Permeability, also called magnetic permeability, is a constant of proportionality that exists between magnetic induction and magnetic field intensity. This constant is equal to approximately 1.257 x 10-6 henry per meter (H/m) in free space (a vacuum). In other materials it can be much different, often substantially greater than the free-space value, which is symbolized µo.

Materials that cause the lines of flux to move farther apart, resulting in a decrease in magnetic flux density compared with a vacuum, are called diamagnetic. Materials that concentrate magnetic flux by a factor of more than 1 but less than or equal to 10 are called paramagnetic; materials that concentrate the flux by a factor of more than 10 are called ferromagnetic. The permeability factors of some substances change with rising or falling temperature, or with the intensity of the applied magnetic field.

In engineering applications, permeability is often expressed in relative, rather than in absolute, terms. If µo represents the permeability of free space (that is, 1.257 x 10-6 H/m) and µ represents the permeability of the substance in question (also specified in henrys per meter), then the relative permeability, µr, is given by:

µr = µ / µo

= µ (7.958 x 105)

Diamagnetic materials have µr less than 1, but no known substance has relative permeability much less than 1. Certain ferromagnetics, especially powdered or laminated iron, steel, or nickel alloys, have µr that can range up to about 1,000,000. When a paramagnetic or ferromagnetic core is inserted into a coil, the inductance is multiplied by µr compared with the inductance of the same coil with an air core. This effect is useful in the design of transformers and chokes for alternating current (AC), audio frequencies (AF), and radio frequencies (RF).

Negative magnetic permeability is when a material, in response to an imposed magnetic field, forms a magnetic dipole in the opposite direction to the imposed field.

It is called 'diamagnetic' and there is a good wiki page to get you started.

Dear Sir,

at my opinion, the metamaterials with the negative permeability and negative permittivity are onyl a fieldtheoretic effect. We have the practical materials and the effect, that the material dispersion effects are only field theoretic. This are not real practical material effects.

Look please at the word " metamaterials" in the internet.

All the best

F. Gräbner

Dear Researchers,

Kindly go through following paper.It may solve your question.

https://arxiv.org/ftp/arxiv/papers/1012/1012.1353.pdf

As regards PLASMA in a Magnetic Field the particles gyration results in a magnetic moment countering the external field. Therefore plasma is diamagnetic.

Permeability, also called magnetic permeability, is a constant of proportionality that exists between magnetic induction and magnetic field intensity. This constant is equal to approximately 1.257 x 10-6 henry per meter (H/m) in free space (a vacuum). In other materials it can be much different, often substantially greater than the free-space value, which is symbolized µo.

Materials that cause the lines of flux to move farther apart, resulting in a decrease in magnetic flux density compared with a vacuum, are called diamagnetic. Materials that concentrate magnetic flux by a factor of more than 1 but less than or equal to 10 are called paramagnetic; materials that concentrate the flux by a factor of more than 10 are called ferromagnetic. The permeability factors of some substances change with rising or falling temperature, or with the intensity of the applied magnetic field.

In engineering applications, permeability is often expressed in relative, rather than in absolute, terms. If µo represents the permeability of free space (that is, 1.257 x 10-6 H/m) and µ represents the permeability of the substance in question (also specified in henrys per meter), then the relative permeability, µr, is given by:

µr = µ / µo

= µ (7.958 x 105)

Diamagnetic materials have µr less than 1, but no known substance has relative permeability much less than 1. Certain ferromagnetics, especially powdered or laminated iron, steel, or nickel alloys, have µr that can range up to about 1,000,000. When a paramagnetic or ferromagnetic core is inserted into a coil, the inductance is multiplied by µr compared with the inductance of the same coil with an air core. This effect is useful in the design of transformers and chokes for alternating current (AC), audio frequencies (AF), and radio frequencies (RF).

By definition magnetic permeability is a second rank tensor that

describes the relationship between the magnetic induction and the magnetic filed vectors. First of all its should be underlined that permeability tensor components in real materials are frequency dependent.

In some cases (the absence of the static magnetic field magnetizing

material and for weak crystalographic anisotropy) the so called initial permeability can be considered as a scalar quantity. Experiments show that in some frequency ranges the initial permeability can be negative.

Also the effective permeability for circularly polarized electromagnetic

field can be negative. In fact the negative effective permeability allows operation of YIG filters and oscillators.

For more information on this topic see e.g.

Jerzy Krupka, "Measurement of the complex permittivity, initial permeability, permeability tensor and ferromagnetic linewidth of gyromagnetic materials", 2018 Meas. Sci. Technol. 29 092001