Analytic results for the Casimir free energy between ferromagnetic metals

TL;DR

This paper derives analytic expressions for the Casimir free energy and entropy between ferromagnetic metals, analyzing the effects of different models and magnetic permeabilities at low temperatures, with implications for thermodynamic consistency.

Contribution

It provides the first perturbation analytic formulas for the Casimir free energy and entropy between dissimilar ferromagnetic plates, considering both plasma and Drude models at low temperatures.

Findings

Casimir entropy vanishes at zero temperature for plasma model ferromagnets.

For Drude model ferromagnets, the entropy approaches a nonzero constant, violating the Nernst theorem.

The behavior depends on the material model and magnetic permeability used.

Abstract

We derive perturbation analytic expressions for the Casimir free energy and entropy between two dissimilar ferromagnetic plates which are applicale at arbitrarily low temperature. The dielectric properties of metals are described using either the nondissipative plasma model or the Drude model taking into account the dissipation of free charge carriers. Both cases of constant and frequency-dependent magnetic permeability are considered. It is shown that for ferromagnetic metals described by the plasma model the Casimir entropy goes to zero when the temperature vanishes, i.e., the Nernst heat theorem is satisfied. For ferromagnetic metals with perfect crystal lattices described by the Drude model the Casimir entropy goes to a nonzero constant depending on the parameters of a system with vanishing temperature, i.e., the Nernst heat theorem is violated. This constant can be positive which is quite different from the earlier investigated case of two nonmagnetic metals.