What is Magnetic Susceptibility - Formula, Definition, Unit, FAQs

Edited By Vishal kumar | Updated on Jul 02, 2025 04:52 PM IST

Magnetic susceptibility gives a measure of the response of the material to an external magnetic field indicating whether it is attracted by the field or repelled. This property is central to defining the magnetic behaviour of substances, i.e., whether they are diamagnetic, paramagnetic, or ferromagnetic. The real importance of magnetic susceptibility manifests in modern technologies such as MRI machines for medical imaging, magnetic storage devices, and even in geophysical aspects of demonstrating the magnetic attributes of the Earth along with mineral explorations.

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What is Magnetic Susceptibility - Formula, Definition, Unit, FAQs

Magnetic Susceptibility Definition?

The magnetic susceptibility of a magnetic substance is defined as the ratio of the intensity of magnetization to the magnetic intensity.

Magnetic Susceptibility Formula

The magnetic Susceptibility Formula is given by, $X_{m}$

$χ_{m} = \frac{I}{H}$

Where,

I is the intensity of magnetization

H is magnetic intensity

The magnetic susceptibility of a magnetic substance gives the measure of its aptness to acquire magnetism. As magnetic susceptibility is the ratio of the two quantities having the same units $(A m^{- 1})$ it has no units.

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Magnetic Materials

On the basis of the magnetic behaviour of different magnetic materials, Faraday divided the magnetic materials into three classes:-

1. Paramagnetic:- The substances, which are placed in a magnetic field are feebly magnetized in the direction of the magnetizing field, and are called paramagnetic substances.

When a paramagnetic substance is placed inside an external magnetic field, the magnetic field inside the paramagnetic field is found to be slightly greater than the external magnetic field. A paramagnetic substance tends to move from the weaker part of the magnetic field to the stronger part when placed in a non-uniform magnetic field. The paramagnetic effects are perceptible only when a strong magnetic field is there. Some of the few examples of paramagnetic substances are aluminium, sodium, antimony, platinum, copper chloride, liquid oxygen etc.

The magnetic susceptibility $χ_{m!}$ of paramagnetic substances has a small positive value. Since, for a paramagnetic substance, ' l ' has a small positive value, from the relation $χ_{m} = \frac{I}{H}$ , it follows that $χ_{m}$ will have a small positive value. It is of the order of $10^{- 5}$ to $10^{- 3}$ .

The susceptibility of paramagnetic substances is inversely proportional to their absolute temperature.

2. Diamagnetic:- The substances, which are placed in a magnetic field are feebly magnetized in a direction opposite to that of the magnetizing field, and are called diamagnetic substances.

When we place a diamagnetic substance inside an external magnetic field, the magnetic field inside the diamagnetic field is found to be slightly less than the external magnetic field. It is also noticed that if a diamagnetic sample is placed inside a non-uniform magnetic field, then it tends to move from the stronger part to the weaker part of the magnetic field. It may be pointed out that the diamagnetic effects are too feeble to be detected unless the applied magnetic field is strong. Some of the few examples of diamagnetic substances are copper, zinc, bismuth, silver, gold, lead, glass, marble, water, helium, etc.

The magnetic susceptibility $χ_{m}$ of a diamagnetic substance has a small negative value. Since, for a diamagnetic substance, I' has a small negative value, from the relation $χ_{m} = \frac{I}{H}$ It follows that $χ_{m}$ will have a small negative value. It is of the order of $10^{- 6}$ to $10^{- 3}$ (negative).

The susceptibility of a diamagnetic substance does not change with temperature for practical purposes. However, bismuth at low temperatures is an exception.

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3. Ferromagnetic:- Those substances, when placed in a magnetic field are strongly magnetized in the direction of the magnetizing field, are called ferromagnetic substances.

When a ferromagnetic substance is placed inside an external magnetic field, the magnetic field inside the ferromagnetic field is found to be greatly enhanced than the external magnetic field. As a result, when a ferromagnetic substance is placed in a non-uniform magnetic field, it quickly moves from the weaker part to the stronger part of the magnetic field. In other words, the ferromagnetic effects are perceptible even in the presence of a weak magnetic field. Some of the few examples of ferromagnetic substances are iron, nickel, cobalt, alnico etc.

