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

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.

Figures (9)

• Figure 1: (a) The Casimir forces per unit area and (b) the transverse magnetic (TM) and transverse electric (TE) contributions to the Casimir force computed using the Drude (D) and plasma (p) models in the configuration of Au-Ni plates and normalized to the high-temperature Casimir force found using the Drude model are shown as the functions of separation.
• Figure 2: (a) The Casimir forces per unit area and (b) the transverse magnetic (TM) and transverse electric (TE) contributions to the Casimir force computed using the Drude (D) and plasma (p) models in the configuration of Ni-Ni plates and normalized to the high-temperature Casimir force found using the Drude model are shown as the functions of separation.
• Figure 3: (a) The magnitudes of real parts of the dielectric permittivities of the Drude and plasma models and (b) the imaginary parts of the dielectric permittivity of the Drude model are shown by the pairs of solid (the Drude model) and dashed (the plasma model) lines as the functions of frequency. In all cases the upper and lower lines in each pair are plotted for Au and Ni plates, respectively.
• Figure 4: (a) The real and (b) imaginary parts of the magnetic permeability of Ni are shown as the functions of frequency.
• Figure 5: The fractions of the evanescent and propagating waves in the transverse magnetic contribution to the Casimir force per unit area of Au-Ni plates computed using the Drude model are shown by the lower and upper dashed lines as the functions of separation. The total transverse magnetic contribution to the Casimir force computed by the Drude model shown by the solid line is reproduced from Figure \ref{['fg1']}b.