributions were observed to undergo phase separation into vortex and Meissner regions, as would be expected in an intermediate mixed state (IMS). The vortex regions in the IMS, such as vortex bundles, tend to be larger in higher fields, in contrast to the Meissner regions, which experience shrinkage. In the field-scanning process, domelike field profiles, which indicate a geometrical barrier with very weak bulk pinning, were observed. The existence of the IMS suggests that cavity-grade Nb is in a type-II/1 superconductor regime, in which attractive interaction between vortices at a length scale of the penetration depth is crucial for the behavior of vortices.

Figure 1

(a) Schematic illustration of the MO imaging setup. Incident polarized light passing through a polarizer, green, and IR-cut filters from a white LED light source, is reflected at the mirror layer of the MO indicator. In the sensor layer of the indicator, the polarization angle rotates linearly depending on the magnitude of the vertical component of the local magnetic field $B$ at the position. In the crossed-Nicol configuration, therefore, a captured image reflects the distribution of $B$. Ideally, the intensity of the reflected light is proportional to $B^2$ after passing through the analyzer. (b) Our experimental processes of the $T$ scan and $H$ scan on the $H_{\mathrm{a}}\text{−}T$ plane.

Figure 2

(a) MO image of the IMS on the mirror-polished surface of the Nb crystal at $5.9\pm 0.05$ K after field cooling in 100 Oe. The two regions with different contrasts separated by zigzag lines are caused by the magnetic domains of the MO sensor. The crystallographic orientation of the Nb sample is indicated by a drawing of the unit cell. (b) MO image of the IMS at the center of the sample in a different experimental run with the same condition of the temperature and field as (a).

Figure 3

MO images of the IMS at higher magnification at $\sim 5.9$ K after field cooling in (a) 100 Oe, (b) 200 Oe, (c) 300 Oe, and (d) 400 Oe. All images are captured at the same position, which is not close to the sample edges. The orientation of the sample is the same as that in Fig. 2.

Figure 4

(a)–(c) Magnetic induction images at 8.3, 7.9, and 5.9 K, respectively, captured in 100 Oe in the $T$-scan process [see Fig. 1] at a position not close to the edges. (d) Temperature dependence of local magnetic induction $B_l\left(T\right)$ in a vortex bundle (red) and Meissner phase (green), the sampling positions of which are indicated in (c). The black circles show the averaged value of $B$ in each entire image. (e) Schematic illustration of phase separation from $T>T_{\mathrm{c}2}$ (right) to lower temperatures (left).

Figure 5

(a)–(d) $B$ images in 300, 320, 360, and 240 Oe, respectively, with increasing field up to 420 Oe and then decreasing field at 7.5 K [$H$-scan process in Fig. 1]. (e) Profiles on the red, blue, and green lines in (b)–(d), respectively, where the origin of the horizontal axis corresponds to the upper edge of the line. Domelike field profiles are observed at the center of the sample in (b) and (c). (f) Local magnetic induction $B_{\mathrm{l}}$ at the position marked by a red cross in (a), with increasing and decreasing applied field $H_{\mathrm{a}}$. The field where vortices start to rapidly penetrate the center is defined as the penetration field $H_{\mathrm{p}}$.

Figure 6

(a) Experimentally obtained temperature dependence of $H_{\mathrm{IMS}}$ (red squares), which is the upper boundary of the IMS, the penetration field of vortices $H_{\mathrm{p}}$ (black circles), and $H_{\mathrm{c}2}$ (blue circles and squares) in the single-crystal niobium. The black and blue solid lines indicate the temperature dependence of $H_{\mathrm{c}1}$ and $H_{\mathrm{c}2}$ obtained by Finnemore et al. [22]. The dashed line is $H_{\mathrm{c}1}$ scaled by a factor of 0.49, to fit to $H_{\mathrm{p}}$. The inset shows the temperature dependence of the lattice constant of the vortex lattice at the upper boundary of the IMS, which is converted from $B_{\mathrm{IMS}}\left(T\right)$. (b) Theoretical phase boundary between type II/2 (normal type II) and type II/1 in the $\kappa \text{−}T$ phase diagram.