Fig. 3: Current-controlled reversible topological transformations occur between four unique phases within the FeNiPdP cuboid.

a Summary for current-controlled topological transformations among single antiskyrmion, skyrmion, bubble, and FM. Insets show the corresponding defocused Fresnel images. A single current pulse with j > jc4 deletes antiskyrmions, skyrmions, or bubbles. Writing requires single pulses: antiskyrmions with j ∈ [jc1, jc2], bubbles with j ∈ [jc2, jc3], and skyrmions with j ∈ [jc3, jc4]. Single-pulse transformations include: antiskyrmion to skyrmion (j ∈ [jc3, jc4]), antiskyrmion to bubble (j ∈ [jc2, jc3]), and bubble to skyrmion (j ∈ [jc3, jc4]). Two-step transformations require sequential pulses: skyrmion to antiskyrmion (first j > jc4 then j ∈ [jc1, jc2]), bubble to antiskyrmion (first j > jc4 then j ∈ [jc1, jc2]), and skyrmion to bubble (first j > jc4 then j ∈ [jc2, jc3]). b Pulse duration w dependence of threshold transformation current density jc. Magnetic field B, 385 mT. c Magnetic field B dependence of the threshold transformation current density jc. Pulse duration w, 40 ns. Field tilt angle, 1.5°. Temperature, 95 K.