Fig. 5: A 3D visualization of the needle domain.

a This needle domain forms around an embedded defect in our micromagnetic computations. b The inset figure shows the needle domain with distinct surfaces (marked by surface-normal vectors n1, n2). The surface n1 approximately satisfies the strain-compatibility condition, however, the surface n2 is not compatible and contributes to nonzero elastic energy in the system. The magnetization is denoted by m.