Electromagnetic Energy, Absorption, and Casimir Forces. Inhomogeneous Dielectric Media

A general, exact formula is derived for the expectation value of the electromagnetic energy density of an inhomogeneous absorbing and dispersive dielectric medium in thermal equilibrium, assuming that the medium is well approximated as a continuum. From this formula we obtain the formal expression for the Casimir force density. Unlike most previous approaches to Casimir effects in which absorption is either ignored or admitted implicitly through the required analytic properties of the permittivity, we include dissipation explicitly via the coupling of each dipole oscillator of the medium to a reservoir of harmonic oscillators. We obtain the energy density and the Casimir force density as a consequence of the van der Waals interactions of the oscillators and also from Poynting's theorem.Comment: 13 pages, no figures. Updated version with generalization to finite temperature and added example

Crystal structure and physical properties of EuPtIn4_{4} intermetallic antiferromagnet

We report the synthesis of EuPtIn$_{4}$ single crystalline platelets by the In-flux technique. This compound crystallizes in the orthorhombic Cmcm structure with lattice parameters $a=4.542(1)$ \AA, $b=16.955(2)$ \AA$\,$ and $c=7.389(1)$ \AA. Measurements of magnetic susceptibility, heat capacity, electrical resistivity, and electron spin resonance (ESR) reveal that EuPtIn$_{4}$ is a metallic Curie-Weiss paramagnet at high temperatures and presents antiferromagnetic (AFM) ordering below $T_{N}=13.3$ K. In addition, we observe a successive anomaly at $T^{*} = 12.6$ K and a spin-flop transition at $H_{c} \sim 2.5$ T applied along the $ac$-plane. In the paramagnetic state, a single Eu$^{2+}$ Dysonian ESR line with a Korringa relaxation rate of $b = 4.1(2)$ Oe/K is observed. Interestingly, even at high temperatures, both ESR linewidth and electrical resistivity reveal a similar anisotropy. We discuss a possible common microscopic origin for the observed anisotropy in these physical quantities likely associated with an anisotropic magnetic interaction between Eu$^{2+}$ 4$f$ electrons mediated by conduction electrons.Comment: 5 pages, 5 figure