Usually magnetic field dependent microwave absorption (Ferromagnetic resonance) affected by the Hc and Ms. These quantities will determine the frequency of operation (Kittel equation).

The ideal intrinsic characteristics that required by electromagnetic wave absorbers are the material must possess permeability and also permittivity. Special for magnetic material, effect of spin resonance between material and wave will determined base on anisotropic field and moment dipole. I think so

By focusing microwaves on ferromagnetic, ferrimagnetic or paramagnetic materials, the target material absorbs them and uses such energy to alter the position of its magnetic spin vector. There are more absorbent materials than others. A material with a high saturation magnetization, absorbs little microwaves, a low saturation magnetizing material absorbs a lot of microwaves, as such a capacity is linked directly to the crystal lattice vibration. Cobalt ferrite is very anisotropic, but not very magnetic. Manganese ferrite is a little anisotropic but very magnetic. Of course it also has to do with the divalent ions that make up the ferrite. The relationship between the two properties is described by the magnetic anisotropy constant: K = 2 * pi * Ha * Ms , at where Ha is anisotropy field and Ms the saturation magnetization.

The losses depend on the vibration amplitude, which is determined by the magnetic parameters and the proximity of the operating frequency to the resonance frequency. Resonance frequency is in turn a function of magnetic parameters. Aside from FMR, which contributes at high frequencies (depends on magnetic anisotropy, and magnetization through the form factor), there is resonance of domain walls that acts in the low frequencies (depends on K, M and Hc (fastening of domain walls leads to dissipation of energy).

The mentioned by you permeability and the area of the hysteresis curve (indicating losses during reversal magnetization), also depend by themselves on the above-mentioned magnetic parameters in different parts of the magnetization curve.

In addition, do not forget about eddy currents in materials with noticeable electrical conductivity of material.

It is worth adding that:

1) the losses also depend on the ratio of the material parameters and the amplitude of the electromagnetic action. For example, hard magnetics have a very high Hc value and a wide hysteresis loop, but in a weak electromagnetic field the material will not be remagnetized (this is impossible to achieve material remagnetization). In this case, soft magnetic materials will absorb energy more efficiently;

2) the formula by Gabriel for Ha is true for uniaxial magnetic materials and cubic magnetics with a positive value of the magnetocrystalline anisotropy constant. In other cases, numerical coefficients may be different.