Volume 34, Issue 4, 01 April 1963
Index of content:
- MAGNETIC ANISOTROPY; SPIN WAVES
34(1963); http://dx.doi.org/10.1063/1.1729403View Description Hide Description
Spin‐wave spectra in thin Permalloy films have been observed as the angle between the applied field and the film is varied from 0 to 90 degrees. The applied field corresponding to the main resonance peak falls very close to its calculated value for all angles. At some critical angle the spin‐wave spectrum collapses to a single peak. The observed critical angle is very near the angle at which the resonance frequency becomes independent of small changes in the magnetization, which supports a dynamic‐pinning model. The separation between the main peak and the subsidiary peaks reaches a maximum at an angle slightly less than the critical angle and drops sharply as the critical angle is approached. At no angle does the wavelength of the spin waves appear to be a submultiple of the film thickness as would be expected if the surface spins were completely pinned.
As the angle between the applied field and the film increases from 0, the linewidth increases and reaches a maximum near 80°. Beyond this angle the linewidth decreases rapidly, and in many films the linewidth at 90° is less that at 0. Simple theory explains the increase in linewidth with angle, locates the angle of maximum linewidth, but fails to predict the narrowness at 90°.
34(1963); http://dx.doi.org/10.1063/1.1729404View Description Hide Description
The pinning of surface spins introduces an effective gap into the spin‐wave spectrum of thin films, causing the magnetization vs temperature curve to lie well above that obtained from use of periodic boundary conditions. The results of detailed calculations are presented for the case of partial surface pinning in a simple cubic lattice, spin ½. For films of greater than 6 atomic layers, and for a surface anisotropy field greater than one‐tenth the surface exchange field, the magnetization is essentially indistinguishable from the Bloch T curve below T/Tc ∼0.2. This may account for recent measurements by Neugebauer on nickel and by Hoffmann on iron.
34(1963); http://dx.doi.org/10.1063/1.1729405View Description Hide Description
A discussion of the origin of surface spin pinning in thin ferromagneticfilms due to a surface layer possessing slightly different magnetic properties is presented. This model predicts that at a critical angle, measured between the normal to the film and the direction of the external magnetic field, the uniform precession condition will be the same in all regions of the film and the magnetization can be excited as a unit in the uniform precession mode. Spin‐wave spectra were obtained at 9.6 and 14.6 kMc from thin films composed of Permalloy (80 Ni−20 Fe) and cobalt. The critical angle depends on the value of ω/4πγ M which varied from 0.167 to 0.667 and gave critical angles that varied from 2° to 15°. These results agree to within ±1° of the predicted values. A critical angle has occurred in every film independent of the substrate material, the cleaning procedure, or the substrate temperature during deposition. The angle dependence of the strength of the spin‐pinning condition as predicted by this model at angles other than the critical angle is also compared with the experimental results.
34(1963); http://dx.doi.org/10.1063/1.1729406View Description Hide Description
A theoretical analysis is presented for spin‐wave resonance in thin ferromagneticfilmsmagnetized in the plane of the film by a dc field. It is shown that, at very high frequencies, a spin‐wave resonance spectrum occurs if a suitable surface anisotropy is present.
The analysis is based on the Landau—Lifshitz equation and Maxwell's equations. Both surfaces of the film are assumed to possess uniaxial surface anisotropies of equal magnitude with the axes normal to the plane of the film.Magnetization precession is excited by a weak rf field applied in the plane of the film but perpendicular to the dc field and equal at both surfaces of the film.
The boundary conditions for the magnetization1 are different for the oscillating component Mn normal to the film and the component Mp in the plane of the film. The component Mn is influenced by the surface anisotropy and, therefore, more or less pinned at the surfaces. However, the surface anisotropy has no influence on the component Mp , and accordingly, the derivative of Mp with respect to the normal direction vanishes at the surfaces. To fulfil these and the electromagneticboundary conditions, three linearly independent wave solutions of the Landau—Lifshitz equation and Maxwell's equations are required.
The amplitude of the spin‐wave modes and their spacing depends not only on the surface anisotropy constant Ks but also on the frequency ω of the rf field. At frequencies ω, much smaller than 4πMγ the precessional cone is very flat with Mn <<Mp . In this case the influence of the surface anisotropy is weakened and the rf field can strongly excite only one spin‐wave mode, the slightly disturbed uniform precession. The other modes are weak. At frequencies equal to or higher than 4πMγ, the cone of precession becomes nearly circular with Mn ≈ Mp , and the pinning action of the surface anisotropy increases correspondingly. At these higher frequencies, two modes are excited strongly.
Theoretical absorption curves for Permalloyfilms with 4πMγ ≈ 2π·30 Gc are calculated for two frequencies and a range of thicknesses. For the surface anisotropy constant a value of 1 erg/cm2 is chosen. At 10 Gc only one strongly excited mode is predicted. At 30 Gc two modes have large amplitudes. The amplitude of one mode increases with increasing film thickness, whereas the amplitude of the other mode remains approximately constant. This theoretical result is similar to the experimental findings of Chen and Morrish2 at 24 Gc which, however, the authors explained in terms of stratified layers within the film.
