What is a volume to size ratio? Never heard of it. In any case by interatomic exchange energy I assume you mean the atomic potential (for the Hamiltonian). Are you asking about boundary conditions or the change in the potential at a boundary?
Dear Lawrence ,
very thanks.you are very kind to me.please see book:Advanced Magnetic Nanostructures,Sellmyer, D.J., Skomski, Ralph (Eds.).
All the best,Abbas
Dear Lawrence ,
wait for your viewpoint about my question?
All the best,
Abbas
By which means you are sure that exhange is stronger in nano-dimensions than in bulk. If you refer to the magnetic ordering temperature this could be explained by the ordering mechanism. In bulk magnets with three-dimensional spin the ordering process is due to a boson field and not due to exchange interactions between spins. This ordering temperature is called a stable fixed point (SFP) by RG theory and is generally lower than expected by atomistic models on the basis of the exchange interactions. If in nano particles the ordering process is really due to exchange interactions the ordering temperature can be higher than in bulk material.
Maybe we have a sort of misunderstanding here. Small particles, usually with diameter less than ~20nm, are single domain. Therefore they seem to be magnetized more strongly (after the field is removed) then their bigger "brothers". Yet, in both cases the exchange interactions between their atoms are the same. Well, indeed they may differ as the interatomic distances need not to be identical in very small particles with those in bigger chunks. Even the crystal structure is not necessarily identical.
I observed that the ordering temperatures of powder samples can be slightly higher than the ordering tempeartures of bulk crystals. Marek is right, one has to be careful in comparing ordering temperatures of bulk material and fine particles. It is absolutely necessary thet the stoichiometry agrees.
A tentative explanation of this effect is: as we know from RG theory the magnetic ordering transition is not driven by exchange interactions between spins but by a boson field. The bosons are the excitations of the continuous magnetic medium. The bosons propagate ballistic. If the mean free path of the bosons is larger than the grain size the bosons get reflected at the inner surface of the grains. This increases the density of the bosons and can enhance the ordering temperature. In other words, the mean free path of the bosons provides a new, hitherto not considered mesoscopic length to the dynamics. This is an interesting point that deserves more detailed investigations (dependence of the ordering temperature on particle size).
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