Composite cores of monopoles and Alice rings in spin-2 Bose-Einstein condensates

Topologically stable point defects analogous to t'Hooft-Polyakov monopoles are known to undergo a core instability resulting in a half-quantum vortex (HQV) ring or Alice ring, recently experimentally observed in a spin-1 Bose-Einstein condensate (BEC). In this work, we characterize the relaxation and dynamics of monopole solutions in a spin-2 BEC. In the uniaxial-nematic (UN) phase, we show that an isolated monopole deforms into a spin-Alice ring with composite core, i.e., with distinct topologies at short and long distances from the singular ring. This is characterized by an outer biaxial-nematic (BN) core with spin-HQV structure, and an inner UN core. Numerical simulations tuned to experimental conditions reveal the presence of dynamical oscillations between the spin-Alice ring and a split-core hedgehog configuration, mediated by ferromagnetic rings carrying mass vorticity within the extended core region. Monopoles can also be associated with an integer spin-vortex line in the BN and cyclic phases. Relaxation of these defects in the BN case leads to spin-Alice rings penetrated by the spin-vortex line, similarly exhibiting dynamical oscillations. In the cyclic phase, monopoles/spin-vortex excitations relax instead to core structures with complex phase interplays, reflecting the various order-parameter configuration symmetries.