Experiments show that in some frequency ranges the initial permeability can be negative. field can be negative. In fact the negative effective permeability allows operation of YIG filters and oscillators.

Can relative permeability negative?

A good magnetic core material must have high permeability. For passive magnetic levitation a relative permeability below 1 is needed (corresponding to a negative susceptibility). Permeability varies with a magnetic field.

How do you get negative permittivity?

Negative refraction can be obtained by using a metamaterial which has been designed to achieve a negative value for (electric) permittivity (ε) and (magnetic) permeability (μ); in such cases the material can be assigned a negative refractive index. Such materials are sometimes called "double negative" materials.