  Stacking transition metal dichalcogenides (TMDs) to form moir\'e
superlattices has provided exciting opportunities to explore many-body
correlation phenomena of the moir\'e trapped carriers. TMDs bilayers, on the
other hand, host long-lived interlayer exciton (IX), an elementary excitation
of long spin-valley lifetime that can be optically or electrically injected.
Here we find that, through the Coulomb exchange between mobile IXs and
carriers, the IX bath can mediate both Heisenberg and Dzyaloshinskii-Moriya
type spin interactions between moir\'e trapped carriers, controllable by
exciton density and exciton spin current respectively. We show the strong
Heisenberg interaction, and the extraordinarily long-ranged
Dzyaloshinskii-Moriya interaction here can jointly establish robust spin spiral
magnetic orders in Mott-Wigner crystal states at various filling factors, with
spiral direction controlled by exciton current.
