Properties Of Magnons Research Articles

Magnons in ultrathin ferromagnetic films with a large perpendicular magnetic anisotropy

We report on an experimental observation of high-energy magnon excitations in ultrathin ferromagnetic films with a perpendicular easy axis. We demonstrate that a transversally spin-polarized beam can be used to excite and probe the high-energy magnons within spin-polarized electron energy-loss spectroscopy experiments. The magnon dispersion relation and lifetime are probed over the entire surface Brillouin zone for a set of body-centered tetragonal FeCo films with a large perpendicular magnetic anisotropy. First-principles calculations reveal that in addition to the tetragonal distortion, which is the origin of the large perpendicular magnetic anisotropy, the interfacial electronic hybridization also has a considerable impact on the properties of magnons.

Tunable Magnonic Spectra in Two‐Dimensional Magnonic Crystals with Variable Lattice Symmetry

AbstractTunable magnonic properties are demonstrated in two‐dimensional magnonic crystals in the form of artificial ferromagnetic nanodot lattices with variable lattice symmetry. An all‐optical time‐domain excitation and detection of the collective precessional dynamics is performed in the strongly magnetostatically coupled Ni80Fe20 (Py) circular dot lattices arranged in different lattice symmetry such as square, rectangular, hexagonal, honeycomb, and octagonal symmetry. As the symmetry changes from square to octagonal through rectangular, hexagonal and honeycomb, a significant variation in the spin wave spectra is observed. The single uniform collective mode in the square lattice splits in two distinct modes in the rectangular lattice and in three distinct modes in the hexagonal and octagonal lattices. However, in the honeycomb lattice a broad band of modes are observed. Micromagnetic simulations qualitatively reproduce the experimentally observed modes, and the simulated mode profiles reveal collective modes with different spatial distributions with the variation in the lattice symmetry determined by the magnetostatic field profiles. For the hexagonal lattice, the most intense peak shows a six‐fold anisotropy with the variation in the azimuthal angle of the external bias magnetic field. Analysis shows that this is due to the angular variation of the dynamical component of magnetization for this mode, which is directly influenced by the variation of the magnetostatic field on the elements in the hexagonal lattice. The observations are important for tunable and anisotropic propagation of spin waves in magnonic crystal based devices.

Relaxation Time of Terahertz Magnons Excited at Ferromagnetic Surfaces

The temporal and spatial properties of terahertz magnons excited at ferromagnetic fcc Co(100) and bcc Fe(110) surfaces are investigated experimentally. The magnon lifetime is found to be a few tens of femtoseconds at low wave vectors, which reduces significantly as the wave vector approaches the Brillouin zone boundary. Surprisingly, the lifetime is very similar in both systems, in spite of the fact that the excitation energy in the Co(100) film is by a factor of two larger than in the Fe(110) film. The magnon wave packets propagate only a few nanometers within their lifetime. In addition to the fact that our results describe the damping mechanism in ultrafast time scales, they may provide a way to predict the ultimate time scale of magnetic switching in nanostructures.

Towards high-frequency negative permeability using magnonic crystals in metamaterial design

We investigate the magnonic properties of thin slabs of one-dimensional magnonic crystals with the aim of obtaining a structure that possesses negative permeability at high frequencies. Metamaterials of this kind could be used within devices based on the negative refractive index phenomenon. We calculate the relative excitation strengths of different spin-wave modes in one-dimensional magnonic crystals. We find that the coupling between light and high-order magnonic modes can be significant for the specific design of the magnonic structure. These results suggest that magnonic crystals are therefore promising candidates for the negative refractive index metamaterials.

On the effect of inhomogeneous magnetoelectric (flexomagnetoelectric) interaction on the spectrum and properties of magnons in multiferroics

The features of the magnon spectrum in easy-plane multiferroics (such as BiFeO3), which allow inhomogeneous magnetoelectric (flexomagnetoelectric) interaction P[(L∇)L − LdivL], where L and P are the antiferromagnetic moment and electric polarization, respectively, have been theoretically analyzed. It has been shown that, in contrast to the magnon spectrum of a usual easy-plane antiferromagnet, a multiferroic with this magnetic structure is characterized by, first, the interaction between magnons of both branches propagating along the weak ferromagnetic moment and the appearance of a minimum (or zero) of the frequency of one of the branches, which reflects the instability of the system with respect to the transition to an inhomogeneous state with increasing flexomagnetoelectric interaction and, second, the nonequivalence (nonreciprocity) of the propagation of spin waves along and against the antiferromagnetism vector, which coincides with the toroidal moment in this system.

