Enhanced repulsive Casimir forces between gold and thin magnetodielectric plates

We calculate repulsive Casimir forces between metallic and magnetic plates and quantitatively probe the magnetic plate's properties as tuning knobs for the repulsion. Namely, the plate's thickness and its low-frequency permittivity and permeability. For a thin magnetic plate ($\leq 10\,\text{nm}$), we find that repulsion can exist as long as $\mu(0) \geq \epsilon(0)$. We also explore the effect of temperature on the repulsion and transition distance between attractive and repulsive interactions. We show how the parameters can be tuned to allow repulsion at sub-micron separation regimes, making it potentially accessible to known high-resolution measurement techniques using magnetic van der Waals materials.