Influence of rotating in-plane field on vertical Bloch lines in the walls of second kind of dumbbell domains

Influence of rotating in-plane field on vertical Bloch lines in the walls of second kind of dumbbell domains (IIDs) was investigated, and a critical in-plane field range [Hip1,Hip2] of which vertical-Bloch lines (VBLs) annihilated in IIDs is found under rotating in-plane field (Hip1 is the maximal critical in-plane-field of which hard domains remain stable, Hip2 is the minimal critical in-plane-field of which all of the hard domains convert to soft bubbles (SBs, without VBLs)). It shows that the in-plane field range [Hip1, Hip2] changes with the change of the rotating angle Δφ Hip1 maintains stable, while Hip2 decreases with the decreasing of rotating angle Δφ. Comparing it with the spontaneous shrinking experiment of IIDs under both bias field and in-plane field, we presume that under the application of in-plane field there exists a direction along which the VBLs in the domain walls annihilate most easily, and it is in the direction that domain walls are perpendicular to the in-plane field