  Wave fields with spiral phase dislocations carrying orbital angular momentum
(OAM) have been realized in many branches of physics, such as for photons,
sound waves, electron beams, and neutrons. However, the OAM states of magnons
(spin waves)$-$the building block of modern magnetism$-$and particularly their
implications have yet to be addressed. Here, we theoretically investigate the
twisted spin-wave generation and propagation in magnetic nanocylinders. The OAM
nature of magnons is uncovered by showing that the spin-wave eigenmode is also
the eigenstate of the OAM operator in the confined geometry. Inspired by
optical tweezers, we predict an exotic "magnetic tweezer" effect by showing
skyrmion gyrations under twisted magnons in exchange coupled
nanocylinder$|$nanodisk heterostructure, as a practical demonstration of
magnonic OAM to manipulate topological spin defects. Our study paves the way
for the emerging magnetic manipulations by harnessing the OAM degree of freedom
of magnons.
