Nanocomposites containing Cr 2 O 3 particles having dimensions in the range 13-35 nm dispersed in a silica matrix have been prepared by a chemical method. X-ray diffraction investigation and high resolution electron microscopy substantiate the formation of Cr 2 O 3 particles. X-ray photoelectron spectroscopy studies show the presence of a small amount of CrO 2 . The samples exhibit ferromagnetic property below 300 K with the hysteresis loop showing an exchange bias. The latter is explained as arising due to exchange interaction between the spins associated with Cr 3+ and Cr 4+ ions. Dc electrical resistivity measurements were analysed by a small polaron hopping model confirming the presence of Cr 4+ ions at the surface of the particles. At temperatures above 100 K the magnetic hysteresis loop shift was such that zero magnetization was observed only for the negative magnetic field. This was explained as being due to a disorder effect on the magnetic spins of Cr 4+ ions.
In the OSp invariant closed string field theory, we construct the states corresponding to parallel D-branes that are located at different points in the space-time. Using these states, we evaluate annulus amplitudes. We show that the results coincide with those of first quantized string theory.
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