Magnetic volume dependence

It has been shown by several authors that fee iron films exhibit a rich magnetic structure, depending very sensitively on the atomic volume. In particular in Fe... 

A simple way to account for this particle volume-dependent narrowing of the SPR spectra, suggested by De Biasi and Devezas [18], consists in averaging the magnetisation and magnetic anisotropy over the thermal fluctuations of the magnetic moment as follows ... 

For heterogeneous objects the equilibrium magnetization Mo depends on space r, and Mofr) is called the spin density. For a 90° pulse, sin a = 1, and the magnetization from the volume element at position r is given by... 

In Fig. 4, we plot the volume dependences of the diffusivities of various model systems, all calculated for argonlike particles, and for the laboratory system methyl cyclohexane, which seems to be representative. Data for the latter are available for two temperatures from the accurate nuclear magnetic resonance (NMR) spin-echo measurements of Jonas et al. To group the data for different systems for better comparison of their behavior, we have obtained a reducing parameter for each liquid by taking advantage of the observations of Batchinski and Hildebrand that fluidities , and diffusivities D of highly fluid molecular liquids vary linearly with volume. 

The magnetization M that a material acquires in a magnetic field depends on the strengths of elementary magnetic moments //, and the number N of magnetic moments (atoms) per volume. 

Fig. 121. Top ZF-M.SR spectrum of CcAlj at lOmK. The broken lines show the decomposition of the fit (solid line) to the spectrum into 3 subspectra (the Bessel-damped oscillatory pattern and the exponentially damped 1/3 signal from the magnetic finction together with the weakly Gaussian-damped spectrum of the paramagnetic fraction). Bottom Temperature dependence of the maximum fi equency in the oscillatory signal of CeAlj (open circles, left-hand scale) and of the magnetic volume fraction (sohd circles, right-hand scale). The lines are guides to the eye. Aflcr Amato (1997).

Fig. 127. Temperature dependences of the magnetic volume fraction (fast relaxing component) (top) and its relaxation rate (bottom). Open squares refer to a superconducting sample with composition CeCujosSij, solid diamonds to a CeCuj 04812 sample that exhibits no bulk superconductivity. After Feyerherm et al. (1997).

Coehoorn (1991) used a similar method to calculate electronic structures of rare-earth-transition-metal compounds. Figure 4b shows schematic representations of his calculation of the dependence of the average magnetic moment on cell volume in bcc-Fe and Y2Fei7. In the case of yttrium-iron compounds, we can estimate the volume dependence of the magnetic properties of the Fe sublattice because of the lack of 4f electrons at rare-earth sites. The cross denotes the moment at the equihbrium volume. 

The same approach has been applied to ferrimagnetic materials with two magnetic sublattices (see Bloch and Pavlovic, 1969). The volume dependence of 0Fi can be related to that of the molecular field coefficients n by the relation... 

In this case one has to know the volume dependence of the Curie temperature as well as the specific magnetization o-q at absolute zero. 

It is well established that the magnetism of magnetic materials is highly volume dependent because it arises from the collective interaction of atomic magnetic dipoles. A variety of magnetic (particularly paramagnetic) nanoparticles have... 

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