Look for materials that are partially conductive, like salt water.  You could mix metal powders with another material to produce a material with high absorption.  I am not sure how you plan to use these absorbers, but you may not want too high of absorption or the material will tend to reflect rather than absorb.  You may also be interested in what is being called "super absorbers."  These are metamaterials designed to provide extremely high absorption.

Take a look at Lectures 2 and 12 at the following course website for some background on this topic.

http://emlab.utep.edu/ee5390em21.htm

Hope this helps!

Carbon powder is a good material to impregnate another with in order to raise the imaginary component of the refractive index of a composite.  You will want to take measurements of fabricated samples with different loadings (percentages) on order to understand the affect of the loading material on the absorption.

The 'trick' is to find a combination of material and layer build-up that matches the impedance of free space (about 376 Ω - cf.  https://en.wikipedia.org/wiki/Impedance_of_free_space ) - from all directions, under all circumstances.

In principle the rules of transmission line theory apply to free space issues as well: any mismatch results in reflection. An additional constraint is the your absorber structure has to cope with the energy absorbed, which will be converted to heat. (There may be further constraints regarding environmental influences, resistance vs. mechanical wear etc.) Permittivity/permeability should be of lesser concern though surely not completely without meaning.

Regards