Universal distribution of magnetic anisotropy of impurities in ordered and disordered nanograins

Szilva, Attila and Balla, Péter and Eriksson, O. and Zaránd, Gergely Attila and Szunyogh, László (2015) Universal distribution of magnetic anisotropy of impurities in ordered and disordered nanograins. PHYSICAL REVIEW B, 91 (13). ISSN 2469-9950

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Abstract

We examine the distribution of the magnetic anisotropy (MA) experienced by a magnetic impurity embedded in a metallic nano-grain. As an example of a generic magnetic impurity with partially filled d-shell, we study the case of d1 impurities imbedded into ordered and disordered Au nano- grains, described in terms of a realistic band structure. Confinement of the electrons induces a magnetic anisotropy that is large, and can be characterized by 5 real parameters, coupling to the quadrupolar moments of the spin. In ordered (spherical) nano-grains, these parameters exhibit symmetrical structures and reflect the symmetry of the underlying lattice, while for disordered grains they are randomly distributed and, – for stronger disorder, – their distribution is found to be characterized by random matrix theory. As a result, the probability of having small magnetic anisotropies KL is suppressed below a characteristic scale ∆E , which we predict to scale with the number of atoms N as ∆E ∼ 1/N 3/2. This gives rise to anomalies in the specific heat and the susceptibility at temperatures T ∼ ∆E and produces distinct structures in the magnetic excitation spectrum of the clusters, that should be possible to detect experimentally.

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