Bulk Spin-wave Modes Research Articles

Antiferromagnetic magnon spintronic based on nonreciprocal and nondegenerated ultra-fast spin-waves in the canted antiferromagnet α-Fe2O3.

Spin-waves in antiferromagnets hold the prospects for the development of faster, less power-hungry electronics and promising physics based on spin superfluids and coherent magnon condensates. For both these perspectives, addressing electrically coherent antiferromagnetic spin-waves is of importance, a prerequisite that has been so far elusive, because, unlike ferromagnets, antiferromagnets couple weakly to radiofrequency fields. Here, we demonstrate the detection of ultra-fast nonreciprocal spin-waves in the dipolar exchange regime of a canted antiferromagnet using both inductive and spintronic transducers. Using time-of-flight spin-wave spectroscopy on hematite (α-Fe2O3), we find that the magnon wave packets can propagate as fast as 20 kilometers/second for reciprocal bulk spin-wave modes and up to 6 kilometers/second for surface spin-waves propagating parallel to the antiferromagnetic Néel vector. We lastly achieve efficient electrical detection of nonreciprocal spin-wave transport using nonlocal inverse spin-Hall effects. The electrical detection of coherent nonreciprocal antiferromagnetic spin-waves paves the way for the development of antiferromagnetic and altermagnet-based magnonic devices.

Narrow Magnonic Waveguides Based on Domain Walls.

The channeling of spin waves with domain walls in ultrathin ferromagnetic films is demonstrated theoretically and through micromagnetics simulations. It is shown that propagating excitations localized to the wall, which appear in the frequency gap of bulk spin wave modes, can be guided in curved geometries and propagate in close proximity to other channels. For Néel-type walls arising from a Dzyaloshinskii-Moriya interaction, the channeling is strongly nonreciprocal and group velocities can exceed 1 km/s in the long wavelength limit for certain propagation directions. The channeled modes represent an unusual analogy of whispering gallery waves that are one dimensional and nonreciprocal with this interaction. Moreover, a sufficiently strong Dzyaloshinskii-Moriya interaction can create a degeneracy of channeled and propagating modes at a critical wave vector.

Ferromagnetic resonance studies of surface and bulk spin-wave modes in a CoFe∕PtMn∕CoFe multilayer film

We studied exchange-dominated surface and bulk spin-wave modes in a single period of CoFe∕PtMn∕CoFe trilayer film grown on a seed layer of Ru with CoFe film compositions being Co-16at.%Fe. The thickness of the ferromagnetic CoFe layers is ∼400Å and that of the antiferromagnetic layer is 120Å. Multimode spin-wave spectra were observed using the ferromagnetic resonance technique, as the sample plane was rotated with respect to the direction of the magnetic field. The effective magnetic anisotropy parameters and the g factor of the magnetic film were calculated from the field corresponding to the main (strongest) resonance peak at different angles. In addition, we identified a high-order standing spin wave in our spectra and found a “critical angle” in the multilayer sample. As H is significantly rotated away from the normal, there is a critical orientation where only a single acoustic spin-wave mode can be observed. We included an effective surface anisotropy field to describe our results. From the surface anisotropy, we are able to analyze the spin-wave resonance spectra in terms of the dynamic surface spin pinning. This allows us to determine the exchange interaction stiffness in the CoFe layers, J∼2.7meV.

Angular dependence of spin-wave resonances and surface spin pinning in ferromagnetic (Ga,Mn) As films

We present a study of exchange-dominated surface and bulk spin-wave modes in (Ga,Mn)As films grown by molecular beam epitaxy. Multimode spin-wave spectra were observed using the ferromagnetic resonance technique, as the direction of the magnetic field $\mathbf{H}$ was varied within the plane of the layer, as well as relative to the plane. The field corresponding to the main (strongest) resonance peak at each angle is used to calculate bulk magnetic anisotropy parameters and the $g$ factor of the magnetic films. The dependence of spin-wave (SW) modes on the orientation of $\mathbf{H}$ is analyzed in terms of two fundamental models: the surface inhomogeneity model and the volume inhomogeneity model. Typically, when $\mathbf{H}$ is normal or near normal to the sample plane (i.e., $\mathbf{H}\ensuremath{\Vert}[001]$), a spectrum consisting of a series of well-resolved SW modes is observed. However, as $\mathbf{H}$ is rotated significantly away from the normal, at some orientation, a ``critical angle'' is found, at which only the single uniform mode is observed. As $\mathbf{H}$ is rotated further and approaches the in-plane direction (such as the [110] direction), a multiple-mode spectrum reemerges, ascribed in part to the appearance of a surface spin excitation due to unpinned surface spins. The analysis of spin-wave resonance spectra in terms of the dynamic surface spin pinning (derived from the surface anisotropy) allows us to determine the value of the exchange stiffness constant $D$.

