  We investigate the vortex lattice configuration in a rotating spin
orbit-coupled spin-2 Bose-Einstein condensate confined in a
quasi-two-dimensional harmonic trap. By considering the interplay between
rotation frequency, spin-orbit couplings, and inter atomic interactions, we
explore a variety of vortex lattice structures emerging as a ground state
solution. Our study focuses on the combined effects of spin-orbit coupling and
rotation, analyzed by using the variational method for the single-particle
Hamiltonian. We observe that the interplay between rotation and Rashba
spin-orbit coupling gives rise to different effective potentials for the
bosons. Specifically, at higher rotation frequencies, isotropic spin-orbit
coupling leads to an effective toroidal potential, while fully anisotropic
spin-orbit coupling results in a symmetric double-well potential. To obtain
these findings, we solve the five coupled Gross-Pitaevskii equations for the
spin-2 BEC with spin-orbit coupling under rotation. Notably, we find that the
antiferromagnetic, cyclic, and ferromagnetic phases exhibit similar behavior at
higher rotation.
