Magnetostatic interactions

RKKY interactions were first considered on an atomic scale, where the oscillation period is on an A scale. In nanostructures, the fast oscillations do not average to zero but increase with the size of the embedded clusters or nanoparticles. However, the increase is less pronounced than that of magnetostatic interactions, and for particles sizes larger than about 1 nm, the magnetostatic interactions become dominant [27, 29], In semiconductors and semimetals, such as Sb, the low density of carriers means that kF is small, and the period of the oscillations is nanoscale [16, 28], This contributes to the complexity of the physics of diluted magnetic semiconductors [30, 31]. 

For the above mentioned FePt particles, the particle diameter is clearly smaller than the critical particle size given by Eq. (8) for coherent rotation. Furthermore the strength of the magnetostatic interaction field acting on nearest neighbor particles is only about 2% of the anisotropy field for a particle distance of 2 nm. Thus the Stoner-Wohlfarth theory can be applied. 

When the 8M formalism of Eq. 4 is applied to samples with varied carbon vol%, the plot in Fig. 10 results. As with the remanence ratio considerations the lowest carbon volume fraction corresponds to a dM that is positive. This is indicative of exchange interactions as discussed above with regard to Eq. 4. With increased carbon content the SM curves become increasingly negative indicating magnetostatic interactions in agreement with the remanence ratio analysis. 

Veitch RJ (1980) Magnetostatic interaction between a single magnetised particle and a surrounding shell of ulvospinel. Phys Earth Planet Inter 23 215-221... 

In a typical ferrofluid the particles will have median radii 2-10 nm so that thermal energy overcomes magnetostatic interaction between the particles and prevents aggregation. The single domain particles are considered to be in a state of uniform magnetization with magnetic moment... 

Breit effects (accounting for magnetostatic interaction) on valence orbital energies and on ionization potentials (IP) of the heaviest elements are small, for example, only 0.02 eV for element 121 [60]. They can, however, reach few % for the fine structure level splitting in tiie 7p elements and are of the order of correlation effects there. In element 121, they can be as large as 0.1 eV for transition energies between states including f orbitals [60]. 

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