Properties Of Spin Waves Research Articles

Multiferroic Materials for Spin-Based Logic Devices

Logical devices based on spin waves offer the potential to avoid dissipation mechanisms that limit devices based on either the charge or spin of mobile electrons. Multiferroic magnetoelectrics, which are materials that combine ferroelectric and magnetic order, allow direct switching of magnetic order and thence of spin-wave properties using an applied electric field. The intrinsic coupling between polarization and magnetic moments, generated by strong electronic correlations in these multiferroic materials, is argued to provide new approaches to spin-wave injection and spin-wave switching using applied voltages with no external magnetic field. These effects are shown to arise in a phenomenological Landau theory of coupled electronic and magnetic orders in multiferroic BiFeO 3 , and found to depend subtly on differences between the crystalline and film states of this material.

Spin-wave excitations in arrays of asymmetric ferromagnetic nanorings

Calculations are reported for the spin-wave excitations in asymmetric ferromagnetic nanorings using a Hamiltonian-based formalism. Both the exchange and dipole-dipole interactions are included, as well as an external magnetic field and single-ion anisotropy. The equilibrium configurations of the nanorings are found by minimizing numerically the energy functional with respect to the spin orientation. Depending on the geometry, particularly the degree of asymmetry and the in-plane applied magnetic field, the nanorings can be in a vortex, onion, or other inhomogeneous state. Spin-dependent Green’s functions are calculated to deduce the dispersion spectra and the mode profiles of the spin waves, and the dependence of the spin-wave properties on the asymmetry factor is studied. The effects of inter-ring dipolar coupling on the spin-wave spectrum are also investigated by considering small arrays (e.g., a 3×3 square array) of nanorings.

Dipole-exchange spin waves in ferromagnetic stripes with inhomogeneous magnetization

Realistic calculations of linear spin waves in thin ferromagnetic stripes are presented using a microscopic method based on a Hamiltonian approach. The theory, which is applicable to inhomogeneously magnetized samples, incorporates both the exchange and dipole-dipole interactions as well as effects of single-ion anisotropy and an external magnetic field applied either parallel or perpendicular to the stripe axis. This approach does not require the specification of phenomenological boundary conditions to study spin waves in these confined configurations. The Green's function theory is applied to Permalloy and nickel stripes to obtain the frequency, spatial distribution, and spectral intensity of discrete spin-wave modes. Through the spin-wave properties, the effective pinning parameters of the dynamic magnetization at the boundaries of the systems are deduced.

Magnetization dynamics in nanocontact current controlled oscillators

This work focuses on the magnetization dynamics driven by spin-polarized currents in nonconfined systems when a point-contact geometry is used. We demonstrate that a generalized formulation of the spin-torque efficiency function, which includes space and angular dependences, combined with the usage of abrupt absorbing boundary conditions, which has been found to be suitable to eliminate spin-wave reflection at the computational boundaries, leads to a quantitative agreement between simulations and experimental observations. A study of the properties of spin waves excited close to the threshold clearly indicates the robustness of Slonczewski's prediction. Nevertheless, full-scale investigations reveal the necessity of introducing additional nonlinearities in the equation of motion under the large-angle oscillation regime.

Microscopic theory of spin-wave excitations in ferromagnetic nanorings

A microscopic theory is developed for the spin-wave excitations in ferromagnetic nanorings where the physical dimensions (inner and outer diameters and height) may be of the same order. Both the dipole-dipole and the exchange interactions are included in the Hamiltonian, together with single-ion anisotropy terms and an external magnetic field assumed to be applied either parallel or perpendicular to the ring axis. The equilibrium configurations of the systems are obtained by minimizing numerically the energy functional with respect to the spin orientations. The nanorings can be in bottleneck, twisted, bidomain, or vortex types of configuration. A Green’s function method is employed to calculate the dispersion spectra and other spin-wave properties. Applications to real systems, such as nickel nanorings, are made by choosing the parameters appropriately.

Effects of the on-site Coulomb repulsion in double-exchange magnets

We investigate the zero-temperature phase diagram and spin-wave properties of a double exchange magnet with on-site Hubbard repulsion. It is shown that even within a simple Hartree-Fock approach this interaction (which is often omitted in theoretical treatments) leads to qualitatively important effects which are highly relevant in the context of experimental data for the colossal magnetoresistance compounds. These include the asymmetry of the doping dependence of spin stiffness, and the zone-boundary ``softening'' of spin wave dispersion. Effects of Hubbard repulsion on phase separation are analyzed as well. We also show that in the ferromagnetic phase, an unusual temperature-dependent effective electron-electron interaction arises at finite $T$. The mean-field scheme, however, does not yield the experimentally observed density of states depletion near the Fermi level. We speculate that the proper treatment of electron-electron interactions may be necessary for understanding both this important feature and more generally the physics of colossal magnetoresistance phenomenon.