THERMOFIELD ANALYSIS OF MAGNON SQUEEZING STATE IN THE FERROMAGNET

In this paper, we introduce the self-consistent field approximation to treat with the nonlinear interaction among spin waves. Then temperature-dependent Bogoliubov transformation is introduced to generate a new representation which engenders the transition from the zero temperature to the finite temperature. At last, temperature-dependent quantum fluctuation properties of magnons are discussed in the thermal field. At lower temperature, we find that the fluctuation of spin-component at some given time regions can be below the zero-point fluctuation level of the vacuum state and exhibit a periodical squeezing behavior. In particular, these squeezed effects vanish with the increasing of temperature. These squeezing effects differ from the previous studies.

Electromagnon excitations in modulated multiferroics

The phenomenological theory of ferroelectricity in spiral magnets presented in [M. Mostovoy, Phys. Rev. Lett. 96, 067601 (2006)] is generalized to describe consistently states with both uniform and modulated-in-space ferroelectric polarizations. A key point in this description is the symmetric part of the magnetoelectric coupling since, although being irrelevant for the uniform component, it plays an essential role for the nonuniform part of the polarization. We illustrate this importance in generic examples of modulated magnetic systems: longitudinal and transverse spin-density wave states and planar cycloidal phase. We show that even in the cases with no uniform ferroelectricity induced, polarization correlation functions follow the soft magnetic behavior of the system due to the magnetoelectric effect. Our results can be easily generalized for more complicated types of magnetic ordering, and the applications may concern various natural and artificial systems in condensed matter physics (e.g., magnon properties could be extracted from dynamic dielectric response measurements).

Spin dynamics in the diluted ferromagnetic Kondo lattice model

The interplay of disorder and competing interactions is investigated in the carrier-inducedferromagnetic state of the Kondo lattice model within a numerical finite-size study in whichimpurity positional disorder is treated exactly. Competition between impurityspin couplings with increasing hole doping results in a strong optimization ofTc at , highlighting the importance of compensation in diluted magnetic semiconductors. The estimatedTc is in good agreement with experimental results forGa1−xMnxAs for corresponding impurity concentration, hole bandwidth, and compensation. Dilution isshown to result in a sharply enhanced density of low-energy magnon modes extended overthe majority bulk spins and high-energy magnon modes localized over impurity spinclusters. The effects of these magnon properties on finite-temperature spin dynamics arestudied quantitatively using a locally self-consistent magnon renormalization scheme.The large enhancement in the density of low-energy magnetic excitations resultsin a rapid thermal decay of magnetization, which fits well with the Bloch formM0(1−BT3/2) at lowtemperature, with B of the same order of magnitude as obtained in recent superconductingquantum interference device (SQUID) magnetization measurements onGa1−xMnxAs samples. Furthermore, strong cluster couplings and correlations are shownto slow down the magnetization decay and prolong magnetic ordering nearTc, as is also observed in magnetization measurements.

Magnon localization in Mattis glass

We study the spectral and transport properties of magnons in a model of a disordered magnet called Mattis glass, at vanishing average magnetization. We find that in two dimensional space, the magnons are localized with the localization length which diverges as a power of frequency at small frequencies. In three dimensional space, the long wavelength magnons are delocalized. In the delocalized regime in 3d (and also in 2d in a box whose size is smaller than the relevant localization length scale) the magnons move diffusively. The diffusion constant diverges at small frequencies. However, the divergence is slow enough so that the thermal conductivity of a Mattis glass is finite, and we evaluate it in this paper. This situation can be contrasted with that of phonons in structural glasses whose contribution to thermal conductivity is known to diverge (when inelastic scattering is neglected).