34(1963); http://dx.doi.org/10.1063/1.1729407View Description Hide Description
The ``one‐ion'' theory of origin of anisotropy has been tested by comparing the calculated value of the gadolinium contribution to the anisotropy of GdIG at 0°K with experimental measurements. Crystal field, dipolar, and dipole—crystal field effects are included in the calculation. The median of the values obtained using the crystal field parameters for Gd3+ in four diamagnetic garnets agrees within 3% with the result of torque measurements on a pure GdIG crystal. The experimental value, −21.9×104 ergs/cc, is approximately 10% lower than previous values for the anisotropy of GdIG. The good agreement between the calculated and experimental anisotropies provides quantitative confirmation of the theory used in the calculations.
34(1963); http://dx.doi.org/10.1063/1.1729408View Description Hide Description
High‐power resonance effects have been observed in thin films of Permalloy. These effects are characterized by a saturation of the main resonance and in some cases the growth of a subsidiary absorption peak at magnetic fields below resonance. The h crit associated with the saturation of the main resonance is found to be sensitive to the film thickness. The size dependence of nonlinear effects in films seems to be associated with a distortion in the spin‐mode dispersion relation at low k numbers.
34(1963); http://dx.doi.org/10.1063/1.1729409View Description Hide Description
The conditions of the surface have been found to have a profound influence on the magnetic properties of thin Permalloyfilms. Quantitative measurements of the surface area were determined by adsorption of a C14‐labeled surfactant. Static hysteresis curves, torque curves, and ferromagnetic resonance spectra have been measured and related to surface roughness. ``Biaxial Anisotropy'' has been observed for films deposited on unidirectionally scratched substrates. The linewidth of the uniform precessional mode with the magnetic field applied parallel to the plane of the film is increased with increasing surface roughness.
34(1963); http://dx.doi.org/10.1063/1.1729410View Description Hide Description
The shape of the surfaceanisotropy energy surface of a thin magnetic film is investigated. By generalizing the exchange boundary condition to include the cases of unequal spin pinning at the two surfaces of a film, calculations of the spin‐wave resonance spectrum were made and compared with the results of surface oxidation experiments. It was found that the surfaceanisotropy is uniaxial with the easy axis perpendicular to the surface of the film: the surfaces of the film being hard planes of magnetization. In addition to the ordinary volume spin‐wave resonance modes due to spin pinning, we found also a set of surface modes whose rf component of the magnetization decreases rapidly from the surface toward the interior of the film. Several surface spin‐pinning mechanisms have been proposed. The implications of these proposals are examined in light of our theoretical and experimental results.
34(1963); http://dx.doi.org/10.1063/1.1729411View Description Hide Description
The temperature dependence of the magnon energy is studied, together with the magnetization, by a self‐consistent treatment of the model hamiltonian obtained by keeping the Heisenberg hamiltonian up to the diagonal term of fourth order in magnon operators. In this formalism, the dispersion relation appears to have the same form as for free magnons, apart from an important temperature‐dependent factor α(T). The calculations have been carried out for simple cubic ferromagnets and CsCl‐type antiferromagnets, with due account taken of the Brillouin zone boundary effect. It is found that no solution for α(T) exists above a maximum temperatureTM which is compared to the values of the Curie and Néel temperatures calculated by the methods of Kramers‐Opechowski and Bethe‐Peierls‐Weiss. At TM the magnetization has about 25 percent of its value at absolute zero. The fact that α(T) is independent of k appears to be a property of the cubic geometry to which the following considerations have been limited.
34(1963); http://dx.doi.org/10.1063/1.1729412View Description Hide Description
Theoretical studies on the magnetization of ferro‐ and antiferromagnets have been investigated by means of the equivalent operators, devised by one of the authors, introduced into the two‐time and temperature‐dependent Green function of Bogolyubov and Tjablikov. Our theory is applicable over the whole range of temperatures for arbitrary magnitudes of spin. At low temperatures, the dependence of magnetization on temperature is in good agreement with that of spin‐wave theory except for an extra term which probably results from the approximation of decoupling the chain of equations for the Green functions. But this term is negligible when the magnitude of spin is more than one for the ferromagnetic case and for the antiferromagnetic case. It should be emphasized that our theory possesses spin‐wave character as the collective modes in the low temperature region, and gradually changes to the individual spin‐mode theory similar to the molecular field theory with increasing temperature.
34(1963); http://dx.doi.org/10.1063/1.1729413View Description Hide Description
The direction of easy magnetization in pyrrhotite deviates from the (001) plane below 205°K. We have measured the thermal variations of the anisotropy constants and the spontaneous magnetization between 4.2° and 292°K and determined the fraction of Fe3+ions on each sublattice.