Thermal properties of surface and bulk spin waves in metamagnets FeBr2 and FeCl2

Surface and bulk spin wave properties are studied in metamagnets, which consist of ferromagnetically ordered layers with the intralayer ferromagnetic exchange coupling being much stronger than the interlayer antiferromagnetic exchange. Using a Green's function method, dispersion relations are calculated for the S = 1 metamagnets FeBr2 and FeCl2 over a broad range of temperatures by considering layer dependent thermal averages for the spins. Results are also deduced for the temperature dependence of the integrated intensities of acoustic and optical spin waves close to the surface.

Self-consistent Ornstein–Zernike approximation for three-dimensional spins

An Ornstein–Zernike approximation for the two-body correlation function embodying thermodynamic consistency is applied to a system of classical Heisenberg spins on a three-dimensional lattice. The consistency condition determined in a previous work is supplemented by introducing a simplified expression for the mean-square spin fluctuations. The thermodynamics and the correlations obtained are then compared with approximants based on extrapolation of series expansions and with Monte Carlo simulations. Many properties of the model, including the critical temperature, are very well reproduced by this simple version of the theory, but it shows substantial quantitative error in the critical region, both above the critical temperature and with respect to its rendering of the spontaneous magnetization curve. A less simple but conceptually more satisfactory version of the SCOZA is then developed, but not solved, in which the effects of transverse correlations on the longitudinal susceptibility is included, yielding a more complete and accurate description of the spin-wave properties of the model.

Localization and scaling properties of spin waves in quasi-periodic magnetic multilayers

We investigate the localization and scaling properties of the spin wave spectra in magnetic multilayers build up following the Fibonacci, Thue-Morse and double-period sequences. We present a quantitative analysis of the localization and magnitude of the allowed bandwidths in the spin wave spectra of these quasi-periodic structures, as well as how they scale as a function of the number of generations of the sequences.

Static and dynamic properties of patterned magnetic permalloy films

Static magnetic and spin-wave properties of square lattices of permalloy micron dots with thicknesses of 500 Å and 1000 Å and with varying dot separations have been investigated. The spin-wave frequencies can be well described taking into account the demagnetization factor of each single dot. A magnetic fourfold anisotropy was found for the lattice with dot diameters of 1 μm and a dot separation of 0.1 μm. The anisotropy is attributed to an anisotropic dipole-dipole interaction between magnetically unsaturated parts of the dots. The anisotropy strength (order of 10 5 erg/cm 3) decreases with increasing in-plane applied magnetic field.

Anisotropic magnetic coupling of permalloy micron dots forming a square lattice

Static magnetic and spin wave properties of square lattices of permalloy micron dots with thicknesses of 500 and 1000 Å and with varying dot separations have been investigated. A magnetic fourfold anisotropy was found for the lattice with dot diameters of 1 μm and a dot separation of 0.1 μm. The anisotropy is attributed to an anisotropic dipole–dipole interaction between magnetically unsaturated parts of the dots. The anisotropy strength (order of 105 erg/cm3) decreases with increasing in-plane applied magnetic field.

Brillouin light scattering investigations of structured permalloy films

The static and spin wave properties of regular square lattices of magnetic dots of 0.5–2 μm dot diameter and 1–4 μm periodicity patterned in permalloy films have been investigated by Brillouin light scattering. The samples have been structured using x-ray lithography and ion beam etching. The Brillouin light scattering spectra reveal both surface and bulk spin wave modes. The spin wave frequencies can be well described taking into account the demagnetization factor of each single dot. For the samples with smallest dot separation of 0.1 μm a fourfold in-plane magnetic anisotropy with the easy axis directed along the pattern diagonal is observed, indicating anisotropic coupling between the dots.

Properties of Standing Spin Waves in a Thin Film of Field-Induced Metamagnet with Modified Surface Exchange Interactions

Characteristic equations and dispersion relations derived in the first paper of this series are applied to investigate the conditions for the occurrence of different types of standing spin waves in the FeBr2 field-induced metamagnetic thin film with (001) surfaces. The spin-wave properties and stability conditions of the system in the paramagnetic phase are examined numerically for modified surface exchange interactions. The essential influence of the film thickness as well as modifications of surface disturbances on the behaviour of standing spin waves is illustrated in stability diagrams. The obtained results enabled the determination of the condition for the appearance of various spin-wave features, the limits on the values of surface exchange interaction parameters and consequently, the range of physical solutions for the considered system.

