Magnetism and Magnetic Materials

• Magnetism is the science studying cooperative effects of orbital and spin moments in matter and spans across various scientific fields.
• The history of magnetism began around 600 BC with the discovery of loadstone, leading to significant advancements and three Magnetic Revolutions.

Seven Ages of Magnetism

• Ancient: Characterized by the exploration of the planet.
• Early scientific: Marked by understanding.
• Electromagnetic: Saw the electromagnetic revolution.
• High-frequency: Led to new applications.
• Applications: Focused of practical uses of magnetism
• Spin electronics: Focuses on spin based electronics
• Information: Utilizes information created by magnetism

The Compass Century

• Defined by the use of printing, gunpowder for warfare, and the compass.

The Electromagnetic Revolution

• Judged by Maxwell's discovery of electrodynamics laws, resulting in:
• 1820: Oersted discovered the magnetic effect of electric currents.
• 1821: Ampere linked magnetism to the molecular current of matter.
• 1821: Sturgeon invented the first practical electromagnet.
• 1825: Faraday built a primitive electric motor.
• 1831: Faraday discovered electromagnetic induction.
• 1833: Gauss and Weber created a 1 km long telegraph with a galvanometer.
• 1845: Faraday discovered paramagnetism and diamagnetism.
• 1847: Helmotz stated the conservation of energy.
• 1858: The first transatlantic telegraph cable was created
• 1864-1873: Maxwell formulated the theory of electromagnetism.
• 1864: Gamme invented a practical dynamo.
• 1879: Swan invented a practical incandescent bulb.
• 1881: The first public electric railway was demonstrated in Berlin.
• 1882: The first Hydroelectric power station was created
• 1885: Morse code was introduced
• 1887: Hertz generated and detected radio waves
• 1888: Tesla invented a practical AC motor.
• 1890: Ewing described hysteresis.
• 1895: Curie described the temperature variation of paramagnetic susceptibility.
• 1896: Marconi patented the radio, transmission signals across the Atlantic in 1901.
• 1898: Valdemar Poulson invented magnetic recording.

Maxwell's Equations

• Completed the classical theory of electromagnetism, unifying electricity, magnetism, and light.
• Summarized in four equations:
• In free space:
  • V · B = 0
  • €ον · E = ρ
  • (1/µ0)∇ × B = j + €0dE/dt
  • ∇ × E = -dB/dt
• Nabla operator (∇) is expressed differently in Cartesian, cylindrical, and spherical coordinate systems.
• Equations relate electric and magnetic fields (E and B) in free space to electric charge and current densities (ρ and j).
• Maxwell's equations show the existence of coupled oscillatory electric and magnetic solutions.
• In matter:
  • VD = P, divD = V.D = p
  • V·B=0, divB = V.B = 0
• Huge efforts are made to design models describing magnetic properties of materials
• 1905 Langevin proposed the theory of diamagnetism and paramagnetism
• 1906 Wiess proposed the theory of ferromagnetism.
• The 1930 Solvay conference focused on understanding magnetism through quantum mechanics and relativity.
• The m-J model was suggested, where:
  • m represents the magnetic moment localized on atoms
  • J represents the exchange coupling of neighboring atoms.
• Heisenberg formulated a Hamiltonian to represent the interaction of neighboring atoms' electronic spins (Si and Sj).

The Information Revolution

• Magnets are at the forefront of modern technology, supporting information technology alongside semiconductors.
• Every year, more transistors and magnets are fabricated than the amount of wheat and rice grown
• Around 10^21 bytes of information are stored magnetically each year.
• Magnetic materials are used to create and distribute electricity, store data (audiotape, videotape, computer disks), and in medical applications (body scanners and implants).
• The home entertainment market relies on magnetic materials in CD players, televisions, game consoles, and loudspeakers.
• Magnetic materials have a global economic importance that is comparable to semiconductors.

The Origin of Atomic Moments

• Macroscopic magnetic properties of materials are due to magnetic moments of individual electrons.
• Each electron's magnetic moments originate from:
• Orbital motion around the nucleus, creating a small current loop and magnetic field.
• Intrinsic spin angular momentum in "up" or "down" directions.
• The nucleus also has a small magnetic moment but is usually insignificant compared to electrons due to its mass.
• The microscopic theory of magnetism is based on quantum mechanics of electronic angular momentum from orbital motion and spin.
• Bound electrons undergo Larmor precession, leading to orbital diamagnetism.
• The description of magnetism differs based on whether electrons are localized on ion cores or delocalized in energy bands.

