Some formulas for ferrite tensor permeability in both demagnetized state and partially magnetized state are derived

which is based on the statistical theory on domains

and these theoretical formulas show good agreement with the experimental results. A concept of eigen line-width （or effective line-width in demagnetized state） is proposed

and the condition to avoid zero-field loss peak is presented. It is shown that YCaV-In substituted and YIG-Al substituted possess lower eigen line-width and are low-loss microwave ferrite materials.