An accurate model of the properties of magnetite $(Fe\sb{3(1-\delta)}O\sb4),$ zinc ferrites $(Fe\sb{(3-x)}Zn\sb{x}O\sb4),$ and titanomagnetites $(Fe\sb{3-y}Ti\sb{y}O\sb4)$ in the vicinity of the ...Verwey Transition (VT) is achieved by adopting a quantum mechanical approach which focuses on quantum states rather than classical concepts, such as particles. Our approach leads to a simple physical picture of the VT which explains all the observed properties at and in the vicinity of the transition. Succinctly stated, the VT is the result of the sudden conversion of trapped states to polaron states. This simple model is capable of explaining all the observed changes which occur in the neighborhood of the transition using only a single order parameter, $\psi.$ The thermodynamic, electron transport, and structural properties as a function of temperature, T, and the nonstoichiometry parameter, $\delta,$ are fully modeled by our polaron mean-field (PMF) theory of the VT. Two approaches are used to obtain the equation of state: Strassler and Kittel mean-field model, and Hijmans and de Boer mean-field order-disorder theory. After careful elucidation of the SK theory, this two state theory is applied to VT. The order parameter and Fermi Dirac statistics are used to compute the number of occupied and empty polaron states. The electron transport properties are then described by the small polaron transport theory of Holstein and Emin. The electron transport properties are shown to be consistent with charge carriers, in the form of small polarons, that move adiabatically by a process called phonon assisted electronic hopping. This is demonstrated by comparison of the theoretically determined values of $\rho(T)$ and $\alpha(T)$ with the measured values of resistivity and the Seebeck coefficient for various values of $\delta.$ The PMF theory is improved by using a more microscopic approach based upon the theory of HB, which treats states as being either occupied polaron states, occupied trapped states, or undistorted vacant states. The three state PMF model gives an improved fit to the measured entropy and the electron transport data.
We consider the limits arising from different electromagnetic systems on the existence of a possible new electromagnetic analog of the fifth force. Although such a force may have no intrinsic ...connection to electromagnetism (or gravity), its effects could be manifested through various anomalies in electromagnetic systems, for appropriate values of the coupling strength and range. Our work generalizes that of Bartlett and Logl (who considered the case of a massive vector field co-existing with massless electrodynamics) to encompass a broad class of phenomenological interactions mediated by both scalar and vector exchanges. By combining data from both gravitational and electromagnetic systems, one can eventually set limits on a new force whose range $\lambda$ extends from the subatomic scale $\rm (\lambda\approx10\sp{-15}m)$ to the astrophysical scale $\rm (\lambda\approx10\sp{22}m).$ A new geomagnetic limit on the photon mass $m\sb\gamma$ is derived from an analysis of satellite measurements of the Earth's magnetic field $\vec{H}.$ The primary effect of a nonzero photon mass is to generate an additional contribution to $\vec{H}$ resembling that from an external source. We find $m\sb\gamma\le8\times10\sp{-16}eV/c\sp2 = 1\times10\sp{-48}g = 4\times10\sp{-9}m\sp{-1}.$ Using Chibisov's method (80) and the discovery of intracluster magnetic fields, we also set a new indirect upper limit on the mass of the photon of $m\sb\gamma\le1\times10\sp{-28}eV/c\sp2 = 2\times10\sp{-61}g.$ A general multipole expansion for radiation from massive vector and scalar fields is developed for periodic sources. This formalism is then combined with data on the binary pulsar PSR 1913+16 to set limits on the electric charge of astrophysical bodies, and on the coupling strength strengths of new weak gravity-like forces.
