In the intermediate mixed state (IMS) of type-II/1 superconductors, vortex lattice (VL) and Meissner state domains coexist due to a partially attractive vortex interaction. Using a neutronbased multiscale approach combined with magnetization measurements, we study the continuous decomposition of a homogeneous VL into increasingly dense domains in the IMS in bulk niobium samples of varying purity. We find a universal temperature dependence of the vortex spacing, closely related to the London penetration depth and independent of the external magnetic field. The rearrangement of vortices occurs even in the presence of a flux freezing transition, i.e. pronounced pinning, indicating a breakdown of pinning at the onset of the vortex attraction.Conventional superconductors are divided by the Ginzburg-Landau parameter κ into type-I (κ < 1/ √ 2) and type-II (κ > 1/ √ 2), which, additionally to the Meissner state (MS) exhibit the Shubnikov state (SS). In the SS, magnetic vortices form a variety of vortex matter (VM), such as the Abrikosov vortex lattice (VL) [1], glassy [2][3][4] or liquid [5][6][7] states. Type-II superconductors are further subdivided, where type-II/2 (κ 1/ √ 2) features a purely repulsive inter-vortex interaction. In type-II/1(κ ≈ 1/ √ 2) the interaction acquires an attractive component [8][9][10], which favors the formation of vortex clusters, leaving behind MS regions. The resulting domain structure is denoted the intermediate mixed state (IMS).The IMS in the type-II/1 superconductor niobium (Nb) is an ongoing research topic since its first observation via Bitter decoration in 1967 [11,12]. Despite numerous experimental [9, 13-16] and theoretical [8, 10, 17, 18] efforts, its properties are not yet fully understood. The interplay of repulsive and attractive vortex interactions and the consequences on the domain structure in superconducting VM have found renewed interest with the discovery of multiband superconductors, especially MgB 2 (sometimes denoted as type-1.5) [19]. Apart from superconducting properties, the IMS is also a model system for universal domain physics [20], as it can be tuned readily by temperature and magnetic field [21].Previous studies primarily investigated the zero field cooled (ZFC) field dependence of the IMS. However, this approach leads to strong magnetic inhomogeneities due to geometric and demagnetization effects reflected in the critical state model [22,23]. In contrast, our systematic study focuses on the temperature dependence during a field cooling (FC) and subsequent field heating (FC/FH) protocol in bulk Nb samples with distinct pinning properties. The phase diagram and the transition from a ho- * alexander.Backs@frm2.tum.de † sebastian.muehlbauer@frm2.tum.de mogeneous VL in the SS to the increasingly dense VL domains in the IMS is sketched in Fig. 1 on a FC path.
FIG. 1.Schematic phase diagram of a type-II/1 superconductor, subdivided into MS, IMS and SS. Arrows depict different measurement protocols: FC, FC/FH and ZFC/FH. For FC measurements, the microscopic magnet...
