Generic skyrmion phase diagram in ferrimagnetic films

Ferrimagnetic skyrmions offer enhanced tunability due to antiferromagnetically coupled sublattices and reduced net magnetization. In chiral magnetic films at zero magnetic field, skyrmion stability is commonly characterized by a dimensionless parameter $\kappa$, yet its applicability to ferrimagnetic systems remains unclear, as most studies assume a fixed, strong inter-sublattice exchange coupling $J$. Here we investigate how variations in $J$ govern relaxed stable and metastable ferrimagnetic skyrmion configurations and introduce a dimensionless parameter $\zeta_{eff}$ to characterize the crossover between strong and weak inter-sublattice locking. In the strong-coupling regime, inter-sublattice locking enables stabilization of skyrmion in a sublattice where intrinsic Dzyaloshinskii-Moriya interaction is absent while the other sublattice has finite DMI, yielding a sublattice with DMI-free ferrimagnetic skyrmions. As $J$ decreases, this locking breaks down, leading to independent sublattice behavior and the failure of an effective $\kappa$-based description. Our results establish a unified framework linking inter-sublattice exchange and skyrmion phase stability in ferrimagnetic systems.