H. Puszkarski

Purely dipolar versus dipolar-exchange modes in cylindrical nanorods

Properties of purely dipolar and dipolar-exchange modes in finite circular rods are investigated numerically, with the sample static magnetization assumed to be uniform and parallel to the rod axis; we study magnetic excitations propagating along this direction. In particular, we demonstrate size-exchange effects induced by modifying the rod aspect ratio (the diameter to length ratio) and the strength of the exchange coupling. Untypical groups of purely dipolar modes are shown to occur in smooth rods: bulk-dead modes, characterized by a dead-amplitude region inside the rod, and comb modes, in which a nearly “dead” region is found at the sample borders, while numerous (“comb-like”) oscillations take place in the bulk. These two mode groups fade to disappear when the sample geometry evolves toward the thin-film one, or when the exchange becomes dominant. The existence of these untypical modes is related to local demagnetizing field profile nonhomogeneity, particularly to two edge wells found in the field pr...

Localization properties of pure magnetostatic modes in a cubic nanograin

We investigate the dynamical properties of a system of interacting magnetic dipoles disposed in sites of an sc lattice and forming a cubic-shaped sample of size determined by the cube edge length (N-1)a (a being the lattice constant, N representing the number of dipolar planes). The dipolar field resulting from the dipole-dipole interactions is calculated numerically in points of the axis connecting opposite cube face centers (central axis) by collecting individual contributions to this field coming from each of the N atomic planes perpendicular to the central axis. The applied magnetic field is assumed to be oriented along the central axis, magnetizing uniformly the whole sample, all the dipoles being aligned parallelly in the direction of the applied field. The frequency spectrum of magnetostatic waves propagating in the direction of the applied field is found numerically by solving the Landau-Lifshitz equation of motion including the local (nonhomogeneous) dipolar field component; the mode amplitude spatial distributions (mode profiles) are depicted as well. It is found that only the two energetically highest modes have bulk-extended character. All the remaining modes are of localized nature; more precisely, the modes forming the lower part of the spectrum are localized in the subsurface region, while the upper-spectrum modes are localized around the sample center. We show that the mode localization regions narrow down as the cube size, N, increases (we investigated the range of N=21 to N=101), and in sufficiently large cubes one obtains practically only center-localized and surface-localized magnetostatic modes.

Spin-wave mode profiles versus surface/interface conditions in ferromagnetic Fe/Ni layered composites

Spin-wave excitations in ferromagnetic layered composite (AB · · · BA; A and B being different homogeneous ferromagnetic materials) are analysed theoretically, by means of the transfer matrix approach. The properties of multilayer spin-wave mode profiles are discussed in relation to multilayer characteristics, such as the filling fraction and the exchange or magnetization contrast; also, surface spin pinning conditions and dipolar interactions are taken into account. The interface conditions are satisfied by introducing an effective exchange field expressed by interface gradients of the exchange constant and the magnetization. This approach provides an easy way to find frequencies and amplitudes of standing spin waves in the multilayer. The developed theory is applied to interpretation of spin wave resonance (SWR) spectra obtained experimentally by Chambers et al in two systems: a bilayer Fe/Ni and a trilayer Ni/Fe/Ni, in perpendicular (to the multilayer surface) configuration of the applied magnetic field. By fitting the SWR spectra obtained experimentally and those found numerically, the surface anisotropies are estimated on multilayer surfaces; then, the observed resonance lines are identified as associated with bulk, surface or interface modes. The theory can be extended to a general case of any multi-component layered system.

Re-orientation transition in molecular thin films: Potts model with dipolar interaction

We study the low-temperature behavior and the phase transition of a thin film by Monte Carlo simulation. The thin film has a simple cubic lattice structure where each site is occupied by a Potts parameter which indicates the molecular orientation of the site. We take only three molecular orientations in this paper, which correspond to the three-state Potts model. The Hamiltonian of the system includes (i) the exchange interaction J(ij) between nearest-neighbor sites i and j, (ii) the long-range dipolar interaction of amplitude D truncated at a cutoff distance r(c), and (iii) a single-ion perpendicular anisotropy of amplitude A. We allow J(ij) = J(s) between surface spins, and J(ij) = J otherwise. We show that the ground state depends on the ratio D/A and r(c). For a single layer, for a given A, there is a critical value D(c) below (above) which the ground-state (GS) configuration of molecular axes is perpendicular (parallel) to the film surface. When the temperature T is increased, a re-orientation transition occurs near D(c): the low-T in-plane ordering undergoes a transition to the perpendicular ordering at a finite T, below the transition to the paramagnetic phase. The same phenomenon is observed in the case of a film with a thickness. Comparison with the Fe/Gd experiment is given. We show that the surface phase transition can occur below or above the bulk transition depending on the ratio J(s)/J. Surface and bulk order parameters as well as other physical quantities are shown and discussed.

