Domain structure and magnetic pinning in ferromagnetic/superconducting hybrids

Magnetic patterns in three iron-garnet films with different magnetic properties covered with 100-nm superconducting Nb film are studied using a magneto-optical imaging technique. In all samples the strong coupling between ferromagnetic domains and vortices noticeably modifies the magnetization process. However, depending on the type and width of the magnetic domains, we observe different flux dynamics in the Nb film. Wide domains give rise to a combined domain structure and type I–like superconducting response resulting in enhanced attenuation of the flux motion due to cooperative pinning of vortices and magnetic domain walls. These combined domains strongly shrink in the ac fields due to a dynamic instability triggered by oscillating domain walls. Combined domains formed on narrow magnetic domains do not shrink but they guide the motion of vortices and, in turn, align in the vortex motion direction. This introduces superconducting current anisotropy due to strong pinning on the magnetic domain walls. Irregular magnetic domain structures with immobilized domain walls stochastically modify the vortex entry patterns. The presence of magnetic domains essentially arrests thermomagnetic avalanches in the superconducting layer. The studied magnetic pinning has a good potential for slowing down vortices in high-$T_c$ superconductors.

Figure 1

Magnetization loops of the garnet film with wide domains in the perpendicular (a) and in-plane and (b) fields at temperatures indicated in the figures. At temperatures below 30 K the signal becomes noisy due to the strongly increased paramagnetic substrate contribution.

Figure 2

Temperature dependence of the saturation magnetization for the garnet film with wide domains constructed using $M$($H$) data in perpendicular fields.

Figure 3

Temperature variations of the domain width $D$ in the garnet film with wide domains. (a) Magneto-optical pictures of domains at different $T$. (b) $D$($T$) dependence. (Inset) The width of domains in the bare garnet and Nb/garnet areas of the sample after the AC equilibration as described in the text. Results of several cooling runs are shown by different colors.

Figure 4

AC-equilibrated domain structure at $T<T_c$ near the boundary of the Nb-covered garnet film with wide domains. The boundary between the bare garnet film (on the left) and Nb-covered area (on the right) is shown by white line.

Figure 5

DC remagnetization of the sample with wide domains in the perpendicular field at 6.2 K. The Nb film is on the right from black line shown in (a). Domain patterns in increasing [(a)–(e)] and decreasing [(f)–(h)] fields. The remagnetization proceeds through the expansion and contraction of appropriate coupled domains.

Figure 6

Remagnetization of the sample with wide domains at 6.2 K when the garnet film is saturated (compare with Fig. 5). The field increased [(a)–(d)] to a maximum of 800 Oe (not shown) and then decreased to 0 in the absence of domains showing a traditional exit of vortices near the Nb edge [(e) and (f)]. Successive increase of negative field nucleates domains, which abruptly expand leaving narrow unfavorable domains [white lines in (h)]. Reduction of field after saturation in -800 Oe yields the trapped flux pattern (i) similarly to (f). Nucleation of domains in a positive field (j) and then decreasing $H$ restores the combined domain remagnetization scenario.

Figure 7

DC remagnetization of the sample with wide domains at 4.5 K. The process in the increasing $H$ [(a)–(d)] is qualitatively similar to that at larger $T$ (Figs. 5 and 6). However, the vortex pinning is increased and chaotically shooting thermomagnetic avalanches appear at reducing field from the saturated state [irregular dark and bright lines on the right of (e)–(h)].

Figure 8

Arrest of the thermomagnetic avalanches appearing in the AC field in the hybrid samples with wide (a) and narrow (b) domains compared to the same Nb film deposited on glass (c).

Figure 9

(a) $M$($H$) loops in the perpendicular field, (b) temperature dependence of the saturation magnetization 4π$M_s$ ($T$), and (c) in-plane magnetization curves for the sample with narrow domains.

Figure 10

DC magnetization of the sample with narrow domains at 4.5 K. Wight line shows the boundary between the bare garnet (right) and Nb covered (left) areas. Values of $H$ are shown on the pictures.

Figure 11

DC remagnetization of the sample with narrow domains at decreasing [(a) and (b)] and changing polarity of the field [(c)–(f)] after saturation in $H$ $=$ $+$600 Oe. $T=4.5$ K. Fields are shown in the left top corners of the pictures.

Figure 12

Development of the combined domain structure in an applied AC field. The initial partially saturated state (a) is obtained after removal of $H_{\mathrm{DC}}$ $=$ 500 Oe at 4.5 K. A 17-Hz AC field is applied perpendicular to the film surface. The amplitude is increasing from 0 to 8.8, 19.8, 48, 120, and 190 Oe in panels (a)–(f), respectively. After jumpwise appearance of new domains they remain practically immobile in the AC field [(b)–(e)]. Some oscillations of domains appear at large field amplitudes in the Nb area near channels of the enhanced vortex dynamics [blurred lines on the left in (f)].

Figure 13

Temperature dependence of the saturation magnetization in the Tb-garnet film.

Figure 14

Domain structure in the Tb-garnet film at 9 K. Panels (a) and (b) show the same place in the sample before and after application and removal of a perpendicular field of 1 kOe.

Figure 15

Flux penetration (bright color) from the edge of the Nb film [black line in (a)] deposited on the Tb-garnet. $T$ $=$ 4.4 K. Values of the increasing normal field are shown on the pictures.

Figure 16

Differences of flux images showing the advancement of the vortex penetration front at 4.4 K on increasing field from 0 to 5.5 Oe. Panels (a) and (b) are obtained in the same conditions but with different domain structures in the Tb-garnet changed as shown in Fig. 14. A close similarity and modest variations of the patterns (front shape and depth of penetration) show the domination of the pinning by defects in the Nb film.

Figure 17

Energy $E$ of combined domains as a function of their width $D$. Solid (red) line corresponds to Eq. (12) for the tunable number of vortices in domains with the parameter $4d_F{(M-{\varepsilon }_0{d}_s/{\Phi }_0{d}_F)}^2/{\sigma }_{\mathrm{DW}}=0.3$. Dashed (black) line corresponds to Eq. (16) for the constant number of vortices in domains with the parameter $N^2{\Phi }_0^2/16d_F{\sigma }_{\mathrm{DW}}=3.8$.

Figure 18

MOI image of combined domains at 5 K after application of $H_{\mathrm{AC}}$(17 Hz) $=$ 90 Oe and intensity profiles (insets) revealing variations of $B_z$ across the domains. Profiles are measured in rectangles outlined by white lines. SC area is below the line marking the Nb edge. Average $B_z$ is larger in wide domains and increases towards DWs. $B_z$ is smaller and smoothly decays toward DWs in shrunken domains.