Universal distribution of magnetic anisotropy of impurities in ordered and disordered nano-grains

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 $d^{1}$ 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 $K_L$ is suppressed below a characteristic scale $\Delta_E$, which we predict to scale with the number of atoms $N$ as $\Delta_E\sim 1/N^{3/2}$. This gives rise to anomalies in the specific heat and the susceptibility at temperatures $T\sim \Delta_E$ and produces distinct structures in the magnetic excitation spectrum of the clusters, that should be possible to detect experimentally

Effects of Nanodots Shape and Lattice Constants on the Spin Wave Dynamics of Patterned Permalloy Dots

Micromagnetic simulations studies on Permalloy (Ni80Fe20) nanodot with different shape and edge-to-edge separation (s) down to 25nm arranged in square lattice are reported. We observe the significant variation of spin-wave (SW) dynamics of nanodots of different shapes (triangular, diamond and hexagon) and of fixed dot diameter 100nm with varying s. Modes for single dot are transformed in an array into multiple quantized, edge and centre modes for different shapes and edge-to-edge separations, with different spin wave frequencies and peak intensities. Specifically, in the triangular dot sample, a broad range of mode frequencies is observed with highest SW frequency 14.7 GHz. For separation less than 100nm, the SW frequencies undergoes significant modification due to the varying nature of the magnetostatic and dipolar interaction in the array while for separation above 100nm, the SW frequency mostly remain constant. The power profiles confirm the nature of the observed modes. The spatial profiles of magnetostatic field are determined by a combination of internal magnetic-field profiles within the nanodots and the magnetostatic fields within the lattice. The inter-dots interaction of magnetostatic field shows dipolar and quadrupole contributions for all the shapes. Interestingly, vortex states with shifted core and polarity are observed in the array for all the shapes at Hbias = 0. Our results provide important understanding about the tunability of SW spectra in the array of triangular, diamond and hexagon shaped nanoelements.Comment: 13 pages, 8 figure

Ferromagnetic resonance of a two-dimensional array of nanomagnets: Effects of surface anisotropy and dipolar interactions

We develop an analytical approach for studying the FMR frequency shift due to dipolar interactions and surface effects in two-dimensional arrays of nanomagnets with (effective) uniaxial anisotropy along the magnetic field. For this we build a general formalism on the basis of perturbation theory that applies to dilute assemblies but which goes beyond the point-dipole approximation as it takes account of the size and shape of the nano-elements, in addition to their separation and spatial arrangement. The contribution to the frequency shift due to the shape and size of the nano-elements has been obtained in terms of their aspect ratio, their separation and the lattice geometry. We have also varied the size of the array itself and compared the results with a semi-analytical model and reached an agreement that improves as the size of the array increases. We find that the red-shift of the ferromagnetic resonance due to dipolar interactions decreases for smaller arrays. Surface effects may induce either a blue-shift or a red-shift of the FMR frequency, depending on the crystal and magnetic properties of the nano-elements themselves. In particular, some configurations of the nano-elements assemblies may lead to a full compensation between surface effects and dipole interactions.Comment: 14 pages, 5 figure