Here we consider micron-sized samples with any axisymmetric body shape and made with a canted antiferromagnet, like hematite or iron borate. We find that its ground state can be a magnetic vortex with a topologically non-trivial distribution of the s
ublattice magnetization $vec{l}$ and planar coreless vortex-like structure for the net magnetization $vec{M}$. For antiferromagnetic samples in the vortex state, in addition to low-frequency modes, we find high-frequency modes with frequencies over the range of hundreds of gigahertz, including a mode localized in a region of radius $sim$ 30--40 nm near the vortex core.
The dependence of the Casimir force on material properties is important for both future applications and to gain further insight on its fundamental aspects. Here we derive a general theory of the Casimir force for low-conducting compounds, or poor me
tals. For distances in the micrometer range, a large variety of such materials is described by universal equations containing a few parameters: the effective plasma frequency, dissipation rate of the free carriers, and electric permittivity in the infrared range. This theory can also describe inhomogeneous composite materials containing small regions with different conductivity. The Casimir force for mechanical systems involving samples made with compounds that have a metal-insulator transition shows an abrupt large temperature dependence of the Casimir force within the transition region, where metallic and dielectric phases coexist.
