Why the Casimir Force for Magnetic Metals Computed by the Lifshitz Theory Using the Drude Model Disagrees with the Measurement Data

TL;DR

This paper investigates why the Lifshitz theory with the Drude model for magnetic metals' dielectric permittivity does not match experimental Casimir force measurements, focusing on wave contributions and magnetic properties.

Contribution

It demonstrates that the discrepancy arises from the transverse electric contribution and highlights the role of magnetic properties and wave fractions in the theoretical predictions.

Findings

Transverse magnetic contribution is model-independent.

Discrepancy mainly due to transverse electric contribution.

Magnetic properties influence propagating wave fractions.

Abstract

We consider the Casimir force in configurations with magnetic metal plates and analyze the reasons why the predictions of the Lifshitz theory using the dielectric permittivity of the Drude model are inconsistent with the measurement data. For this purpose, the contributions of the electromagnetic waves with the transverse magnetic and transverse electric polarizations to the Casimir force are computed using the Lifshitz theory expressed in terms of the pure imaginary Matsubara frequencies. Furthermore, the fractions of the evanescent and propagating waves in these contributions are found using an equivalent formulation of the Lifshitz theory along the real frequency axis. All computations are performed for Au-Ni and Ni-Ni plates using the Drude model and the experimentally consistent plasma model over the separation region from 0.5 to 6~mum, where the total force value is determined by conduction electrons. It is shown that the transverse magnetic contribution to the Casimir force does not depend on the used model of the dielectric permittivity, so that the total difference between the predictions of the Lifshitz theory using the Drude model and the measurement data is determined by the transverse electric contribution. In doing so, as opposed to the case of nonmagnetic metals, both fractions of the evanescent and propagating waves in this contribution depend on the model of the dielectric permittivity used in computations, whereas the magnetic properties of the plate metal influence the Casimir force solely through the fraction of propagating waves in the transverse electric contribution. The issue of a more adequate theoretical description of the electromagnetic response of magnetic metals is discussed.