Ernst Schlömann

Demagnetizing Field in Nonellipsoidal Bodies

A general method for calculating the (nonuniform) demagnetizing field in ferromagnetic bodies of arbitrary shape is described. The theory is based upon the assumption that the magnitude of the magnetization vector is constant throughout the sample and that its direction coincides with the direction of the local magnetic field at any point within the sample. The total magnetic field is expressed as a series of ascending powers in M/H0, where M is the saturation magnetization and H0 the applied magnetic field. The first term of this series expansion (first‐order theory) gives the demagnetizing field for very large applied fields, i.e., for a uniformly magnetized sample. The higher‐order corrections (we consider in detail only the first correction term; second‐order theory) take account of the fact that the sample is not in general uniformly magnetized. The general theory has been applied to rectangular slabs and circular cylinders. The first‐order demagnetizing field has been calculated for rectangular slab...

Recent Developments in Ferromagnetic Resonance at High Power Levels

The influence of inhomogeneities on the saturation of the ferromagnetic resonance is investigated. In the region of moderate power levels, the susceptibility at resonance χ′′ varies linearly with the square of the rf field h. The magnitude of the slope ∂χ′′/∂h2 depends on the nature of the dominant scattering mechanism. If the uniform mode scatters primarily to spin waves of very large wavelength, the slope should be negative. Scattering to spin waves of short wavelength gives a positive contribution to the slope and can lead to a reversal of the sign. The theoretical predictions agree with measurements at X band on various polycrystalline garnets and ferrites.At very high power levels the opening angle of the precessing magnetization vector approaches a limiting value, which is related to the “line width” ΔHk of z directed spin waves having the same frequency as the uniform mode. Experiments on single crystals and polycrystals of rare earth substituted garnets show that ΔHk increases approximately linear...

Spin-wave analysis of ferromagnetic resonance in polycrystalline ferrites

Abstract A theory of ferromagnetic resonance is developed in which dipolar interaction is taken into account by means of the spin-wave formalism. Due to crystalline anisotropy and the poly-crystalline character of the material, the homogeneous mode of precession interacts with spin waves whose wavelength is of the order of, or larger than, the average linear grain size. The moments of the absorption line are calculated for the case of vanishingly small single-crystal linewidths. Linewidth and lineshift due to crystalline anisotropy are calculated by a perturbation-like approach in which interactions which do not involve the homogeneous mode are neglected. The theory predicts a very strong frequency- and shape-dependence of the linewidth for the case in which the homogeneous mode is approximately degenerate with long-wavelength spin waves propagating in directions perpendicular to the d.c. field.

Generation of Phonons in High‐Power Ferromagnetic Resonance Experiments

The magnetoelastic energy of ferromagnets leads to a coupling between spin waves and elastic vibrations. Because of this coupling the normal modes are not purely magnetic or purely elastic but contain admixtures of both kinds of excitation, the mixing being strongest when the unperturbed waves have the same frequency and wavelength. It is shown theoretically that under suitable conditions (of frequency, dc field, and sample shape) coupled magnetoelastic waves with wavelengths of the order of 1 μ or less can be generated in high‐power ferromagnetic resonance experiments. The magnetoelastic interaction increases the threshold precession angle of the uniform mode, the fractional increase being proportional to the group velocity times the relaxation time for spin waves divided by the same quantity for transverse phonons.

Ferromagnetic resonance in polycrystalline ferrites with large anisotropy—I: General theory and application to cubic materials with a negative anisotropy constant

Abstract If the anistropy field is much larger than the single-crystal line width and the saturation magnetization, the shape of the resonance line is essentially determined by the spreading of resonance frequencies for different grains due to crystalline anisotropy. More precisely, if w ( H ) dH is proportional to the number of grains that have their resonance in the range of applied d.c. field between H and ( H ) dH , the absorption versus field curve should be a smeared-out image of the distribution function w ( H ). The distribution function has characteristic singularities arising from the stationary points of the resonance field versus orientation surface. The behavior of w ( H ) in the vicinity of the singularities is calculated for first-order cubic anisotropy, and w ( H ) is obtained by interpolation. For small anisotropy fields, the calculated line shape has a single peak which corresponds to grains in which a [110] direction is aligned with the d.c. field. For larger anisotropy fields (γH a /lΩ> 0.5) , a secondary peak occurs. It corresponds to grains in which an easy axis is aligned with the d.c. field. The theory accounts for secondary resonance peaks at low fields observed in ferrimagnetics near the compensation point.

