We critically analyze the anomalies in the frequency dispersion of the magnetic permeability, showing that it may be sometimes—without contradicting causality—inconsistent with the Kramers-Kronig relations for passive materials, as formulated by Landau and Lifshitz, even at extremely low frequencies where the permeability has definitely a very precise physical meaning. This suggests that in general the permeability may not satisfy the Kramers-Kronig formulas for passive materials, and an alternative set of relations to link the real and imaginary parts of the permeability in the frequency region where the permeability retains its physical meaning is proposed.

• Received 13 September 2010

DOI:https://doi.org/10.1103/PhysRevB.83.165119