The magnetic susceptibility $χ_{m}$ of ferromagnetic substances has a large positive value. It follows from the relation $χ_{m} = \frac{I}{H}$ . It is of the order of several thousand. The susceptibility of ferromagnetic substances decreases with the rise in temperature.

Frequently Asked Questions (FAQs)

1. If a diamagnetic substance is brought near north or South Pole of a bar magnet, it is

a) attracted by both the poles.

b) repelled by both the poles.

c) attracted by the north pole and repelled by the south pole.

d) repelled by the north pole and attracted by the south pole.

Option (b) is correct. The diamagnetic substances are feebly repelled by a magnet.

2. In which type of magnetic material the magnetic susceptibility does not depend on temperature?

The magnetic susceptibility in case of a diamagnetic material does not depend on temperature.

3. Why is diamagnetism, in contrast, almost independent of temperature?

The atoms of a diamagnetic do not have intrinsic magnetic dipole moment. While placing a diamagnetic sample in a magnetic field, the magnetic moment of the sample is always opposite to the direction of the field. It is not affected by the thermal motion of the dipoles.

4. How is magnetic susceptibility defined mathematically?

Magnetic susceptibility (χ) is defined as the ratio of magnetization (M) induced in a material to the strength of the applied magnetic field (H). Mathematically, it is expressed as χ = M/H.

5. What is the difference between positive and negative magnetic susceptibility?

Positive magnetic susceptibility indicates that the material is attracted to a magnetic field (paramagnetic or ferromagnetic), while negative magnetic susceptibility means the material is repelled by a magnetic field (diamagnetic).

6. What is the Curie-Weiss law, and how does it relate to magnetic susceptibility?

The Curie-Weiss law describes how the magnetic susceptibility of a ferromagnetic material varies with temperature above its Curie point. It states that χ = C / (T - θ), where C is the Curie constant, T is the temperature, and θ is the Weiss constant.

7. What are the units of magnetic susceptibility?

Magnetic susceptibility is a dimensionless quantity, meaning it has no units. However, in some systems, it may be expressed in units of volume susceptibility (e.g., m³/kg) or mass susceptibility (e.g., m³/kg).

8. Can magnetic susceptibility change with temperature?

Yes, magnetic susceptibility can vary with temperature. For many materials, susceptibility decreases as temperature increases due to increased thermal agitation of magnetic moments.

9. What is magnetic susceptibility?

Magnetic susceptibility is a measure of how much a material becomes magnetized when placed in an external magnetic field. It quantifies the degree to which a substance responds to and enhances or opposes an applied magnetic field.

10. How does magnetic susceptibility differ from magnetic permeability?

Magnetic susceptibility measures how much a material becomes magnetized in response to an applied field, while magnetic permeability describes how easily a material allows magnetic field lines to pass through it. They are related by the equation μ = μ₀(1 + χ), where μ₀ is the permeability of free space.

11. What is volume magnetic susceptibility?

Volume magnetic susceptibility (χᵥ) is the magnetic susceptibility per unit volume of a material. It is a dimensionless quantity that describes how much a material becomes magnetized in response to an applied magnetic field, relative to its volume.

12. How do diamagnetic materials affect magnetic susceptibility?

Diamagnetic materials have a small, negative magnetic susceptibility. They slightly weaken the magnetic field within the material and are repelled by external magnetic fields. Examples include water, copper, and most organic compounds.

13. What is the relationship between magnetic susceptibility and relative permeability?

The relationship between magnetic susceptibility (χ) and relative permeability (μᵣ) is given by the equation μᵣ = 1 + χ. This means that the relative permeability is always greater than or equal to 1, as χ can be positive, negative, or zero.

14. How does quantum mechanics explain the origin of diamagnetism?

Quantum mechanics explains diamagnetism as a consequence of Lenz's law at the atomic level. When a magnetic field is applied, it induces small changes in the orbital motion of electrons, creating tiny current loops that generate a magnetic field opposing the applied field. This quantum effect is present in all materials but is usually overshadowed by stronger paramagnetic or ferromagnetic effects.

