Magnetic susceptibility

In electromagnetism, it is called magnetic susceptibility χ χ {displaystyle chi } (lat. susceptibilis, "receptive") to a constant of dimensional proportionality that indicates the degree of sensitivity to the magnetization of a material influenced by a magnetic field. A parameter to which it is directly related is that of permeability, which expresses total magnetization per unit of volume.

Definition of volumetric susceptibility

La volumetric magnetic susceptibilityrepresented as χ χ v{displaystyle chi _{v}} (on occasion only χ χ {displaystyle chi } or also written as χ χ m{displaystyle chi _{m}} to distinguish it from electrical susceptibility), is defined in the International System by the following relationship:

M=χ χ vH{displaystyle mathbf {M} =chi _{v}mathbf {H} },

where:

M is the magnetization of the material (or magnetic moment per unit of volume), measured in amps divided by meter;

H is the intensity of magnetic field, also given in amperes per metre

from where it comes from χ χ v{displaystyle chi _{v}} It's a dimensional magnitude.

The magnetic induction B can be calculated by:

B=μ μ 0(H+M)=μ μ 0(1+χ χ v)H=μ μ H{displaystyle mathbf {B} =mu _{0}(mathbf {H} +mathbf {M}) = mu _{0}(1+chi _{v})mathbf {H} =mu mathbf {H} } }

where μ₀ is the magnetic permeability of the vacuum and (1+χ χ v){displaystyle (1+chi _{v}}} represents the relative permeability of the material. It follows that volumetric magnetic susceptibility χ χ v{displaystyle chi _{v}} and magnetic permeability μ μ {displaystyle mu } are related by the following formula:

μ μ =μ μ 0(1+χ χ v){displaystyle mu =mu _{0}(1+chi _{v}),}.

Sometimes an auxiliary quantity called "magnetizing intensity" (or magnetic polarization I), given in teslas, defined as:

I=μ μ 0M{displaystyle mathbf {I} =mu _{0}mathbf {M} ,}.

This allows an alternative description of the magnetization phenomenon using the terms I and B, instead of M and H.

Mass susceptibility and molar susceptibility

There are others of susceptibility, the magnetic susceptibility of mass, (χ_mass or χ_g, sometimes χ_m), in units of m³ kg⁻¹ in SI or cm³ g⁻¹ in CGS, and the molar magnetic susceptibility (χ_mol) measured in m³ mol⁻¹ (SI) or cm³ mol⁻¹ (CGS), defined below, where ρ is the density in kg·m⁻³ (SI) or g·cm⁻³ (CGS) and M is the molar mass in kg·mol⁻¹ (SI) or g·mol⁻¹ (CGS).

χ χ mass=χ χ v/ρ ρ {displaystyle chi _{text{masa}}=chi _{v}/rho }

χ χ mol=Mχ χ mass=Mχ χ v/ρ ρ {displaystyle chi _{text{mol}}=Mchi _{text{masa}=Mchi _{v}/rho }

Signs of susceptibility: diamagnetism and other magnetic manifestations

If χ is positive for a material, it can be paramagnetic. In such a case, a magnetic field passing through it will be strengthened by induced magnetization effect. Conversely, if χ is negative, the material is diamagnetic and a magnetic field passing through it will be weakened. In general, non-magnetic materials can be para- or diamagnetic since they do not maintain a permanently magnetized state when the external magnetic influence is extinguished. Ferromagnetic, ferrimagnetic, or antiferromagnetic materials have positive magnetic susceptibility and maintain their magnetized state after the field that caused it is no longer in place.

Experimental methods of determining magnetic susceptibility

Volume magnetic susceptibility can be measured as a force experienced by a substance when a gradient magnetic field is applied to it. In early experimentation, it was measured using a Gouy balance, where a sample of the material was hung between the poles of a electromagnet. The weight change experienced when it was turned on is proportional to the magnetic susceptibility of the sample. Today superconducting magnets are used. An alternative and currently widely used method is the so-called Evans balance, in which the deflection force on two pairs of magnets is measured. For liquid samples, the susceptibility can be measured by the frequency dependence of their resonance. nuclear magnetic.

Examples

Magnetic susceptibility of some materials

Material	Temperature	Pressure	χ χ mol{displaystyle chi _{text{mol}}} (groans)		χ χ mass{displaystyle chi _{text{masa}}} (mass matter)		χ χ v{displaystyle chi _{v}} (volume subc.)		M (moaning)	ρ ρ {displaystyle rho } (density)
Units	(°C)	(atm)	Yes (m3·mol−1)	CGS (cm3·mol)−1)	Yes (m3·kg−1)	CGS (cm3·g−1)	Yes	CGS (emu)	(10)−3 kg/mol) or (g/mol)	(10)3 kg/m3) o (g/cm3)
water	20	1	−1.631×10−10	−1.298×10−5	−9.051×10−9	−7.203×10−7	−9.035×10−6	−7.190×10−7	18.015	0.9982
bismuto	20	1	−3.55×10−9	−2.82×10−4	−1.70×10−8	−1.35×10−6	−1.66×10−4	−1.32×10−5	208.98	9.78
diamond diamond	temperature	1	−7.4×10−11	−5.9×10−6	−6.2×10−9	−4.9×10−7	−2.2×10−5	−1.7×10−6	12.01	3.513
graphite χ χ {displaystyle chi _{perp}}(to the "c" axis)	temperature	1	−7.5×10−11	−6.0×10−6	−6.3×10−9	−5.0×10−7	−1.4×10−5	−1.1×10−6	12.01	2.267
graphite χ χ 日本語日本語{displaystyle chi _{abi}	temperature	1	−3.2×10−9	−2.6×10−4	−2.7×10−7	−2.2×10−5	−6.1×10−4	−4.9×10−5	12.01	2.267
graphite χ χ 日本語日本語{displaystyle chi _{abi}	-173	1	−4.4×10−9	−3.5×10−4	−3.6×10−7	−2.9×10−5	−8.3×10−4	−6.6×10−5	12.01	2.267
He	20	1	−2.38×10−11	−1.89×10−6	−5.93×10−9	−4.72×10−7	−9.85×10−10	−7.84×10−11	4.0026	0.000166
Xe	20	1	−5.71×10−10	−4.54×10−5	−4.35×10−9	−3.46×10−7	−2.37×10−8	−1.89×10−9	131.29	0.00546
O2	20	0.209	4.3×10−8	3.42×10−3	1.34×10−6	1.07×10−4	3.73×10−7	2.97×10−8	31.99	0.000278
N2	20	0.781	−1.56×10−10	−1.24×10−5	−5.56×10−9	−4.43×10−7	−5.06×10−9	−4.03×10−10	28.01	0.000910
Al		1	2.2×10−10	1.7×10−5	7.9×10−9	6.3×10−7	2.2×10−5	1.75×10−6	26.98	2.70
Ag	961	1					−2.31×10−5	−1.84×10−6	107.87