I am not really sure why the law of conservation of angular momentum should hold true in the Einstein - de Haas effect.
Consider the following excerpt about the phenomenon (taken from Magnetism in Condensed Matter by Blundell) -
"....a ferromagnetic rod is suspended vertically, along its axis, by a thin fibre. It is initially at rest and unmagnetized, and is subsequently magnetized along its length by the application of a vertical magnetic field. This vertical magnetization is due to the alignment of the atomic magnetic moments and corresponds to a net angular momentum. To conserve total angular momentum, the rod begins turning about its axis in the opposite sense."
Now, consider the conservation theorem for total angular momentum (taken from Classical Mechanics by Goldstein) -
"L is constant in time if the applied (external) torque is zero."
The conservation law should hold only when there is no external torque. But the applied magnetic field does exert a torque on each individual magnetic moment, which is what aligns it to the magnetic field direction. Then how can one explain the Einstein - de Haas effect using the conservation law, when apparently it doesnt seem to be holding true??
Is there a refined version of the conservation theorem which I am missing? Or if the law still holds true, then why?