Abstract: Ferromagnetic resonance determination of magnetic profiles (invited)
Authors: Wilts C. H. 
Published: February 2003

Due to altered magnetic properties in the implanted layer of a garnet film, this layer will support standing surface spin-wave modes which in some circumstances may be used to determine changes in surface properties such as magnetization, uniaxial anisotropy, crystalline anisotropy, exchange, and g value. The material presented here is directed to systems which remain magnetic throughout the surface layer; however, much of what follows can be readily adapted or extended to situations where the implantation level is so high that nonmagnetic layers have been formed. The amount of information that can be obtained from FMR spectra is strongly dependent on the number of resolvable surface modes. For perpendicular resonance with a negative change in surface uniaxial anisotropy, a good estimate of the number of modes is given by n≊δ/π[M(ΔHk)ave/2A]1/2, where δ is the depth of implantation and (ΔHk)ave the average decrease in anisotropy. Since this is only an estimate, it is reasonable to use the bulk values of M and A rather than their yet unknown surface values. These modes are distributed in a field range of about (ΔHk)max Oe and their resolution require a linewidth substantially below (ΔHk)max/n. If this is not satisfied, some of the modes will not be resolved and the information obtainable will be reduced. The mode location Ha in perpendicular resonance is an eigenvalue of an equation given approximately by d2m/dz2 = (M/2A) [Ha−Hun(z)]m so that the most one can expect from matching the experimental data is a profile of the local uniform field Hun(z) = (ω/γ+4πM−Hk +2H1/3) and an average or, perhaps, a rough profile of the ratio M/A. If in addition the predicted and experimental mode amplitudes are matched, one obtains specific information about the relative values of M in the unimplanted and implanted regions, and it becomes possible to separate the variation of M and A, though the accuracy attainable here is not nearly as good as that for Hun(z). Practical computer programs are now available for obtaining the eigenvalues for the coupled equations of parallel resonance. When the implant depth δ and ΔHk are large enough, this gives additional information about an effective parallel field Hpar(z) = [ω/γ−(4πM−Hk)/2+H1/4], so that, in principle, further separation of the magnetic variables is made possible. A further extension is provided by a study of the location of the principal (highest) surface mode at a number of angles between perpendicular and parallel configurations. It is shown that this gives approximate but still useful information about the crystalline anisotropy field H1 near the region of greatest change in Hk and near the surface of the film. The accuracy of all determinations can be improved by using x-ray diffraction rocking curves to give an absolute scale to the measurement of distance through the implanted layer and a profile of strain which is directly though not linearly related to the change in anisotropy. The profile determination is also aided by using a sequence of measured milling or etching steps followed by remeasurement of the FMR spectra. An implantation which reaches a depth of 5000 Å with anisotropy change of 2000 or 3000 Oe will support about 6–8 surface modes. If these can all be resolved, the profile in Hun(z) can be obtained with an accuracy of a few percent, but the change in M and A is only known to an accuracy of about 10% or 20% of the original value.  C. H. Wilts and S. Prasad, IEEE Trans. Magn. 17, 2405 (1981).  V. S. Speriosu, J. Appl. Phys. 52, 6094 (1981).