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We present a mechanism for deterministic control of the Bloch chirality inmagnetic domain walls and skyrmions, originating from the interplay between aninterfacial Dzyaloshinskii$-$Moriya interaction (DMI) and a perpendicularmagnetic field. Although conventional interfacial DMI favors chiral N\'eelskyrmions, it does not break the energetic symmetry of the two Blochchiralities in mixed Bloch$-$N\'eel skyrmions. However, the energy barrier toswitching between Bloch chiralities does depend on the sense of rotation, whichis dictated by the direction of the driving field. Our analytical andmicromagnetic analyses of steady-state Dzyaloshinskii domain wall dynamicsculminates in a switching diagram akin to the Stoner$-$Wohlfarth astroid,revealing the existence of achiral, chiral, and precessional Bloch regimes; wefurther show that in view of established energetic models, skyrmions shouldexhibit the same fundamental behavior. Finally, we discuss a recent theory ofvertical Bloch line$-$mediated deterministic Bloch chirality in theprecessional regime and extend these arguments to lower driving fields. Thiswork establishes that the Bloch chirality of magnetic solitons can be switchedon demand with applied fields, as indicated by the Dzyaloshinskii astroid.

Deterministically switching the Bloch chirality of domain walls and skyrmions: the Dzyaloshinskii astroid