Anisotropy in ferromagnetic nanoparticles: Level-to-level fluctuations of a collective effectG. Usaj1 and H. U. Baranger2
1 Instituto Balseiro and Centro Atómico Bariloche - (8400) Bariloche, Argentina
2 Department of Physics, Duke University - Durham, NC 27708-0305, USA
received 14 June 2005; accepted in final form 4 August 2005
published online 31 August 2005
We calculate the mesoscopic fluctuations of the magnetic anisotropy of ferromagnetic nanoparticles; that is, the effect of single-particle interference on the direction of the collective magnetic moment. A microscopic spin-orbit Hamiltonian considered as a perturbation of the much stronger exchange interaction first yields an explicit expression for the anisotropy tensor. Then, assuming a simple random matrix model for the spin-orbit coupling allows us to describe the fluctuation of such a tensor analytically. In the case of uniaxial anisotropy, we calculate the distribution of the anisotropy constant for a given number of electrons, and its variation upon increasing this number by one. The magnitude of the latter scales inversely with the number of atoms in the particle and is sufficient to account for the experimental data.
73.22.-f - Electronic structure of nanoscale materials: clusters, nanoparticles, nanotubes, and nanocrystals.
73.23.Hk - Coulomb blockade; single-electron tunneling.
75.75.+a - Magnetic properties of nanostructures.
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