Magnetic field effects in the Casimir force between two parallel anti-ferromagnetic slabs

We study the Casimir force F between two parallel anti-ferromagnetic slabs taking into account an external magnetic field in the Voigt configuration. Using a frequency and magnetic field dependent magnetic permeability tensor and a frequency independent dielectric permittivity, to describe the slabs, we calculate the Casimir force using non-normal incidence reflectivity of the electromagnetic waves in the free space between the slabs. We determine the Casimir force by performing two-dimensional calculations. F is investigated as a function of the layer thickness d, the vacuum gap width L between slabs, and the external magnetic field strength H. Features of F as function of the external field include the presence of sharp dips and peaks, which appear in the vicinity of the resonance frequency, and are consequences of the interaction of the external magnetic field with the electron spin. In addition, an external field may diminish F, which is an important effect not found in any other system.