Casimir free energy and pressure for magnetic metal films

TL;DR

This study compares the Casimir free energy and pressure of magnetic metal films using Drude and plasma models, revealing significant differences and implications for thin film stability and theoretical approaches.

Contribution

It provides a detailed comparison of the Drude and plasma model approaches to Casimir effects in magnetic films, highlighting their differing predictions and physical implications.

Findings

Significant differences in Casimir free energy magnitude and sign between models.

Plasma model predicts exponential decay of free energy with film thickness.

Drude model approaches reach classical limit at ~150 nm thickness.

Abstract

We examine the Casimir free energy and pressure of magnetic metal films, which are free-standing in vacuum, sandwiched between two dielectric plates, and deposited on either nonmagnetic or magnetic metallic plates. All calculations are performed using both the Drude and plasma model approaches to the Lifshitz theory. According to our results, the Casimir free energies and pressures calculated using both theoretical approaches are significantly different in the magnitude and sign even for thin films of several tens of nanometers thickness. Thus, for the Ni film of 47\,nm thickness deposited on a Fe plate the obtained magnitudes of the Casimir free energy differ by the factor of 5866. We show that the Casimir free energy and pressure of a magnetic film calculated using the plasma model approach do not possess the classical limit, but exponentially fast drop to zero with increasing film thickness. If the Drude model approach is used, the classical limit is reached for magnetic films of about 150\,nm thickness, but the Casimir free energy remains nonzero in the limit of ideal metal, contrary to expectations. For the plasma model approach the Casimir free energy of a film vanishes in this case. Numerical computations are performed for the magnetic films made of Ni, nonmagnetic plates made of Cu and Al, and magnetic plates made of Fe using the tabulated optical data for the complex indexes of refraction of all metals. The obtained results can be used for a discrimination between the plasma and Drude model approaches in the Casimir physics and in the investigation of stability of thin films.