## 3 Experiments
### Experimental Results
In order to quantify neutron spin interaction of the trapped field, it was calculated for each \(\text{B}_{\text{trap}}=\text{B}_{\text{trap}}(\text{f}\), offset) in 0\({}^{\circ}\) sample orientation, which provided clearer information than the 90\({}^{\circ}\) sample orientation (not shown here). Figure 3: Nb\({}_{oxid}\) sample: orientation 0\({}^{\circ}\), \(\text{B}_{\text{offset}}=\) 0 mT...5 mT (horizontal images) and increasing AC-frequency f = 0.1 Hz, 0.25 Hz and 0.5 Hz (vertical images), blue \(\sim\)0.5 and red \(\sim\)0.9 normalized intensity, see text. Figure 4: Nb\({}_{\rm{bak}}\) sample orientation 0\({}^{\circ}\), B\({}_{\rm{offset}}\) = 0 mT...5 mT (horizontal images) and increasing AC-frequency f = 0.1 Hz, 0.25 Hz and 0.5 Hz (vertical images), yellow boxes show the projected volumes of yellow circles in Figure 6, blue \(\sim\)0.5 and red \(\sim\)0.9 normalized intensity, see text. Figure 5: Nb\({}_{\rm{axial}}\) sample orientation 90\({}^{\circ}\), B\({}_{\rm{offset}}\) = 0 mT...5 mT (horizontal images) and increasing AC-frequency f = 0.1 Hz, 0.25 Hz and 0.5 Hz (vertical images), blue \(\sim\)0.5 and red \(\sim\)0.9 normalized intensity, see text. Figure 6: Nb\({}_{\rm{bak}}\) sample orientation = 90\({}^{\circ}\), B\({}_{\rm{offset}}\) = 0 mT...5 mT (horizontal images) and increasing AC-frequency f = 0.1 Hz, and 0.25 Hz and 0.5 Hz (vertical images), blue \(\sim\)0.5 and red \(\sim\)0.9 normalized intensity, see text. The best agreement with the experimental data was found under the assumption that the trapped field behaves similar to that of a magnetized coil. The 2D projection images of the 3D trapped fields (see Figure 2) were calculated and compared with the experimental ones, using line plots, as is shown in Figures 7 and 8. As can be seen, the trapped field is always larger than the nominal size of the external field, due to the AC contribution. This behavior suggests the assumptions of an homogeneously trapped field and of a possible frequency dependency of field trap, which is best seen for the offset = 4 mT and 5 mT; however, a general frequency dependence can not yet proven. Figure 8: AC f = 0.5 Hz, Nb\({}_{oxid}\), trapped field experiments and calculations, trapped field as function of offset field B = 0 mT...5 mT (compare third row in Figure 3), blue \(\sim\)0.5 and red \(\sim\)0.9 normalized intensity, line plots correspond to projections onto the vertical axis of the 2D plots within the central areas. Figure 7: AC f = 0.1 Hz : trapped field experiments and calculations, sample = Nb\({}_{oxid}\), trapped field B = Br\({}_{trap}\) as function of offset field B = 0 mT...5 mT (compare first row in Figure 3), blue \(\sim\)0.5 and red \(\sim\)0.9 normalized intensity, line plots correspond to projections onto the vertical axis of the 2D plots within the central areas. It was necessary to prove whether a frequency dependence of magnetic flux trapping another calculation was applied to the data. If flux trapping depends on applied AC fields, then the size of trap in a given sample volume is supposed to change with frequency. For this purpose, the central area (pixel field) of all images were selected and the size of the trapped flux was determined as a function of the AC field and frequency. If there is a frequency dependency, the magnitude of the trapped field in the sample must change with AC-frequency for a given offset field. For this reason, 32 pixel \(\times\) 32 pixel = 1024 pixel (1.37 mm \(\times\) 1.27 mm = 1.89 mm\({}^{2}\)) of each image in Figure 3 (sample orientation 0\({}^{\circ}\)) and in Figure 5 (sample orientation 90\({}^{\circ}\)) were selected from the central area and the intensities were summed up (integrated). If one plots integrated intensity of the trapped field of the central area (1024 pixel) of the images in Figure 3 (Nb\({}_{oxid}\), sample orientation = 0\({}^{\circ}\)) and Figure 5 (Nb\({}_{oxid}\), sample orientation = 90\({}^{\circ}\)) vs. the offset field for f = 0.1 Hz, 0.25 Hz and 0.5 Hz, corresponding graphs must remarkably differ from each other.