Eur. Phys. J. B (2018) 91: 131
https://doi.org/10.1140/epjb/e2018-80515-1

Regular Article

Diamagnetism and the dispersion of the magnetic permeability

¹ Department of Electronic Systems, NTNU – Norwegian University of Science and Technology, 7491 Trondheim, Norway
² Department of Technology Systems, University of Oslo, Box 70, 2027 Kjeller, Norway

^a e-mail: johannes.skaar@its.uio.no

Received: 8 September 2017
Received in final form: 8 February 2018
Published online: 22 June 2018

Abstract

It is well known that the usual Kramers–Kronig relations for the relative permeability function μ(ω) are not compatible with diamagnetism (μ(0) < 1) and a positive imaginary part (Im μ(ω) > 0 for ω > 0). We demonstrate that a certain physical meaning can be attributed to μ for all frequencies, and that in the presence of spatial dispersion, μ does not necessarily tend to 1 for high frequencies ω and fixed wavenumber k. Taking the asymptotic behavior into account, diamagnetism can be compatible with Kramers–Kronig relations even if the imaginary part of the permeability is positive. We provide several examples of diamagnetic media and metamaterials for which μ(ω, k) ↛  1 as ω →∞.