Statistical distribution of the internal field in planar ferrites

Abstract

The lateral size of planar ferrite elements in current microwave and mm wave devices is on the order of the mm. For optimal operation the thickness of these ferrites, h, should be considerable as compared to the lateral size L, i.e. these ferrites have a finite aspect ratio o = h/L. Device modeling and development is assisted by numerical analysis, however, the models used for thin films can't be used for the finite planar shape. Moreover, due to the decreasing size, the surface to volume ratio increases and the effect of comers and edges might become critical.Fenites, magnetized perpendicular to their plane, typically operate in an extemal dc bias field HO = 4nM3, tacitly assuming uniform zero internal field, whereas the internal field for a thin film, H, = HO -N,M, = 0 (N, = 4~ is the demagnetizing tensor component for a thin film). For finite size 3D ferrites the demagnetizing tensor elements, Nu, depend on the position, and as a result, the direction of the magnetization and the internal field Hi deviates from the direction of the applied field, Hp. It was shown for YIG that the inhomogeneity of the internal field in Ho= 4nM, =I730 Oe causes a Considerable canting of the magnetization at the comers and edges of the rectangular ferrite. Device designers are aware that for optimum performance a bias field higher than HO = 4nM, should be applied, leading to the unforlunate consequence of a bigger and more expensive permanent magnet. To facilitate design optimization the present work investigates the statistical distribution of the intemal field, H,(r), depending on the shape and on the dc bias field Ho. It was anticipated that an "ezfictive size" ofthe ferrite can be defined, where M, and H, are almost constant, and only the "rim" has considerably different properties.The present work is the continuation of our previous numerical micromagnetic calculations of the non-collinear intemal field distribution Hdr) [1,2,3]. The Landau-Lifshitz equation is solved iteratively by the Finite Difference Method to obtain the equilibrium internal field (and magnetization) distribution for the dc bias field, applied perpendicular to the plane of the ferrite. Calculations are performed for YIG (Y3Fe5012) as a model material. The distribution of the internal field is studied for rectangular shapcs, having aspect ratios n=2/40, 4/40, and 8/40. The bias field is set from Xu= 800 Oe up to 2400 Oe.The results show that, as expected, the canting of the magnetization at the comers is the strongest for a Lxwxh = 40x40~8 shape YIG. In Hm =I730 G the in-plane internal field components around the comem are on the order of 700 G, corresponding to a canting of the internal field and the magnetic moments at the comers by about € I =21°. For a thinner ferrite, h 4 , the canting of the magnetization from the I direction at the comers is 0 =18'. The canting decreases as the bias field increases, but at 2400 Oe for h 4 it is still IO". The canting decreases toward the bulk part of the ferrite, and it becomes negligible around the center. For the...