CP(2) skyrmions and skyrmion crystals in realistic quantum magnets

Magnetic skyrmions are nanoscale topological textures that have been recently observed in different families of quantum magnets. These objects are called CP(1) skyrmions because they are built from dipoles—the target manifold is the 1D complex projective space, CP(1) ≅ S(2). Here we report the emergence of magnetic CP(2) skyrmions in a realistic spin-1 model, which includes both dipole and quadrupole moments. Unlike CP(1) skyrmions, CP(2) skyrmions can also arise as metastable textures of quantum paramagnets, opening a new road to discover emergent topological solitons in non-magnetic materials. The quantum phase diagram of the spin-1 model also includes magnetic field-induced CP(2) skyrmion crystals that can be detected with regular momentum- (diffraction) and real-space (Lorentz transmission electron microscopy) experimental techniques.