Generation of Spin Waves in Nonuniform Magnetic Fields. I. Conversion of Electromagnetic Power into Spin‐Wave Power and Vice Versa

The conversion of electromagnetic power into spin‐wave power and vice versa is investigated from a theoretical point of view. The analysis applies to a rod of ferromagnetic material whose two ends are each in a resonant cavity that is connected to a waveguide. The dc magnetic field is assumed to be nonuniform in such a way that the effective wavelength of the spin waves becomes large in those regions of the sample that protrude into the cavities. The theoretical analysis of the excitation process leads to a differential equation which is of the same form as the well‐known wave equation except that the wavenumber is a function of position. The conversion efficiency depends on the solution of this wave equation through a simple integral over the wavefunction which has the physical significance of a coupling length. A numerical estimate indicates that substantially complete conversion should be possible.

Theory of Magnetostatic Modes in Long, Axially Magnetized Cylinders

The characteristic equation determining the eigenfrequencies of the magnetostatic modes is derived from the equations of motion and the boundary conditions. The solutions may be classified as pertaining to surface and to volume modes. Surface‐mode solutions exist only for sufficiently small wave numbers, and their eigenfrequencies are larger than those of volume modes. The eigenfrequencies generally decrease with increasing wave number. Approximate, analytic expressions for the dependence of the eigenfrequencies on wave number have been obtained for the regions in which the wavelength is either much smaller or much larger than the cylinder radius. The approximate expressions are compared with numerical results obtained by means of an electronic computer.

Generation of spin waves in nonuniform magnetic fields, with application to magnetic delay lines

The theory of spin-wave generation in nonuniform magnetic fields is reviewed. Detailed theoretical results concerning the photon-magnon conversion, the magnon-phonon conversion, the frequency- and field-dependence of the delay time, and the insertion loss are presented. A general theory of the nonuniform demagnetizing field of nonellipsoidal samples is described. Experimental results concerning the field dependence of the delay time are presented both for the case in which the spin waves generated are exchange dominated and for the case in which they are dominated by the magnetostatic interaction. The insertion loss was found to vary with the applied magnetic field in an approximately periodic fashion showing two distinct periods of the order of 1 Oe and 100 Oe. The fast variation (period approximately 1 Oe) has been definitely identified as arising from the excitation of magnetoelastic resonances in the nonuniform magnetic field near the endfaces of the sample. The slow variation (period approrimately 100 Oe) is tentatively attributed to the interference of different partial waves arising from the reflection of the primary wave at the sidefaces of the sample.

Generation of Spin Waves in Nonuniform Magnetic Fields. III. Magnetoelastic Interaction

If a spin wave propagates through a region of nonuniform magnetic field in which the effective magnon wavenumber equals the phonon wavenumber, it is partially converted into an elastic wave. The conversion efficiency depends primarily on the field gradient (H′) at the crossover point. Theories have been developed both for the case of weak magnetoelastic coupling and strong magnetoelastic coupling. For weak coupling the magnon‐phonon conversion efficiency ηmp is ηmp=H′crit/|H′| (for |H′|>>H′crit), whereas for strong coupling ηmp = 1−π2exp(−H′crit/|H′|) (for |H′|<<H′crit). Here H′crit=πb22 ω/cMμ is a critical field gradient, b2 is one of the magnetoelastic constants, ω/2π the signal frequency, c the velocity of (transverse) sound, M the saturation magnetization, and μ the shear modulus. It has been assumed that the dc magnetic field is applied along a cube edge of a cubic crystal and that the material is elastically isotropic. For yttrium iron garnet (YIG) at room temperature and a signal frequency of 3×109...

Ferromagnetic Resonance in Polycrystalline Nickel Ferrite Aluminate

Line broadening because of crystalline anisotropy and the random orientation of the crystallites is investigated for the case in which the anisotropy field is much larger than the saturation magnetization. The theory predicts an absorption line with shoulders on each side which correspond to grains in which a hard or an easy direction is aligned with the dc field. With increasing anisotropy the low‐field side of the line becomes more prominent and for γHa/ω≳·5 a secondary absorption peak occurs on the low‐field side of the main resonance. Measurements in nickel ferrite aluminates at X band agree reasonably well with the predictions, if it is assumed that the first order anisotropy constant is negative and that all higher order anisotropy constants are zero.