New magnetostatic modes in small nonellipsoidal magnetic particles

Magnetostatic normal modes are investigated here in elongated rods. The dipolar field resulting from the dipole-dipole interactions is calculated numerically in points of the axis connecting opposite rod face centers (central axis) by collecting individual contributions to this field coming from each of the atomic planes perpendicular to the central axis. The applied magnetic field is assumed to be oriented along the central axis, and the magnetization to be uniform throughout the sample. The frequency spectrum of magnetostatic waves propagating in the direction of the applied field is found numerically by solving the Landau-Lifshitz equation of motion with the spatially nonhomogeneous dipolar field taken into account; the mode amplitude profiles are depicted as well. While energetically highest modes have bulk-extended character, the modes forming the lower part of the spectrum are localized in the subsurface region (bulk-dead modes). Between these two mode types, magnetostatic modes of a new type (comb modes) are found to occur, characterized by two clearly discernible regions: a zone of fast amplitude oscillations inside the rod, and narrow slow-oscillation regions at the borders. Absorbing virtually no energy from an applied alternating field, comb modes will have no significant contribution to the magnetic noise.

Interface-mode absorption line in ferromagnetic resonance of antiferromagnetically coupled bilayer films: II. Effects of static field configuration and film thickness

We present a further development of our microscopic theory of the interface spin-wave mode (IM) in exchange coupled bilayer films using the Heisenberg model and including interface inhomogeneity in the spin (exchange, Zeeman and interface uniaxial anisotropy) Hamiltonian. Our theory holds for arbitary (with respect to the film normal) configuration angle theta of the film magnetization, arbitrary ferro/antiferromagnetic interface exchange coupling Ji and arbitrary (easy-axis/easy-plane) uniaxial interface anisotropy Di. Conditions for the occurrence of the IM peak in the bilayer ferromagnetic resonance spectrum are discussed in detail, and a method of resorting to this peak for measuring the interface coupling and pinning anisotropy is proposed. In particular we predict the existence of a critical configuration angle theta c for IM emergence at film magnetization rotation; for antiferromagnetic coupling theta c is a function of the ratio Ji/Di. Our estimates for real specimens lead to the general conclusion that observation of the IM peak becomes possible already at interface antiferromagnetic exchange coupling of the order of one-hundredth of the exchange bulk coupling.

Magnetic properties of two-dimensional nanodots: Ground state and phase transition

We study the effect of perpendicular single-ion anisotropy, −Asz2, on the ground-state structure and finite-temperature properties of a two-dimensional magnetic nanodot in presence of a dipolar interaction of strength D. By a simulated annealing Monte Carlo method, we show that in the ground state a vortex core perpendicular to the nanodot plane emerges already in the range of moderate anisotropy values above a certain threshold level. In the giant-anisotropy regime the vortex structure is superseded by a stripe domain structure with stripes of alternate domains perpendicular to the surface of the sample. We have also observed an intermediate stage between the vortex and stripe structures, with satellite regions of tilted nonzero perpendicular magnetization around the core. At finite temperatures, at small A, we show by Monte Carlo simulations that there is a transition from the the in-plane vortex phase to the disordered phase characterized by a peak in the specific heat and the vanishing vortex order pa...

Spin-waves in thin films with Dzyaloshinskii-Moriya interaction

Using the Green’s function method, we calculate the spin-wave (SW) spectrum in a thin film with quantum Heisenberg spins interacting with each other via an exchange interaction J and a Dzyaloshinskii-Moriya interaction of magnitude D. Due to the competition between J and D, the ground state is non collinear. We show that for large D, the first mode in the SW spectrum is proportional to the in plane wave-vector k at the limit k tending to zero. For small D, it is proportional to k2. We show that the surface modes may occur depending on the surface exchange interaction. We calculate the layer magnetizations at temperature T and the transition temperature as a function of the film thickness.

The effect of cross-sectional geometry and size on magnetostatic modes in nanorods

We study the effect of cross-sectional geometry and size on the spectrum of magnetostatic modes in dipole-coupled magnetic nanorods of circular or square cross section. The scope of this study is confined only to excitations propagating along the central axis of the nanorod; at the same time, the direction of the central axis is assumed to correspond to that of the magnetization of the sample. We find that a modification of the cross-sectional geometry results in nonuniform changes in the local field profile and the effect proves especially strong in the range of nanometer lateral dimensions. Moreover, the effect of cross-sectional geometry on the magnetostatic spectrum of a nanorod is found to be the most significant in peripheral regions of elongated rods. This is due to the occurrence of dipolar local field wells in these very regions. The shape of these peripheral wells affects first of all the bulk-dead and surface modes, which are “stuck” in them; frequencies of these modes prove to increase when th...

Size Effects in Dynamics of Dipolar Planar Nanosystems

The equations of motion are derived for a magnetic planar system with dipolar interactions taken into account. Magnetostatic waves propagating perpendicularly to the sample surface and dipolar field static and dynamic components are calculated for the case when saturating field is applied perpendicularly to the sample surface. The corresponding frequency spectra and mode profiles are computed numerically with emphasis laid on size effects. It is established that two lowest-frequency modes are surface-localized modes. These modes preserve their surface-localized character with growing sample dimensions.