### Abstract

We examine the distribution of the magnetic anisotropy experienced by a magnetic impurity embedded in a metallic nanograin. As an example of a generic magnetic impurity with a partially filled d shell, we study the case of d1 impurities embedded into ordered and disordered Au nanograins, described in terms of a realistic band structure. Confinement of the electrons induces a magnetic anisotropy that is large, and can be characterized by five real parameters, coupling to the quadrupolar moments of the spin. In ordered (spherical) nanograins, 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 ΔE, which we predict to scale with the number of atoms N as ΔE∼1/N3/2. This gives rise to anomalies in the specific heat and the susceptibility at temperatures T∼ΔE and produces distinct structures in the magnetic excitation spectrum of the clusters that should be possible to detect experimentally.

Original language | English |
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Article number | 134421 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 91 |

Issue number | 13 |

DOIs | |

Publication status | Published - Apr 20 2015 |

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

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## Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*91*(13), [134421]. https://doi.org/10.1103/PhysRevB.91.134421