  Three-dimensional topological solitons attract a great deal of interest in
fields ranging from particle physics to cosmology but remain experimentally
elusive in solid-state magnets. Here we numerically predict magnetic
heliknotons, an embodiment of such nonzero-Hopf-index solitons localized in all
spatial dimensions while embedded in a helical or conical background of chiral
magnets. We describe conditions under which heliknotons emerge as metastable or
ground-state localized nonsingular structures with fascinating knots of
magnetization field in widely studied materials. We demonstrate magnetic
control of three-dimensional spatial positions of such solitons, as well as
show how they interact to form molecule-like clusters and possibly even
crystalline phases comprising three-dimensional lattices of such solitons with
both orientational and positional order. Finally, we discuss both fundamental
importance and potential technological utility of magnetic heliknotons.
