Effect of dipolar interactions on the magnetization of a cubic array of nanomagnets

We investigated the effect of intermolecular dipolar interactions on a cubic 3D ensemble of 5X5X4=100 nanomagnets, each with spin $S = 5$. We employed the Landau-Lifshitz-Gilbert equation to solve for the magnetization $M(B)$ curves for several values of the damping constant $\alpha$, the induction sweep rate, the lattice constant $a$, the temperature $T$, and the magnetic anisotropy field $H_A$. We find that the smaller the $\alpha$, the stronger the maximum induction required to produce hysteresis. The shape of the hysteresis loops also depends on the damping constant. We find further that the system magnetizes and demagnetizes at decreasing magnetic field strengths with decreasing sweep rates, resulting in smaller hysteresis loops. Variations of $a$ within realistic values (1.5 nm - 2.5 nm) show that the dipolar interaction plays an important role in the magnetic hysteresis by controlling the relaxation process. The $T$ dependencies of $\alpha$ and of $M$ are presented and discussed with regard to recent experimental data on nanomagnets. $H_A$ enhances the size of the hysteresis loops for external fields parallel to the anisotropy axis, but decreases it for perpendicular external fields. Finally, we reproduce and test an $M(B)$ curve for a 2D-system [M. Kayali and W. Saslow, Phys. Rev. B {\bf 70}, 174404 (2004)]. We show that its hysteretic behavior is only weakly dependent on the shape anisotropy field and the sweep rate, but depends sensitively upon the dipolar interactions. Although in 3D systems, dipole-dipole interactions generally diminish the hysteresis, in 2D systems, they strongly enhance it. For both square 2D and rectangular 3D lattices with ${\bm B}||(\hat{\bm x}+\hat{\bm y})$, dipole-dipole interactions can cause large jumps in the magnetization.Comment: 15 pages 14 figures, submitted to Phys. Rev.

Anomalously Soft and Stiff Modes of Transition-Metal Nanoparticles

We propose an explanation for the enhanced low- and high-energy tails of the vibrational density of states (VDOS) of nanoparticles (NPs) with respect to their bulk counterparts. Density functional theory calculations of the frequency and eigenvector of each mode allow us to identify radial breathing/multipolar and nonradial tidal/shear/torsional vibrations as the modes that populate such tails. These modes have long been obtained from elasticity theory and are thus analogous to the widely studied and observed pulsations in variable stars. The features particular to the VDOS of NPs are rationalized in terms of the charge density distribution around low-coordinated atoms, the quasi-radial geometric distribution of NPs, force constant variations, degree of symmetry of the nanoparticle, discreteness of the spectrum, and the confinement of the eigenmodes. Our results indicate that the high- and low-energy tails of the VDOS may be a powerful tool to reveal information about the chemical composition and geometric structure of small NPs. In particular, the size of the confinement gap at the low-frequency end of the VDOS and the extent by which the high-frequency end surpasses the bulk limit signal whether a NP is bulk-like or non-bulk-like and the extent to which it is disordered. © 2014 American Chemical Society

Surface Phonons: Theoretical Methods and Results

peer reviewedThe theoretical methods currently in use for the calculation of surface phononsurface phonon dispersion curves and how they have evolved from the phenomenological force-constant models to the present day first principles theories are discussed. A selection of paradigmatic examples for the different classes of crystal surfaces is presented with comparisons to the experimental data obtained from helium atom scattering or electron energy-loss spectroscopy. © 2020, Springer Nature Switzerland AG