Surface Magnetic Anisotropy of Epitaxial La0.7Mn1.3O2.84Thin Films

A spin-wave resonance technique was used to collect information on elementary magnon excitations in high quality epitaxial La0.7Mn1.3O2.84 films prepared by dc-magnetron sputtering. It was found that besides bulk spin-wave modes, the spin-wave resonance spectrum includes also the surface spin waves. The value of spin-wave stiffness constant D = 156 meV·A was found. The values of the surface magnetic anisotropy on both surfaces and their angular dependence were determined. The experimentally found spin-wave resonance spectra were explained based on the surface-inhomogeneity model. The effect of surface anisotropy on the spin-wave excitation conditions in epitaxial La0.7Mn1.3O2.84 films was investigated. Spin-wave resonance data give an indirect evidence of periodic charge-ordered stripes formation.

Bulk and surface spin excitations in thin films of manganites

A review of experimental studies of magnon excitations in manganites is presented. A microwave resonance technique, in particular a spin-wave resonance (SWR) technique, is shown to allow the study of not only bulk properties but also surface properties of manganite films. There are two main theoretical approaches used to interpret the SWR spectra: the volume inhomogeneity and the surface inhomogeneity models. The latter, introduced by Puszkarski, allows the interpretation of the observed surface magnon excitations in thin films. It is found that SWR spectra show evidence of manganites, besides bulk spin-wave modes, and also of surface spin-waves. This observation is used to determine the surface magnetic anisotropy. The effect of surface anisotropy on the spin-wave excitation conditions in epitaxial La 0.7 Mn 1.3 O 3-δ films is investigated in detail. SWR data give indirect evidence of periodic charge-ordered stripe formation. A strong effect of thermal annealing on stripe structure is observed and discussed.

Surface and bulk spin-wave resonances in La0.7Mn1.3O3films

In this work, we present the measurements of exchange-dominatednonpropagating surface and bulk spin-wave modes in the La-deficientepitaxial La0.7Mn1.3O3 films prepared by dc-magnetronsputtering. The angular and temperature dependences of the modes observedare discussed. The main result obtained is the observation of the spin-waveresonance (SWR) consisting of a series (17) of well resolved standingspin-wave modes in the perpendicular external magnetic field geometry. Thesurface spin-wave modes have been observed in manganites for the firsttime. As the magnetization is rotated out of perpendicular to the filmsurface, a `critical angle', φcr, is fixed, at which thesurface and first spin-wave modes have been transformed into the uniformmode. It is shown that only the uniform mode exists in the region0<φ<φcr. The surface mode data are consistent with thesurface-inhomogeneity model in which the surface-anisotropy field acts onthe surface spin. Possible origins of the surface anisotropy are discussed.Based on the temperature and angular dependences of SWR spectra, the mainmicroscopic parameters (the spin-wave stiffness, exchange constant andg-factor value) are established.

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.

Spin wave spectra in semi-infinite magnetic superlattices with nonuniaxial single-ion anisotropy

A microscopic theory, based on the Heisenberg model, is employed to investigate the spin wave spectra in a semi-infinite superlattice made up of two ferromagnetic materials, where the constituents may present both the uniaxial and nonuniaxial components of the single-ion anisotropy. Our calculations are carried out for the exchange-dominated regime, and a transfer-matrix approach is used to simplify the algebra, which otherwise could be quite heavy. The calculated spectra show that, in addition to bulk spin wave modes, there may be surface modes associated with the truncation of the superlattice.

Dipole-exchange theory for Brillouin light scattering from hybridized spin waves in ferromagnetic thin films.

A Green-function theory is presented for the Brillouin light scattering from hybridized surface and bulk spin-wave modes propagating in perpendicularly magnetized films with general asymmetric pinning at the surfaces. The calculations include a spin-wave theory with mixed exchange boundary conditions for the excitation spectrum and a Green-function (linear-response) formalism for light scattering from magnetic films. The influence of dipole-dipole hybridization of the spin-wave dispersion branches on the calculated light-scattering intensities is taken into account, and the dependence of the Brillouin spectra on the pinning conditions is evaluated. Applications of the theory to thin films of Fe and EuO are described.

Investigations of surface and bulk spin wave modes in as-prepared and annealed FeNi multilayers by spin wave resonance

Magnetic multilayers consisting of alternating layers of polycrystalline Fe and Ni were investigated by spin wave resonance experiments at room temperature. Nonpropagating surface spin wave modes, as well as standing volume modes, could be observed in the perpendicular field configuration. The appearance of the surface modes is connected with the surface anisotropy at the bottom and the top layers of the structure. The experimental SWR spectra have been compared with the results of calculations. Values of the surface anisotropy, the effective spin wave stiffness constant, and the effective magnetization of the multilayered structure were deduced from the measured spectra for as-prepared and annealed samples. The results are compared with those obtained by torque measurements.

