Electrons have magnetic dipole moment. This magnetic moment will be influenced in an electric field in case the electron get moved non-parallel to the current. The magnetic moments will be more or less aligned. During the movement of an electron in a wire under the influence of an electric potential, the electron has a chaotic movement, in addition to a drift velocity along the wire.
What is the sum of the magnetic moments after such a walk? Consider only some straight length of the wire, not the electrons "at rest" in the source and in the sink.
Answer
The magnetic moment of an electron is associated with its spin angular momentum. In the absence of a spin-orbit sort of interaction to transfer angular momentum from the mechanical degree of freedom (the electrons go around the circuit) to the spin degree of freedom, the electrons in a current-carrying wire will be unpolarized and the their net magnetic moment will be zero.
I did recently learn about half-metallic ferromagnetics, materials whose band structure conspires to make them conducting for one electron polarization and insulating for the other.
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