Magnetic anisotropy due to the Casimir effect

We consider the Casimir interaction between a ferromagnetic and a nonmagnetic mirror and show how the Casimir effect gives rise to a magnetic anisotropy in the ferromagnetic layer. The anisotropy is out of plane if the nonmagnetic plate is optically isotropic. If the nonmagnetic plate shows a uniaxial optical anisotropy (with optical axis in the plate plane), we find an in-plane magnetic anisotropy. In both cases, the energetically most favorable magnetization orientation is given by the competition between polar, longitudinal, and transverse contributions to the magneto-optical Kerr effect and will therefore depend on the interplate distance. Numerical results will be presented for a magnetic plate made out of Fe and nonmagnetic plates of Au (optically isotropic), quartz, calcite, and barium titanate (all uniaxially birefringent).

Figure 1

(a) Polar, longitudinal, and transverse contributions to the Casimir energy per unit area and (b) the Casimir force per unit area between an Fe and an Au mirror.

Figure 2

Dielectric functions for (a) quartz, (b) calcite, and (c) barium titanate. Solid and dashed lines correspond to the ordinary and extraordinary dielectric functions, respectively.

Figure 3

Amplitude of the anisotropy energy (per unit area) for a magnetic Fe mirror placed opposite of a nonmagnetic birefringent mirror made out of quartz, calcite, or barium titanate. Interplate distance (a) $D=10\hspace{0.5em}\text{nm}$ and (b) $D=5\hspace{0.5em}\mu \text{m}$. The amplitude is multiplied by 10 for quartz in both figures and for calcite in (b).

Figure 4

Amplitude of the anisotropy energy (per unit area) as a function of interplate distance $D$ for a magnetic Fe mirror placed opposite of a nonmagnetic mirror made out of quartz, calcite, or barium titanate.