Figure 2

MFM images at discrete magnetic fields and the corresponding arrow diagrams for the two samples (Fig. 1a,b) and description of magnetic charges. (a,c,e,g) are MFM images of the stained glass window sample (Fig. 1a) at \(\mu _0H_\text{{ext}}=\) 250 mT, − 10 mT, − 42.5 mT and − 45 mT, respectively. (b,d,f,h) are corresponding arrow diagrams clarifying the orientation of the net magnetizations in the nanomagnets. The circles at the central vertex position in (f,o) indicate emergent monopole-like magnetic charge excitations. (i,k,m,q) are MFM images of the deformed stained glass window sample (Fig. 1b) at \(\mu _0H_\text{{ext}}=\)250 mT, − 10 mT, − 35 mT and − 50 mT, respectively. (j,l,n–p,r), clarifies the orientations of magnetizations at the corresponding fields. The dotted stadium shapes in the MFM images indentify the actual shapes of the nanomagnets and the dotted (magenta) arrows in the arrow diagrams for both samples show the switched nanomagnets at the corresponding fields. (n–p) show the three switchings at the bias field of − 35 mT. (o,p) are tip-induced switchings (Fig. 2m) at tip scan line positions indicated by SW-I and SW-II while tip scanning in the downward direction. The charge distribution in units of \(Q_m\) in the monopole states for undeformed (s) and deformed stained glass window (t).