T. Wolfram

Dipole‐Exchange Spin Waves in Ferromagnetic Films

The effects of exchange on the magnetostatic surface and bulk spin waves of a ferromagnetic film in the regime where the dipole and exchange fields are both important are determined from the solutions of a sixth‐order differential equation. The eigenstates are admixtures of bulk and surface waves. With an applied magnetic field parallel to the film surface and for small values of the wave vector parallel to the surface, k, the Damon and Eshbach surface state is split into segments which join adjacent bulk branches. No sharp cutoff of the surface branch occurs as the angle between k and the applied field is increased, instead the character of the branch changes continuously from surface‐like to bulk‐like. For values of |u2009ku2009|≳104 a number of branches have significant surface character so that no single branch can be identified with the Damon‐Eshbach surface state. When the applied field is perpendicular to the surface a new type of surface spin wave occurs below the bulk manifold and is characterized by a c...

Coherent Exchange Scattering of Low‐Energy Electrons by Antiferromagnetic Crystals

Coherent exchange scattering has been observed by low‐energy electron diffraction from antiferromagnetic NiO. Below the Neel temperature, low‐energy electron diffraction from the (100) surface, exposed by cleavage in ultrahigh vacuum, has revealed one‐half order beams that correspond to the magnetic periodicity; these diffraction beams disappear at the Neel temperature. The intensity of the additional half‐order ``magnetic beams relative to that of the integer order beams is 2%–6%. Because direct dipole‐dipole and spin‐orbit interactions are much too weak to produce beams of the observed intensity, the occurrence of half‐order beams is attributed entirely to exchange scattering. The interpretation of the experimental results is discussed with the aid of a Heisenberg model Hamiltonian. Theoretical expressions for the elastic exchange cross section are in accord with the experimental data. The temperature dependence of the intensity of the exchange scattering is qualitatively explained by a molecular‐fiel...

Characteristics of Magnetostatic Surface Waves for a Metalized Ferrite Slab

Detailed calculations of the characteristics of the magnetostatic surface waves in a ferrite slab with a metalized surface are presented. The region of validity of the effective boundary condition model (EBCM) discussed by Seshadri is established. It is shown that the dispersion characteristics of overlayed magnetic systems can be modified and tailored to have a variety of frequency‐versus‐wavenumber properties. In general the modes are lossy and the degree of damping depends critically on the characteristic lengths of the problem.

MAGNETOSTATIC SURFACE MODES IN AN AXIALLY MAGNETIZED ELLIPTICAL CYLINDER

The spin‐wave spectrum of a long axially magnetized strip of noncircular cross sections is examined. The results are related to the limiting cases of the (1) ferromagnetic slab and (2) the circular cylinder. It is found that the elliptical cylinder results can be identified with the infinite‐film results of Damon and Eshbach when k, the propagation constant along the long axis of the ellipse, is identically equal to zero. This identification leads to a geometrical quantization of the wave vector in the infinite‐film calculation. For k ≠ 0 no simple quantization scheme can be used to relate the elliptical cylinder results to the infinite film results.

Effect of exchange on the magnetic surface states of yttrium iron garnet films

Abstract The spin-wave modes of a thin yttrium iron garnet film are calculated including dipole, exchange and finite thickness effects. The surface state dispersion curve is repelled by the exchange state curves and split into segments. At long wavelengths these segments closely follow the Damon-Eshbach magnetostatic dispersion curve. States with surface character exist at shorter wavelengths where the exchange energy is large but no continuous surface state dispersion curve can be defined.

Wavelength dependence of the photoenhancement of nonlinear surface‐wave convolution

The wavelength dependence of the photoenhancement of surface‐wave convolution on piezoelectric ZnO exhibits peaks which correspond to the exciton transitions observed in optical reflectivity and absorption experiments. A possible model for ``exciton resonance enhancement of nonlinear elastic‐wave interactions is proposed.

Optical surface spin-waves in the Heisenberg ferromagnet

Abstract An optical-like surface spin-wave branch lying above the bulk spectrum exists for the Heisenburg nearest neighbour exchange coupled ferromagnet when the surface exchange parameter exceeds that of the bulk.

Dipole-exchange modes of a thin ferromagnetic film

Abstract The spin-wave modes of a thin ferromagnetic film magnetized parallel to the surface are obtained including both dipole and exchange interactions.

A NEW TYPE OF SURFACE SPIN WAVE IN FERROMAGNETIC FILMS

A new type of surface spin wave occurs in a ferromagnetic film with an applied magnetic field perpendicular to the surface when the dipole and exchange energies are comparable. The surface wave propagates parallel to the surface but has a wave vector whose normal component is complex. States having a high degree of localization of the spin wave amplitude near the surfaces can occur.

Experimental test for pinned spins in ferromagnetic resonance: Parallel resonance

It has been shown that the magneto exchange rather than the usual magnetostatic modes occur in perpendicular resonance in thin ferromagnetic films when the spins are pinned. New branches of this type also occur in parallel resonance even though the basic symmetry and dipole-exchange equations are entirely different. Formulae are derived which can be used with experimental ferromagnetic resonance data to distinguish between the pinned and unpinned conditions. Recent conflicting results are shown to be erroneous.