Spin-waves on a planar heisenberg frustrated antiferromagnet with Dzyaloshinsky-Moriya type coupling

A semi-infinite bidimensional Heisenberg frustrated antiferromagnet system is considered, where the magnetic frustration phenomena are due to the competition of the first inter-sublattice ( J 1v AB) and the second intra-sublattice ( J 2v AA(BB)) exchange interactions. The bulk and surface spin-waves are calculated as a function of the frustration parameter J 1 v AB J 2 v AA(BB) , accounting for Dzyaloshinsky-Moriya (DM) type coupling. The principle of the matching method is detailed by coupling the properties of bulk magnons with evanescent spin-waves along the direction perpendicular to the surface. It is shown that the behaviour of the bulk magnon, as well as acoustic and optic surface spin-waves, is very sensitive to surface exchange and anisotropy. The evolutions of acoustic and optic surface modes are interpreted by means of a frustration parameter, and the DM term induces a bulk magnon gap band, consistent with an anisotropic term

Magnon properties of the one-dimensional quasiperiodic system

At low excitations, the ferromagnetic spin-wave problem of the one-dimensional quasiperiodic system is converted into the one which is analogous to the electronic and phonon problems. The ferromagnetic magnon properties are studied by the transfer-matrix technique and it is concluded that the frequency spectrum is a Cantor set. It is also shown that, at low excitations, the antiferromagnetic spin-wave problem of the one-dimensional quasiperiodic system can be converted in a similar way to the ferromagnetic one, and the antiferromagnetic magnon properties can be studied by the transfer-matrix technique.

Nonreciprocal surface waves

Some surface waves have the property that a simple reversal of the direction of propagation leads to a surface wave with a different frequency. In this paper we explore the properties of such nonreciprocal waves for a variety of excitations and structures. For a semi-infinite geometry the nonreciprocity can be quite dramatic. For example in some magnetic systems, a surface wave exists for propagation in one direction, but no surface wave exists for propagation in the reverse direction. In thin films, it is generally the localization of the surface wave which is nonreciprocal. Thus a surface wave travelling along the + x axis may be localized at the upper surface of the film, while a surface wave travelling along the - x axis is localized at the lower surface of the film. We will discuss nonreciprocal surface excitations which occur in a variety of systems. The elementary properties of nonreciprocal surface plasmons, polaritons, phonons and magnons are derived. We briefly review some of the applications of nonreciprocal surface waves to practical signal processing devices. Finally we discuss the microscopic origin of nonreciprocity.

Reflectivity of Uniaxial Antiferromagnetic and Ferrimagnetic Crystals

AbstractFormulae for the reflectivity of uniaxial antiferromagnetic and ferrimagnetic crystals are derived for normal incidence parallel to the optical axis. The formulae show that in general the reflected waves are elliptically polarized. In particular, they can be used to fix the zeros of the off‐diagonal elements of the permeability tensor. Besides, the formulae are suitable to determine the properties of magnons from reflectivity spectra of uniaxial antiferromagnetic and ferrimagnetic crystals.

Diffuse phase transition in rare earth ion doped SBN : S. Kuroda and K. Kubota, Faculty of Science, Kwansei Gakuin University, Nishinomiya, Japan.

