  This investigation delves into the intricate entanglement dynamics exhibited
by qubit-qutrit systems when subjected to the intricate dynamics of both the
XXX isotropic Heisenberg model and the anisotropic XYZ model. These models are
enriched by the presence of Dzyaloshinskii-Moriya (DM) interactions and
external magnetic fields, creating a complex interplay of quantum phenomena.
The exploration commences by initializing the system in a superposition of
spin-coherent states, setting the stage for a nuanced analysis of entanglement
evolution over time. By employing the negativity metric as the pivotal
criterion for assessing entanglement, we gain insights into the subtle
relationships between DM interactions, external magnetic fields, and the
entanglement dynamics within this composite system. Through this comprehensive
investigation, we aim to unravel the intricate dynamics and behaviors that
emerge from the interplay of these fundamental elements, shedding light on the
underlying principles governing quantum entanglement in this context.