A dipole-exchange theory for Brillouin light scattering from ferromagnetic thin films

A dipole-exchange theory is presented for Brillouin light scattering from the surface and bulk spin-wave modes propagating in perpendicularly magnetized films with general asymmetric pinning at the surfaces. The approach is based on a spin-wave theory with mixed exchange boundary conditions and a Green’s-function (linear-response) formalism for light scattering from magnetic films. The influence of dipole-dipole hybridization of the spin-wave dispersion branches on the calculated light-scattering intensities is taken into account, and the dependence of the Brillouin spectra on the pinning conditions investigated. Applications of the theory to Fe thin films are discussed.

Local spin-wave excitations in ferromagnetic electron-gas superlattices.

The spin-wave excitations are studied within a factorization approximation for ferromagnetic-electron-gas superlattices. An equation for determining the excitations is obtained. For a superlattice containing a defect layer whose charge (spin) density of the electrons and their effective mass, for instance, are different from those in the other layer planes of the superlattice, we find, in addition to the bulk spin-wave modes, another spin-wave mode localized by this defect layer.

Theory for Brillouin light scattering from dipole-exchange surface spin waves in ferromagnetic films

A theory is presented for Brillouin light scattering from spin-wave excitations in ferromagnetic films. The approach is based on a tensorial Green-function theory of the dipole-exchange spin wave spectrum in magnetic films. Mixed exchange boundary conditions are used, and the particular case of antisymmetric pinning in perpendicularly magnetized ferromagnetic films is discussed in detail. Explicit analytical expressions for the light-scattering cross sections are obtained in this case of scattering from both surface and bulk spin-wave modes. Applications of the theory to films of Fe and EuO are discussed. >

Spin waves in a semi-infinite Heisenberg ferromagnet with an impurity layer

A Heisenberg model is employed in a theoretical study of the effect of a magnetic impurity layer embedded in a semi-infinite ferromagnet. Using a Green’s function formalism we find that, in addition to bulk spin-wave modes, there may be localized spin-wave modes associated with the impurity layer and with the surface. The spin correlation functions are also calculated as a function of the impurity-layer distance from the surface. Results are also deduced for the temperature dependence of the magnetization in different layers of the ferromagnet.

Surface spin waves in a tight-binding itinerant-electron ferromagnet

We present the first theoretical study of surface spin waves in an itinerant-electron ferromagnet, using a single tight-binding band for d-electrons on a simple cubic lattice. All previous studies of bounded ferromagnets were based on a Heisenberg Hamiltonian with spins localized at sites. The surface is introduced in the Hubbard Hamiltonian by ignoring hopping between Wannier sites across a plane. Within a Wannier site representation, we set up the self-consistent field theory for the transverse spin-spin correlation function χ+−. When a ferromagnet has a planar boundary, χ+−. will exhibit a surface spin wave branch, in addition to the usual bulk spin wave modes. We solve the RPA integral equation for χ+− using a uniform spin polarization approximation for the static magnetization with classical specular scattering of electrons at the boundary. We find that a weakly damped surface branch splits off the top of the bulk spin continuum, rather than below as in the analogous Heisenberg model. The time-dependent magnetization associated with this mode is shown to be strongly localized within the first few surface layers, becoming more spread out as the static magnetization decreases. Our tight-binding Hubbard model with only on-site exchange leads to results very similar to those found by Griffin and Gumbs for a bounded electron gas model with an exchange interaction of finite range λ if we take this to be equal to the lattice spacing.

A magnetostatic theory of the response functions for a finite-thickness ferromagnetic slab and the application to Brillouin scattering

Calculations are given for the spin-dependent response functions (or Green functions) of a finite-thickness ferromagnetic slab using magnetostatic theory. The results are employed to obtain expressions for the integrated intensities for Brillouin scattering from the surface (magnetostatic) modes and bulk spin-wave modes of a ferromagnetic slab. Numerical estimates are made to compare the theory with recent experimental measurements for Fe and EuO, and it is found that many of the experimental observations can be satisfactorily explained.

The spin correlation functions of a semi-infinite Heisenberg ferromagnet

Results are derived for the dynamic correlation functions between a pair of spin operators at any two sites within a semi-infinite Heisenberg ferromagnet at low temperatures, T<<Tc. The correlation functions are found to contain terms describing the effects of the bulk spin-wave modes and the surface spin-wave modes, together with appropriate weighting factors. The results are employed to evaluate the spin deviation in the ferromagnet as a function of temperature and distance from the surface.

Surface spin waves in anisotropic Heisenberg ferromagnets: II

For pt. I see abstr. A12257 of 1969. A discussion of surface spin waves in anisotropic Heisenberg ferromagnets is given in the case where the interactions of the spins on the surface with other spins differs from the bulk spin interactions. It is shown that optical surface spin waves exist which lie above the bulk spin wave modes but the anisotropy has the effect of reducing the range of wave vectors over which they exist (as compared with the isotropic case).