Volume 106, Number 1, April 2014
|Number of page(s)||6|
|Section||Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties|
|Published online||01 April 2014|
Modification of the Bloch law in ferromagnetic nanostructures
1 Horia Hulubei National Institute for Physics and Nuclear Engineering - 077125 Magurele, Romania
2 Dipartimento di Fisica “E. R. Caianiello”, Università degli Studi di Salerno - 84084 Fisciano (SA), Italy
3 Spin-CNR, Unit of Salerno - 84084 Fisciano (SA), Italy
Received: 26 November 2013
Accepted: 18 March 2014
The temperature dependence of magnetization in ferromagnetic nanostructures (e.g., nanoparticles or nanoclusters) is usually analyzed by means of an empirical extension of the Bloch law sufficiently flexible for a good fitting to the observed data and indicates a strong softening of magnetic coupling compared to the bulk material. We analytically derive a microscopic generalization of the Bloch law for the Heisenberg spin model which takes into account the effects of size, shape and various surface boundary conditions. The result establishes explicit connection to the microscopic parameters and differs significantly from the existing description. In particular, we show with a specific example that the latter may be misleading and grossly overestimates magnetic softening in nanoparticles. It becomes clear why the usual dependence appears to be valid in some nanostructures, while large deviations are a general rule. We demonstrate that the combination of geometrical characteristics and coupling to environment can be used to efficiently control magnetization and, in particular, to reach a magnetization higher than in the bulk material.
PACS: 75.75.-c – Magnetic properties of nanostructures / 73.21.-b – Electron states and collective excitations in multilayers, quantum wells, mesoscopic, and nanoscale systems / 75.50.Tt – Fine-particle systems; nanocrystalline materials
© EPLA, 2014
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