15. How does magnetic susceptibility anisotropy affect the orientation of molecules in strong magnetic fields?

Magnetic susceptibility anisotropy refers to the directional dependence of a molecule's magnetic susceptibility. In strong magnetic fields, molecules with anisotropic susceptibility tend to orient themselves to minimize their energy. This effect is exploited in techniques like magnetic field-induced alignment of liquid crystals or biological macromolecules for structural studies.

16. How does mass magnetic susceptibility differ from volume magnetic susceptibility?

Mass magnetic susceptibility (χₘ) is the magnetic susceptibility per unit mass of a material, while volume magnetic susceptibility (χᵥ) is per unit volume. They are related by the equation χₘ = χᵥ / ρ, where ρ is the density of the material.

17. What causes paramagnetism, and how does it influence magnetic susceptibility?

Paramagnetism is caused by unpaired electrons in atoms or molecules. Paramagnetic materials have a small, positive magnetic susceptibility, meaning they are weakly attracted to magnetic fields and slightly enhance the field within the material.

18. How does ferromagnetism differ from paramagnetism in terms of magnetic susceptibility?

Ferromagnetic materials have a much larger positive magnetic susceptibility compared to paramagnetic materials. They exhibit strong magnetic properties, can retain magnetization even in the absence of an external field, and often show nonlinear behavior in their magnetic response.

19. What is the significance of the Curie temperature in relation to magnetic susceptibility?

The Curie temperature is the point at which a ferromagnetic or ferrimagnetic material transitions to a paramagnetic state. Above this temperature, the material's magnetic susceptibility decreases dramatically as thermal energy overcomes the alignment of magnetic domains.

20. How does magnetic anisotropy affect magnetic susceptibility?

Magnetic anisotropy refers to the directional dependence of a material's magnetic properties. In anisotropic materials, the magnetic susceptibility can vary depending on the orientation of the applied magnetic field relative to the material's crystal structure or shape.

21. What is the Pauli paramagnetism, and how does it contribute to magnetic susceptibility?

Pauli paramagnetism is a weak form of paramagnetism observed in conduction electrons in metals. It arises from the spin of unpaired electrons and contributes a small, temperature-independent component to the overall magnetic susceptibility of the material.

22. How does the Langevin theory explain the magnetic susceptibility of paramagnetic materials?

The Langevin theory describes the magnetic susceptibility of paramagnetic materials by considering the thermal motion of magnetic dipoles. It predicts that the susceptibility is inversely proportional to temperature, following the Curie law: χ = C/T, where C is the Curie constant and T is the absolute temperature.

23. What is magnetic hysteresis, and how does it relate to magnetic susceptibility?

Magnetic hysteresis is the dependence of a material's magnetization on its magnetic history. It occurs in ferromagnetic materials and results in a nonlinear relationship between magnetization and applied field. This nonlinearity means that the magnetic susceptibility is not constant but varies with the field strength and the material's magnetic history.

24. How do superconductors behave in terms of magnetic susceptibility?

Superconductors exhibit perfect diamagnetism below their critical temperature, known as the Meissner effect. They have a magnetic susceptibility of χ = -1, which means they completely expel magnetic fields from their interior, regardless of whether the field was applied before or after the material became superconducting.

25. What is the van Vleck paramagnetism, and how does it differ from other forms of paramagnetism?

Van Vleck paramagnetism is a quantum mechanical effect that arises from the mixing of ground and excited states in atoms or molecules. Unlike Curie paramagnetism, van Vleck paramagnetism is largely temperature-independent and can contribute to the magnetic susceptibility even at very low temperatures.

26. How does the free electron model explain the magnetic susceptibility of metals?

The free electron model describes conduction electrons in metals as a gas of non-interacting particles. It predicts two contributions to magnetic susceptibility: Pauli paramagnetism from electron spins and Landau diamagnetism from orbital motion. The net susceptibility is usually paramagnetic because the Pauli contribution typically dominates.

27. What is the Kondo effect, and how does it influence magnetic susceptibility?

The Kondo effect is a phenomenon in which conduction electrons in a metal interact with magnetic impurities, leading to anomalous behavior in electrical resistance and magnetic properties. It can cause a logarithmic increase in magnetic susceptibility as temperature decreases, deviating from the expected Curie-Weiss behavior.

