Magnetization is a crucial concept in electromagnetism, describing how materials respond to magnetic fields. It involves the alignment of magnetic dipole moments within a substance, resulting in a net magnetic field.

Understanding magnetization is key to grasping the behavior of different materials in magnetic fields. From diamagnetic to ferromagnetic substances, each type exhibits unique properties that shape their interactions with external magnetic fields.

Magnetization of materials

• Magnetization is a fundamental property of materials that describes their response to an applied magnetic field
• Materials can be classified into different categories based on their magnetic properties, including diamagnetic, paramagnetic, ferromagnetic, antiferromagnetic, and ferrimagnetic
• The magnetization of a material depends on various factors such as the strength of the applied magnetic field, temperature, and the intrinsic properties of the material itself

Magnetic dipole moments

• Magnetic dipole moments are the fundamental building blocks of magnetism in materials
• They arise from the orbital and spin angular momenta of electrons in atoms and molecules
• The net magnetic dipole moment of a material is the vector sum of all the individual dipole moments within the material
• The alignment of magnetic dipole moments in response to an external magnetic field gives rise to the macroscopic magnetization of the material

Magnetization vector M

• The magnetization vector M represents the net magnetic dipole moment per unit volume of a material
• It is a vector quantity that points in the direction of the net magnetic dipole moment
• The magnitude of M is given by the magnetic dipole moment divided by the volume of the material ($M = μ/V$)
• The units of magnetization are typically expressed in amperes per meter (A/m) or emu per cubic centimeter (emu/cm³)

Magnetic susceptibility χ

• Magnetic susceptibility χ is a dimensionless quantity that measures the degree to which a material becomes magnetized in response to an applied magnetic field
• It is defined as the ratio of the magnetization M to the applied magnetic field H ($χ = M/H$)
• Materials with positive susceptibility are called paramagnetic, while those with negative susceptibility are called diamagnetic
• The susceptibility of a material can vary with temperature, applied magnetic field, and other factors

Diamagnetic vs paramagnetic susceptibility

• Diamagnetic materials have a negative magnetic susceptibility, meaning they are slightly repelled by an applied magnetic field
• Examples of diamagnetic materials include copper, silver, gold, and most organic compounds
• Paramagnetic materials have a positive magnetic susceptibility, meaning they are slightly attracted to an applied magnetic field
• Examples of paramagnetic materials include aluminum, platinum, and oxygen gas
• The susceptibility of diamagnetic materials is typically much smaller in magnitude than that of paramagnetic materials

Magnetization curves

• Magnetization curves describe the relationship between the magnetization M of a material and the applied magnetic field H
• They are obtained by measuring the magnetization of a sample as a function of the applied field strength
• The shape of the magnetization curve depends on the type of material (diamagnetic, paramagnetic, ferromagnetic, etc.) and its magnetic properties
• Magnetization curves provide valuable information about the magnetic behavior of materials, such as saturation magnetization, remanence, and coercivity

Initial vs anhysteretic magnetization

• Initial magnetization curves describe the magnetization of a material starting from a demagnetized state
• They are obtained by applying an increasing magnetic field to a sample and measuring the resulting magnetization
• Anhysteretic magnetization curves, on the other hand, are obtained by applying an alternating magnetic field with decreasing amplitude to a sample
• Anhysteretic curves represent the ideal magnetization behavior of a material, free from the effects of magnetic hysteresis
• Comparing initial and anhysteretic magnetization curves can provide insights into the role of magnetic domain walls and pinning sites in the magnetization process

Magnetic permeability μ

• Magnetic permeability μ is a measure of the ability of a material to support the formation of a magnetic field within itself
• It is defined as the ratio of the magnetic flux density B to the magnetic field intensity H ($μ = B/H$)
• The units of permeability are typically expressed in henries per meter (H/m) or gauss per oersted (G/Oe)
• Materials with high permeability, such as ferromagnets, are easily magnetized and can enhance the strength of an applied magnetic field

Relative vs differential permeability

• Relative permeability μᵣ is the ratio of the permeability of a material to the permeability of free space μ₀ ($μᵣ = μ/μ₀$)
• It is a dimensionless quantity that indicates how much a material enhances or reduces the strength of an applied magnetic field compared to vacuum
• Differential permeability, on the other hand, is defined as the slope of the B-H curve at a particular point ($μ_d = dB/dH$)
• Differential permeability varies with the applied magnetic field and can be used to characterize the nonlinear magnetic behavior of materials

Magnetic field intensity H

• Magnetic field intensity H is a measure of the strength of an applied magnetic field
• It is defined as the magnetic flux density B divided by the permeability of the material μ ($H = B/μ$)
• The units of magnetic field intensity are typically expressed in amperes per meter (A/m) or oersteds (Oe)
• Magnetic field intensity is an important parameter in the study of magnetization, as it determines the degree to which a material becomes magnetized

Magnetic flux density B

• Magnetic flux density B is a measure of the total magnetic field in a material, including both the applied field and the field generated by the material's magnetization
• It is related to the magnetic field intensity H and the magnetization M by the equation $B = μ₀(H + M)$, where μ₀ is the permeability of free space
• The units of magnetic flux density are typically expressed in teslas (T) or gauss (G)
• Magnetic flux density is an important quantity in many applications, such as the design of electromagnetic devices and the study of magnetic materials

