Motivated by recent theoretical predictions of a square-shaped skyrmion lattice (S-SkL) in centrosymmetric tetragonal Ce-based magnets [Y. Zha and S. Hayami, Phys. Rev. B 111, 165155 (2025)], we perform a comprehensive theoretical investigation into the role of multiorbital effects and momentum-based frustrated exchange interactions in stabilizing such topologically nontrivial magnetic textures. By employing self-consistent mean-field calculations over a broad range of model parameters, we demonstrate that the cooperative interplay among interorbital coupling, frustrated exchange interactions at higher-harmonic wave vectors, and crystal-field-induced anisotropy is crucial for the stabilization of the S-SkL. Furthermore, the competition between the easy-plane intraorbital anisotropy and the easy-axis interorbital anisotropy leads to a significant enhancement of the S-SkL stability region. We also identify a rich variety of multi-$Q$ states, including a topologically nontrivial S-SkL state with a slight breaking of fourfold rotational symmetry $\left({\mathrm{S}\text{−}\mathrm{SkL}}^{\prime }\right)$, magnetic bubble lattices (MBLs), and double-$Q$ phases with a local/net scalar chirality. Our findings elucidate the microscopic mechanism responsible for the emergence of S-SkLs in prototypical Ce-based magnets and provide a route toward realizing skyrmion lattices in a broader class of $f$-electron materials beyond conventional Gd- and Eu-based systems lacking orbital angular momentum.

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• Exchange interaction
• Frustrated magnetism
• Magnetic anisotropy
• Magnetic order
• Magnetic phase transitions
• Magnetic texture
• Multipole order
• Skyrmions
• Spin-orbit coupling
• Rare-earth ions
• Square lattice
• Magnetic moment
• Crystal-field theory
• Heisenberg model
• Mean field theory