Magnetic materials and the problem of thermal Casimir force

TL;DR

This paper analyzes how magnetic properties of materials influence the thermal Casimir force, finding that only ferromagnets significantly affect the force through zero-frequency contributions, and proposes experiments to test these effects.

Contribution

It provides a detailed theoretical analysis of magnetic effects on the thermal Casimir force, especially for ferromagnets, and suggests experimental methods to verify the influence of magnetic properties.

Findings

Magnetic properties do not influence the Casimir force for diamagnets and paramagnets.

Ferromagnets affect the Casimir force mainly through the zero-frequency term.

Casimir repulsion can occur with ferromagnetic dielectrics near nonmagnetic metals under the plasma model.

Abstract

We investigate the thermal Casimir interaction between two magnetodielectric plates made of real materials. On the basis of the Lifshitz theory, it is shown that for diamagnets and for paramagnets in the broad sense (with exception of ferromagnets) the magnetic properties do not influence the magnitude of the Casimir force. For ferromagnets, taking into account the realistic dependence of magnetic permeability on frequency, we conclude that the impact of magnetic properties on the Casimir interaction arises entirely from the contribution of the zero-frequency term in the Lifshitz formula. The computations of the Casimir free energy and pressure are performed for the configurations of two plates made of ferromagnetic metals (Co and Fe), for one plate made of ferromagnetic metal and the other of nonmagnetic metal (Au), for two ferromagnetic dielectric plates (on the basis of polystyrene), and for a ferromagnetic dielectric plate near a nonmagnetic metal plate. The dielectric permittivity of metals is described using both the Drude and the plasma model approaches. It is shown that the Casimir repulsion through the vacuum gap can be realized in the configuration of a ferromagnetic dielectric plate near a nonmagnetic metal plate described by the plasma model. In all cases considered, the respective analytical results in the asymptotic limit of large separations between the plates are obtained. The impact of the magnetic phase transition through the Curie temperature on the Casimir interaction is considered. In conclusion, we propose several experiments allowing to determine whether the magnetic properties really influence the Casimir interaction and to independently verify the Drude and plasma model approaches to the thermal Casimir force.