28. How does spin-orbit coupling affect magnetic susceptibility?

Spin-orbit coupling is the interaction between an electron's spin and its orbital angular momentum. It can significantly influence magnetic susceptibility by altering the energy levels of electrons in atoms or molecules, leading to changes in their magnetic response to applied fields.

29. What is the difference between intrinsic and extrinsic magnetic susceptibility?

Intrinsic magnetic susceptibility is an inherent property of a material that depends on its atomic and electronic structure. Extrinsic magnetic susceptibility, on the other hand, is influenced by external factors such as impurities, defects, or sample shape and can vary between different samples of the same material.

30. How does the shape of a sample affect its apparent magnetic susceptibility?

The shape of a sample can affect its apparent magnetic susceptibility due to demagnetizing fields. For example, a long, thin sample aligned with the applied field will have a higher apparent susceptibility than a flat, disc-shaped sample of the same material. This effect is described by the demagnetization factor.

31. What is the relationship between magnetic susceptibility and magnetic moment?

Magnetic susceptibility is related to the average magnetic moment per unit volume or mass of a material. In paramagnetic materials, the susceptibility is proportional to the square of the magnetic moment of the constituent atoms or molecules, as described by the Curie law.

32. What is the significance of the Néel temperature for antiferromagnetic materials?

The Néel temperature is the critical point at which an antiferromagnetic material transitions to a paramagnetic state. Below this temperature, the material exhibits antiferromagnetic ordering, with adjacent magnetic moments aligned in opposite directions. Above the Néel temperature, thermal energy disrupts this ordering, and the material behaves paramagnetically, affecting its magnetic susceptibility.

33. How does magnetic susceptibility change in the vicinity of a phase transition?

Near a magnetic phase transition, such as the Curie point for ferromagnets or the Néel temperature for antiferromagnets, magnetic susceptibility often exhibits anomalous behavior. It may show a sharp peak or divergence as the system becomes highly sensitive to small changes in the applied field or temperature.

34. What is the AC magnetic susceptibility, and how does it differ from DC susceptibility?

AC magnetic susceptibility is measured using an alternating magnetic field, while DC susceptibility uses a static field. AC measurements can provide information about the dynamics of magnetic systems, including relaxation processes and phase transitions, which are not accessible through DC measurements alone.

35. How does the crystal structure of a material influence its magnetic susceptibility?

The crystal structure determines the arrangement and interactions of atoms in a material, which directly affects its magnetic properties. For example, certain crystal structures may favor ferromagnetic or antiferromagnetic ordering, while others may lead to more complex magnetic behaviors, all of which influence the material's magnetic susceptibility.

36. What is the Van Vleck equation, and how is it used in calculating magnetic susceptibility?

The Van Vleck equation is a general formula for calculating magnetic susceptibility that takes into account both paramagnetic and diamagnetic contributions. It considers the energy levels of atoms or molecules in the presence of a magnetic field and is particularly useful for understanding the magnetic properties of transition metal complexes and rare earth compounds.

37. How does magnetic susceptibility relate to magnetic shielding in NMR spectroscopy?

In NMR spectroscopy, magnetic susceptibility differences between molecules or parts of molecules can lead to local variations in the magnetic field experienced by nuclei. This effect, known as magnetic shielding, influences the chemical shifts observed in NMR spectra. Understanding magnetic susceptibility is crucial for interpreting these shifts and extracting structural information.

38. What is the Brillouin function, and how does it describe the magnetic susceptibility of paramagnetic materials?

The Brillouin function is a quantum mechanical description of the magnetization of an ideal paramagnet. It extends the classical Langevin theory to account for the quantization of magnetic moments. The Brillouin function helps describe how the magnetic susceptibility of paramagnetic materials varies with temperature and applied field strength, especially at low temperatures where quantum effects become significant.

39. What is the relationship between magnetic susceptibility and magnetic resonance imaging (MRI)?

In MRI, magnetic susceptibility differences between tissues create local variations in the magnetic field, affecting the relaxation times of protons. These susceptibility-induced field inhomogeneities can cause image artifacts but are also exploited in techniques like susceptibility-weighted imaging (SWI) to enhance contrast and visualize structures such as blood vessels and iron deposits in tissues.

