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We investigate the vortex lattice configuration in a rotating spinorbit-coupled spin-2 Bose-Einstein condensate confined in aquasi-two-dimensional harmonic trap. By considering the interplay betweenrotation frequency, spin-orbit couplings, and inter atomic interactions, weexplore a variety of vortex lattice structures emerging as a ground statesolution. Our study focuses on the combined effects of spin-orbit coupling androtation, analyzed by using the variational method for the single-particleHamiltonian. We observe that the interplay between rotation and Rashbaspin-orbit coupling gives rise to different effective potentials for thebosons. Specifically, at higher rotation frequencies, isotropic spin-orbitcoupling leads to an effective toroidal potential, while fully anisotropicspin-orbit coupling results in a symmetric double-well potential. To obtainthese findings, we solve the five coupled Gross-Pitaevskii equations for thespin-2 BEC with spin-orbit coupling under rotation. Notably, we find that theantiferromagnetic, cyclic, and ferromagnetic phases exhibit similar behavior athigher rotation.

Vortex Lattice Formation in Spin-Orbit-Coupled Spin-2 Bose-Einstein Condensate Under Rotation