Where do the electric charge carriers for the current for earth's magnetic field come from?
Although Temperature boundary conditions at the mantle do affect the dynamo that sustains itself in the earth's core, it is unlikely that the dynamo's genesis came out of polarized regions in the earth's mantle. 

Regardless of the manner of genesis of the core, it is now a self-sustaining dynamo where electric current creates a magnetic field which in turn generates electric current owing to rotation of the earth much as in an electric generator. If you want to read more about it in detail, I would recommend an excellent review paper by Prof. Binod Sreenivasan available at http://ceas.iisc.ernet.in/~bsreeni/currsci10.pdf