40. How does the concept of magnetic susceptibility apply to metamaterials?

Metamaterials are engineered structures designed to have properties not found in nature. By carefully controlling the magnetic susceptibility (and electric permittivity) of constituent elements, researchers can create metamaterials with exotic properties, such as negative refractive index or electromagnetic cloaking devices.

41. What is magnetic susceptibility mapping, and how is it used in geophysics?

Magnetic susceptibility mapping is a technique used in geophysics to measure and map variations in the magnetic properties of rocks and soils. It helps in identifying mineral deposits, studying geological structures, and understanding the magnetic history of an area. This technique is valuable in mineral exploration, archaeological surveys, and environmental studies.

42. How does the presence of impurities affect the magnetic susceptibility of a material?

Impurities can significantly alter the magnetic susceptibility of a material. Magnetic impurities, such as iron in otherwise non-magnetic materials, can introduce localized magnetic moments that contribute to paramagnetism. In some cases, even small amounts of impurities can dramatically change the magnetic behavior, as seen in the Kondo effect or in dilute magnetic semiconductors.

43. What is the difference between local and bulk magnetic susceptibility?

Local magnetic susceptibility refers to the magnetic response of a specific region or site within a material, while bulk magnetic susceptibility is the average response of the entire sample. In inhomogeneous materials, local susceptibilities can vary significantly from the bulk value, which is important in understanding magnetic properties at the microscopic level.

44. How does pressure affect the magnetic susceptibility of materials?

Pressure can alter the magnetic susceptibility of materials by changing interatomic distances and electronic structures. In some materials, high pressure can induce phase transitions that dramatically change magnetic properties. For example, some materials may transition from paramagnetic to ferromagnetic under pressure, or vice versa.

45. What is the role of magnetic susceptibility in the study of spin glasses?

Spin glasses are disordered magnetic systems with complex interactions. Magnetic susceptibility measurements are crucial in studying spin glasses, as they reveal characteristic behaviors such as a cusp in the susceptibility at the freezing temperature and frequency-dependent effects in AC susceptibility measurements. These studies help in understanding the nature of magnetic frustration and disorder in materials.

46. How does magnetic susceptibility relate to the concept of magnetic percolation?

Magnetic percolation describes the onset of long-range magnetic order in systems with randomly distributed magnetic elements. As the concentration of magnetic components increases, the system undergoes a percolation transition, which is reflected in changes in magnetic susceptibility. This concept is important in understanding the magnetic properties of dilute magnetic systems and composite materials.

47. What is the Griffiths phase, and how does it affect magnetic susceptibility?

The Griffiths phase is a region in the phase diagram of disordered magnetic systems where rare, strongly coupled clusters of spins persist above the bulk ordering temperature. It is characterized by anomalous behavior in magnetic susceptibility, including a divergence of the nonlinear susceptibility and unusual temperature dependence. The Griffiths phase is important in understanding the magnetic properties of materials with chemical or structural disorder.

48. How does the magnetic susceptibility of nanoparticles differ from that of bulk materials?

Nanoparticles often exhibit magnetic properties different from their bulk counterparts due to surface effects and finite-size phenomena. As particle size decreases, the ratio of surface to volume atoms increases, leading to enhanced surface anisotropy and modified exchange interactions. This can result in phenomena such as superparamagnetism, where the magnetic susceptibility shows unique size-dependent and temperature-dependent behaviors.

49. What is the significance of the Pauli exclusion principle in determining the magnetic susceptibility of metals?

The Pauli exclusion principle plays a crucial role in determining the magnetic susceptibility of metals by limiting the number of electrons that can contribute to paramagnetism. In metals, only electrons near the Fermi level can respond to an applied magnetic field, leading to Pauli paramagnetism. This principle explains why the magnetic susceptibility of most metals is relatively small and temperature-independent, in contrast to the behavior of localized magnetic moments in insulators.

50. How does magnetic susceptibility help in understanding the properties of high-temperature superconductors?

Magnetic susceptibility measurements are valuable in studying high-temperature superconductors. They can reveal the onset of superconductivity through the Meissner effect, provide information about the nature of the superconducting state (e.g.,