B vs H curves

• B vs H curves, also known as magnetization curves, show the relationship between the magnetic flux density B and the magnetic field intensity H for a given material
• The shape of the B-H curve depends on the type of material (diamagnetic, paramagnetic, ferromagnetic, etc.) and its magnetic properties
• For linear magnetic materials, such as diamagnets and paramagnets, the B-H curve is a straight line with a slope equal to the magnetic permeability μ
• For nonlinear magnetic materials, such as ferromagnets, the B-H curve is a hysteresis loop, which exhibits saturation, remanence, and coercivity

Hysteresis in ferromagnetic materials

• Magnetic hysteresis is a phenomenon observed in ferromagnetic materials, where the magnetization of the material depends not only on the current applied magnetic field but also on its magnetic history
• Hysteresis occurs due to the presence of magnetic domains in ferromagnetic materials and the pinning of domain walls by defects and impurities
• The hysteresis loop is characterized by several important parameters, including saturation magnetization, remanent magnetization, and coercive field
• Hysteresis leads to energy losses in the form of heat when the material is subjected to alternating magnetic fields, which is an important consideration in the design of electromagnetic devices

Hysteresis loss vs eddy current loss

• Hysteresis loss and eddy current loss are two types of energy losses that occur in ferromagnetic materials subjected to alternating magnetic fields
• Hysteresis loss arises from the irreversible work done in moving domain walls during the magnetization and demagnetization processes
• Eddy current loss, on the other hand, is caused by the induction of electric currents in the material due to the changing magnetic field
• Eddy currents generate heat through Joule heating, which contributes to the overall energy loss in the material
• Minimizing both hysteresis and eddy current losses is important for improving the efficiency of electromagnetic devices, such as transformers and electric motors

Curie temperature of ferromagnets

• The Curie temperature is a critical temperature above which a ferromagnetic material loses its spontaneous magnetization and becomes paramagnetic
• It is named after Pierre Curie, who discovered the phenomenon in 1895
• At temperatures below the Curie point, the exchange interaction between neighboring magnetic dipole moments is strong enough to maintain a spontaneous magnetization in the absence of an applied field
• Above the Curie temperature, thermal fluctuations overcome the exchange interaction, and the material becomes paramagnetic
• The Curie temperature is an important parameter in the study of ferromagnetic materials and their applications, as it determines the temperature range over which the material can maintain its magnetic properties

Magnetization of superconductors

• Superconductors are materials that exhibit zero electrical resistance and perfect diamagnetism below a critical temperature and magnetic field
• The magnetization of superconductors is characterized by the Meissner effect, which is the complete expulsion of magnetic fields from the interior of the superconductor
• In the superconducting state, the material generates surface currents that exactly cancel the applied magnetic field inside the superconductor
• The magnetization of superconductors is a result of the formation of Cooper pairs, which are bound states of two electrons with opposite spins and momenta
• The study of the magnetization of superconductors is important for understanding their fundamental properties and for developing applications such as superconducting magnets and levitation devices

Meissner effect in superconductors

• The Meissner effect is a hallmark of superconductivity, characterized by the complete expulsion of magnetic fields from the interior of a superconductor
• It was discovered by Walther Meissner and Robert Ochsenfeld in 1933
• When a superconductor is cooled below its critical temperature in the presence of a weak magnetic field, the field is expelled from the interior of the material as it enters the superconducting state
• The expulsion of the magnetic field is a consequence of the generation of surface currents that exactly cancel the applied field inside the superconductor
• The Meissner effect demonstrates that superconductivity is a thermodynamic state of matter and not merely a state of perfect conductivity
• The study of the Meissner effect is crucial for understanding the fundamental properties of superconductors and for developing applications such as magnetic levitation and shielding

Magnetization measurement techniques

• Various techniques are used to measure the magnetization of materials, depending on the type of material, the required sensitivity, and the experimental conditions
• Some common magnetization measurement techniques include vibrating sample magnetometry (VSM), superconducting quantum interference device (SQUID) magnetometry, and alternating gradient magnetometry (AGM)
• These techniques typically involve applying a known magnetic field to a sample and measuring the resulting magnetization using a sensitive detector
• Magnetization measurements provide valuable information about the magnetic properties of materials, such as susceptibility, saturation magnetization, remanence, and coercivity
• Advances in magnetization measurement techniques have enabled the study of novel magnetic materials and the development of new applications in fields such as spintronics and magnetic data storage

Vibrating sample vs SQUID magnetometers

• Vibrating sample magnetometers (VSMs) and superconducting quantum interference device (SQUID) magnetometers are two widely used techniques for measuring the magnetization of materials
• VSMs work by vibrating a sample in a uniform magnetic field and measuring the induced voltage in a set of pickup coils
• The induced voltage is proportional to the sample's magnetic moment, which can be used to calculate the magnetization
• VSMs are relatively simple and inexpensive, with a sensitivity of around 10⁻⁶ emu, making them suitable for a wide range of materials
• SQUID magnetometers, on the other hand, are based on the Josephson effect and the quantum interference of superconducting currents
• They are the most sensitive magnetization measurement devices available, with a sensitivity of up to 10⁻¹² emu
• SQUIDs are particularly useful for measuring the magnetization of small samples, thin films, and materials with weak magnetic signals
• However, SQUID magnetometers are more complex and expensive than VSMs and require cryogenic temperatures for operation