A review of magnon properties of yttrium-iron garnet (YIG), a classical object for experimental studies in magnetism, is presented. Both experimental and theoretical results concerned with thermodynamics and kinetics of YIG are described. The main purposes of the review are to introduce a new method of approximate calculation of the magnon spectra in magnets with large unit cell and to obtain by means of this method some basic properties of YIG. In particular, it is shown that the problem of calculating the frequencies of all the 20 magnon branches over the entire Brillouin zone contains two small parameters. First, because of the large number of magnetic atoms in the unit cell the distance between the nearest interacting magnetic atoms is small in comparison with the lattice constant and, accordingly, with the wavelength of a spin wave. An effective long-wavelength character thus arises in the problem. Second, there are a large number of wave-vector directions along which many elements of the Hamiltonian matrix vanish by symmetry in the basis which diagonalizes this matrix for k = 0. These matrix elements thus have an additional, angular smallness for arbitrary directions of k. These matrix elements can be taken into account using perturbation theory. As a result, the large elements of the Hamiltonian matrix are few in number, and they can be eliminated by several two-dimensional rotations. Approximate expressions, differing from the computer calculations by ⪅ 10%, are thus obtained for the frequencies.Neutron scattering data are used to find the values of the exchange integrals in YIG and to obtain the magnon spectra. It is shown that in the energy range T ⪅ 260 K only magnons of the lower branch are excited; the spectrum of these “ferromagnons” is quadratic in the wave vector only up to 40 K and becomes linear in the region ωk ⪆ 40 K. For temperatures up to 400 K the temperature dependence of the magnetization is calculated in the spin-wave approximation and good agreement with experimental data is found.A brief review of experimental data on magnon relaxation in YIG is presented. The magnon-magnon interactions which cause the magnon relaxation are described. The amplitude of the four-magnon exchange interaction is determined, and the temperature correction to the frequency is evaluated. This temperature correction is positive, in contrast to the case of simple cubic ferromagnet with nearest-neighbour interaction. The exchange relaxation rate is calculated for normal and umklapp processes. It is shown that the magnetic dipole interaction is important only for the ferromagnons; the amplitude of this interaction and the corresponding relaxation rate are determined. Three-magnon scattering processes are allowed only for wave vectors larger than a certain k/; at k = k/ there is a discontinuity in the wave-vector dependence of the damping. A calculation is given for the nonvanishing contribution to the relaxation at k = 0 on account of scattering processes involving optical magnons; this contribution is due to the local uniaxial anisotropy. The relative role of each of the investigated relaxation mechanisms is discussed, and the correspondence of the present results with the experimental data is examined.

Spin waves in rare earth metals including non-linear s-f exchange interaction effect

Magnon dispersions in ferromagnetic and screw structures are calculated including non-linear s-f exchange interaction effect, in particular in their instability regions. They explain naturally anomalous magnon properties in Gd and Ho.

THE EFFECT OF SURFACES ON THE PROPERTIES OF MAGNETIC MATERIALS

In the first portion of the paper, we derive the form of the T-matrix that describes the scattering of a magnon from the surface of a Heisenberg ferromagnet. The model employed allows the exchange constants in the surface layer of spins to differ from the values appropriate to the bulk crystal. We also obtain the form of the T-matrix without the need to specify the detailed geometrical arrangement of spins in the layers parallel to the surface, or the range of the exchange interaction in directions parallel to the surface. The T-matrix, and the resulting Green's function may thus be applied to compute properties of the semi-infinite crystal for a wide variety of geometries. In this work, we obtain the surface magnon dispersion relation by examining the poles of the T-matrix. The results are illustrated with applications to a specific model considered by Fillipov, where acoustical surface magnons below the bulk spin wave band, or optical surface magnons above the bulk band may result. We then use the T-matrix to compute the lifetime of spin waves from scattering off the surface. We find the lifetime τ(k) of a spin wave of wave vector k is given by the simple expression τ = L/|[MATH].VG(k)| where L is the crystal thickness, [MATH] a unit vector normal to the surface, and VG(k) the magnon group velocity. This result is valid even for large values of k, and is unaffected by changes in exchange constants near the surface. In a second portion of the paper, we provide a brief review of recent theoretical studies of the semi-infinite Heisenberg ferromagnet. The behavior of the mean spin deviation near the surface, and the effect of surface pinning fields and changes in the exchange constants near the surface on the surface specific heat will be examined. Some features of the theory of low energy electron scattering from the magnetic degrees of freedom will be described. Finally, the properties of surface magnons in antiferromagnets and the surface spin flop transition will be discussed briefly.

Theory of infra-red and optical spectra of antiferromagnets

Abstract The contributions of magnons to the optical properties of antiferromagnets having the rutile structure are discussed. The properties considered are electric-dipole active two-magnon absorption in the infra-red, and magnon sidebands on sharp-line exciton transitions in the visible. The discussion is based on a thorough treatment of the properties of excitons and magnons in the antiferromagnetically ordered state. The site-group and space-group symmetries of the magnetic excitations are derived and the selection rules for electric and magnetic dipole transitions are determined. The occurrence of magnetic Davydov splittings of the excitons is investigated, and their symmetry properties throughout the Brillouin zone are derived. The functional dependences of exciton energy on wave vector are calculated. Applications of the theory are made to experimental results on excitons and magnons in MnF2, FeF2 and CoF2. The possible mechanisms for two-magnon and magnon-sideband absorption are discussed, and the...