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 apply the general Lifshitz theory of the Casimir force to low-conducting compounds, or poor metals. For distances in the micrometer range, the Casimir force for a large variety of such materials is described by universal equations containing a few parameters: the effective plasma frequency p , dissipation rate ␥ of the free carriers, and electric permittivity ϱ for Ն p ͑in the infrared range͒. This theory of the Casimir force for poor metals can also describe inhomogeneous composite materials containing small regions with different conductivity. The Casimir force for systems involving samples made with compounds that have a metal-insulator transition shows a drastic change of the Casimir force within the transition region, where the metallic and dielectric phases coexist. Indeed, the Casimir force can increase by a factor of 2 near this transition.
We analyze theoretically the novel pathway of ultrafast spin dynamics for ferromagnets with high enough single-ion anisotropy. This longitudinal spin dynamics includes the coupled oscillations of the modulus of the magnetization together with the quadrupolar spin variables, which are expressed through quantum expectation values of operators bilinear on the spin components. Even for a simple single-element ferromagnet, such dynamics can lead to a magnetization reversal under the action of an ultrashort laser pulse.
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 nontrivial distribution of the sublattice magnetization l ជ and planar coreless vortexlike structure for the net magnetization M ជ . 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 ϳ30-40 nm near the vortex core.
We show that stable localized topological soliton textures ͑skyrmions͒ with 2 topological charge Ն 1 exist in a classical two-dimensional Heisenberg model of a ferromagnet with uniaxial anisotropy. For this model the soliton exists only if the number of bound magnons exceeds some threshold value N cr depending on and the effective anisotropy constant K eff . We define soliton phase diagram as the dependence of threshold energies and bound magnons number on anisotropy constant. The phase boundary lines are monotonous for both = 1 and Ͼ 2 while the solitons with = 2 reveal peculiar nonmonotonous behavior, determining the transition regime from low to high topological charges. In particular, the soliton energy per topological charge ͑topological energy density͒ achieves a minimum neither for = 1 nor high charges but rather for intermediate values =2 or = 3. We show that this peculiarity is related to the character of convergence of integrals defining soliton energy and number of bound magnons at different .
The dynamic properties of a magnet with magnetic ion spin of 3/2 and an isotropic spin interac tion of a general form have been investigated. Only four phase states can be realized in the system under con sideration at various relationships between the material parameters: the ferro and antiferromagnetic phases with saturated spin and the states with tensor order parameters, the nematic and antinematic ones. For these phases, the spontaneous symmetry breaking is determined by the octupole order parameter containing the mean values trilinear in spin operator components at a given site. The spectra of elementary excitations have been determined in all phases. Additional branches of excitations arise in all four phase states
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