A lunar core and the moon's magnetic field
The suggestion that the moon's magnetic field is due to adiabatic magnetohydrodynamic convection of a molten core has been made by a number of recent authors. Considerations based on petrology, mass and rotational inertia limit the size of this hypothetical core to a few hundred kilometers at the most. A proposal has been made that this core is either molten iron or iron sulfide. The properties are known of both molten iron and iron-sulfide at lunar core pressures. No way can be found to maintain circulation in a hypothetical lunar core, as circulation is contingent upon a temperature gradient being greater than the adiabatic gradient, or an internal heat source.
Kennedy, G. C.↗