Sum rules on the dynamic permeability of hexagonal ferrites

A general sum rule has been established recently, bounding the integral of the gyromagnetic losses weighted by the frequency, by the square of the saturation magnetization [O. Acher and A. L. Adenot, Phys. Rev. B 62, 11324 (2000)]. This rule has been established for soft materials with internal anisotropy fields small compared to B-s. In this article, this result is extended to the case of hexagonal ferrites with strong planar anisotropy. It is shown that the bound on the integral is a simple expression of the saturation magnetization and of the out-of-plane anisotropy field. Experimental results on polycrystalline (Ba3Co2Fe24O41)-Co(2)Z and (BaCo1.25Ti1.25Fe9.5O19)-M hexagonal ferrites are presented. It is shown that the dynamic properties measured up to 18 GHz are bounded in agreement with our predictions. (C) 2002 American Institute of Physics.