Casimir effect for magnetic media: Spatially nonlocal response to the off-shell quantum fluctuation

TL;DR

This paper extends the Lifshitz theory to magnetic media with nonlocal responses, analyzing the Casimir force between magnetic plates and comparing local and nonlocal models, with implications for resolving longstanding issues in Casimir physics.

Contribution

It introduces a method to incorporate spatially nonlocal dielectric responses into Lifshitz theory for magnetic materials, providing more accurate predictions of Casimir forces.

Findings

Nonlocal and local plasma response functions yield similar Casimir pressures at 100-800 nm separations.

At micrometer separations, nonlocal and local models differ significantly, by tens of percent.

The nonlocal response model agrees well with experimental measurements of Casimir force gradients.

Abstract

We extend the Lifshitz theory of the Casimir force to the case of two parallel magnetic metal plates possessing a spatially nonlocal dielectric response. By solving Maxwell equations in the configuration of an electromagnetic wave incident on the boundary plane of a magnetic metal semispace, the exact surface impedances are expressed in terms of its magnetic permeability and longitudinal and transverse dielectric functions. This allows application of the Lifshitz theory with reflection coefficients written via the surface impedances for calculation of the Casimir pressure between magnetic metal (Ni) plates whose dielectric responses are described by the alternative nonlocal response functions introduced for the case of nonmagnetic media. It is shown that at separations from 100 to 800~nm the Casimir pressures computed using the alternative nonlocal and local plasma response functions differ by less than 1\%. At separations of a few micrometers, the predictions of these two approaches differ between themselves and between that one obtained using the Drude function by several tens of percent. We also compute the gradient of the Casimir force between Ni-coated surfaces of a sphere and a plate using the alternative nonlocal response functions and find a very good agreement with the measurement data. Implications of the obtained results determined by the off-shell quantum fluctuations to a resolution of long-standing problems in the Casimir physics are discussed.