The PDF file includes:

• Section S1. Sample characterizations
• Section S2. Interplay between superconductivity and ferromagnetism in EuFe₂(As_0.79P_0.21)₂: Supplementary MFM maps
• Section S3. Energy balance between FM and SC states
• Section S4. Simultaneous V-AV nucleation at FM domain boundaries
• Fig. S1. Resistance temperature dependence.
• Fig. S2. M(H) and χ(T) curves acquired on EuFe₂(As_0.79P_0.21)₂ crystal.
• Fig. S3. Full set of images of spontaneous V-AV generation.
• Fig. S4. Full set of maps demonstrating the domain structure evolution at DMS/DVS transition.
• Fig. S5. The total energy of the domain structure Ẽ_DS in the Meissner and normal states.
• Fig. S6. Schematics of the local V-AV nucleation.
• References (32–38)

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Other Supplementary Material for this manuscript includes the following:

• Movie S1 (.mp4 format). Movie of the local V-AV nucleation and domain structure evolution at DMS/DVS.