Maintaining the magnetic field in gas giants in the future?

Let's set a planetary system similar to the Solar system in the far future, where the gas giants have cooled down significantly.

Eventually, would the fluid metallic hydrogen layer solidify?

And if it does, would it maintain the metallic conducting properties that would induce currents to keep producing a magnetic field (even if it were weaker)?

For example, if a big gas giant (or even a brown dwarf) despite being cold still induced a lot of pressure so that we would have a solid metallic hydrogen layer and a fluid metallic helium layer, would the shear between these layers maintain the currents to keep the magnetic field going on?