Spin-wave excitation in a quasi-one-dimensional organic ferromagnet.

The spin-wave properties of a quasi-one-dimensional organic ferromagnet model are investigated. By unrestricted Hartree-Fock approximation, it is shown that the ferromagnetic ground state is stable due to topological structure of the system. The spin-wave excitation is investigated using the random-phase approximation. The typical spectrum of such a model is obtained, including an acoustic spin-wave mode and two optical modes below the Stoner gap. It is found that the excitation possesses the general feature of antiferromagnetic order. Especially, the acoustic spin-wave mode has rather large stiffness.

Interface quality and magnetic properties of Co/Au multilayers investigated by Brillouin light scattering

The magnetic properties of ion-beam-sputtered Co/Au multilayers have been investigated by Brillouin light scattering. Annealing the samples enhances the perpendicular anisotropy and also gives evidence for perpendicularly magnetized domains. Upon annealing the saturation magnetization is reduced. The spin-wave properties and the obtained magnetic parameters are discussed with respect to interface sharpness and roughness.

A bipartite spin 1/2 Heisenberg model with a gap to excitations

The author considers the nearest neighbour quantum mechanical Heisenberg model acting on two simple one-dimensional chains of spin 1/2 atoms. By showing that these models can be mapped onto a chain of spin 1 composites, the author deduces that the spectrum has a gap, provided that the spin 1 chain has a gap. This result is in contrast to that found for the chain of spin 1/2 atoms and suggests that a distinction between integer and half-integer spins is restricted to the linear chain. The author presents a simple interpretation for the spin correlations of the low energy excitations and give new numerical evidence for a gap in the spectrum of the spin 1 chain. The lowest lying spin 1/2 chain excitation is a domain wall, but the lowest laying spin 1 chain excitation has previously been suggested to have spin-wave properties, this hypothesis is tested numerically.

Magnetic properties of Co/Pd multilayers determined by Brillouin light scattering and SQUID magnetometry

Co/Pd multilayers with modulation wavelengths between 4 and 220 Å have been prepared by magnetically enhanced dc-triode sputtering on single-crystal sapphire substrates. Their saturation magnetization and volume and interface anisotropies have been investigated using Brillouin light scattering from collective spin waves and by SQUID magnetometry. The saturation magnetization of Co is found to be independent of the Co layer thickness and reduced by about 20% from the Co bulk value. From the comparison of the results of the two experimental methods, clear evidence for a Pd polarization is found and the polarization depth is estimated. Samples with Co thicknesses of 2 atomic layers and Pd thicknesses ≥5 atomic layers exhibit a perpendicular magnetization due to a large negative out-of-plane interface anisotropy. The properties of spin waves in Co/Pd multilayers with the direction of magnetization pointing out-of-plane are discussed with respect to an appropriate theoretical model.

Bilayer ferromagnetic film with tensorial interface exchange coupling. Localized modes

We present some results of a new theory of standing spin-wave excitations in bilayer magnetic film with exchange coupling across the interface between two ferromagnetic layers. The model Hamiltonian includes exchange and Zeeman energies, as well as anisotropy terms at the free surfaces and at the interface. Exchange coupling across the interface is assumed in tensorial form with (two) in-plane J | int and out-of-plane J ± int exchange integral components. We discuss the interface effects using the concept of effective pinning parameters and dynamical coupling parameters for the spin-waves at the interface. It is found that for certain values of the ratio of the inteface exchange intergral components ϵ = J ± int/ J | int the constituent magnetic sublayers may be considered as effectively decoupled as regards the spin-wave properties. When studying the existence conditions of localized modes in the bilayer magnetic film one comes upon quite novel features that do not occur in the analysis of the respective existence conditions for a single film.

The effect of correlation on the mobility edge in random Heisenberg ferromagnets

The localisation properties of spin waves for Heisenberg ferromagnets with random uniaxial anisotropy energy and random exchange interaction is studied in the framework of the weak localisation theory. The correlation effect is found to influence the phase diagrams near the band edge region strongly.

Four-spin interaction as an effective interaction in high-T c copper oxides

The lowest states of an undoped copper-oxide cluster are determined numerically and fitted by a spin Hamiltonian containing a cyclic 4-spin exchange interaction. The size of this interaction is found to be about a quarter of the size of the nearest-neighbor Heisenberg exchange. The 4-spin exchange leads to a renormalization of spin-wave properties and to extra features in magnetic Raman scattering. The calculated exchange parameters are consistent with the observed spin-wave velocity.