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In magnetic resonance, and in particular, in superparamagnetic resonance studies at variable temperatures, a correlation between the apparent resonance magnetic field and the apparent linewidth is often observed. In order to account for this correlation, we consider the resonance lineshapes resulting from different phenomenological equations of damped motion of the magnetic moments in the cases of a linear paramagnet and of a perfect soft ferromagnet. The Bloch-Bloembergen, modified Bloch, Gilbert, Landau-Lifshitz and Callen equations are analysed. In most cases we obtain analytical expressions for the apparent resonance-field shift. Finally, we report an experimental variable-temperature study of the superparamagnetic resonance of ultrafine Fe2O3 particles in sol-gel glass. Computer simulations using the Landau-Lifshitz lineshape provide good fits of the resonance spectra at different temperatures for the same magnetic and morphological parameters of the particles.

In this work, we study borate glasses doped with a low concentration of iron oxide by X band (9.5 GHz) electron magnetic resonance. These glasses (composition: 0.63B2O3–0.37Li2O–0.75×10−3 Fe2O3 in mole %) were annealed at increasing temperatures Ta, starting at the glass transition temperature. A new composite resonance at gef≈2.0 arises in the spectra measured at room temperature (300 K). The narrow component of this resonance is predominant in glasses annealed at lower Ta while the broad component increases in intensity as Ta increases. This resonance is ascribed to an assembly of superparamagnetic nanoparticles of a crystalline iron-containing compound. Numerical simulations assuming a lognormal particle volume distribution show that the mean particle diameter increases from 5.3 to 8.5 nm as Ta increases from 748 to 823 K. The integrated spectra intensity shows that the total number of spins in the nanoparticles increases rapidly with Ta. At lower anneal temperatures Ta, a striking increase occurs in the particle diameters, while at higher Ta these diameters reach a limit value. When the measurement temperature is increased, the resonance spectra show a reversible narrowing and an increase in intensity. The temperature dependence of the individual linewidths is attributed to thermal fluctuations of the orientations of the magnetic moments with respect to the magnetic anisotropy axes.

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Computer simulations of Fe3+ electron paramagnetic resonance specmaat X (9.5 GHz) and Q (34 GHz) bands in the alkali borate glass LizO-ZB203 doped with Fez03 have been carried out using nn approach b m d on the eigenfield method applied to the 'rhombic' spin Hamiltonian. which contains only the Zeeman and quadrupole fine-structure term. In order to account for the structurd disorder in the glass, two different distribution densities of finestructm parameters D md E have been tried: a two-dimensional Gaussian function of D and ). = IE/DI. and the 'Czjzek function', analogous to the one used in Mdssbauercffect studies.In simulating the experimental spectra, care has been taken to fit not only to the most prominent features arising at &t = 4.3 (at X and Q bands) and 64 2.0 (at Q band), but also to an obvious platenu of the derivative of the absorption, which extends down to the magnetic field corresponding to fisf 1 9.7 (at both bands). As a result, the Qjjzek function can be ruled out. The agreement bemeen the experimental and computer-simulated spectra found with the Gaussian distribution density suggests the existence, besides orthorhombic symmetry sites (with A 2 113). of a considerable number of Fe3+ sites with axial or feebly rhombic distortions 0 . < 0.08). The relatively high mean value of the mid finestructure parameter D is consistent with a highly distorted environment of Fe)+ ions in the glass.

Three different models of a magnetic dipole, viz., a uniformly magnetised sphere, a circular current loop and a pair of fictitious magnetic charges, have been systematically analysed within the formalism based on the vector potential of the magnetic field. The expressions of the potentials and magnetic fields produced by each dipole model have been obtained. A computer code has been put forward in order to visualise magnetic field lines for different dipole models. It has been shown that the magnetic field outside the uniformly magnetised sphere coincides with that of a point dipole. The other two models give considerably different results at distances small or intermediate in comparison with the dipole size.