Magnetic Moment

• A rotating system of charged particles has a magnetic moment that is proportional to its angular momentum.
• For a particle with mass M, charge q, moving in a circle of radius r with speed v and frequency f:
  • Current: i = qf = qv / 2πr
  • Magnetic moment: μ = iA = q(v / 2πr) (πr²) = q(L / 2M)
• If q is positive, the magnetic moment is in the same direction as the angular momentum they are antiparallel if q is negative
• The proportionality between magnetic moment and angular momentum is a general result: μ = γL, where γ is the gyromagnetic ratio
• The Einstein-de Haas effect proved this relation in 1915.

Magnetization

• It is a measure of how a material responds when a magnetic field is applied.
• Two unit systems:
  • mks (metres-kilograms-seconds): Adopted as SI units.
  • cgs (centimeters-grams-seconds): Also known as the Gaussian system.
• The cgs system is used because of the numerical equivalence of magnetic induction (B) and the applied field (H).
• Conversion factors exist between SI and CGS units for magnetic terms.

Table of conversions and values for magnetic materials

• Magnetic Induction (B): Tesla (T) in SI, Gauss (G) in CGS (1 T = 10^4 G).
• Magnetic Field (H): Amperes/meter (A/m) in SI, Oersted (Oe) in CGS.
• Magnetization (M): A/m in SI, emu/cm³ in CGS.
• Other magnetic properties also have corresponding units and conversion factors
• A magnetic solid has many atoms with magnetic moments.
• Magnetization (M) is the magnetic moment per unit volume, considered a smooth vector field except at the edges of the solid.
• Discussion of macroscopic field quantities begins by defining magnetic properties of materials.
• Two fundamental quantities:
  • Magnetic induction (B): Magnetic flux density in Wb/m² (Tesla) or Gauss.
  • Magnetic field (H): In A/m (Oersted).
• Both are axial vector quantities, and are collinear (parallel), and can be treated as scalar quantities (B and H).
• The magnetic field H is produced by the flow of current in wires and magnetic induction B is the total magnetic field lines through a material's cross-section
• In free space, B is related to H by:
  • B = µ0H (SI)
  • B = H (CGS)
• Permeability of the vacuum (µ0) is 4π × 10^-7 H/m in SI units, it is taken as 1 in cgs units
• The units of B, H, and M for both systems are given in tables. In a magnetic material the magnetic induction: -. B = µ0(H + M) (SI)
• B = H + 4πM (CGS)
• Magnetization M is net dipole moment per unit volume, expressed as M = χmH.
• The constant of proportionality Xm is the magnetic susceptibility.
• Represents the degree of magnetization
• Could be positive, negative, or zero.
• Demonstrates the strength and type of magnetic effect.
• Superconductors act as perfect diamagnets.

Magnetic Materials

• Can be divided into five groups depending on the response of the applied magnetic field
• Diamagnetic Materials: Xm = -1 (SI), Xm = -1/4π (CGS)
  • Note that the magnetic susceptibility is a polar second-rank tensor.
  • It is considered one of the scalar quantities, given B and H are collinear
  • Susceptibility is dimensionless in SI and emu cm³ Oe⁻¹ in CGS
• Mass susceptibility (xm) is quoted in m³/kg and calculated by material's susceptibility / density
• To continue using induction, field, and magnetization, B = µH
• Formulas for the magnetic field in both systems are
  • B = μο(1 + Xm)H (SI)
  • B = (1 + 4πXm) H (CGS)
• Can determine relative permeability like so
  • με = (1 + Xm) (SI
  • με = 1 + 4πXm (CGS)
• Relative permeability (µr) enhances factor of the flux density and is an intrinsic material property with respect to magnetization
• An important parameter in S.I. units is the magnetic polarization (J), also know as intensity of magnetization is calculated as:
  • J=µ0M
• Five classes of magnetic materials
• Diamagnetic Materials
• Paramagnetic Materials
• Ferromagnetic Materials
• Antiferromagnetic Materials
• Ferrimagnetic Materials
• Materials can be classified by their behavior
• Diamagnetism and paramagnetism is most common
• Represented by most elements in the periodic table
• Those elements are nonmagnetic
• Magnetic ones are ferromagnetic and antiferromagnetic

Fields Due to Electric Currents And Magnetic Moments

• Oersted discovered the connection between electricity and magnetism
• He demonstrated that a current-carrying wire produced a circumferential field able to deflect a compass needle.
• The magnetic field (dB):
  • dB created by a small current element (dl = I dl) at a point P is given by the Biot-Savart law:
    • dB = (µ0 / 4π) (r × dl / r^3), where r goes from the current element to the point.
• Magnetic moment associated with a loop, the magnetic field that is created at the center must be calculated
  • Circular loop of radius a has given the magnetic field Bo = μ0I / 2a.
• Magnetic moment the electrical potential can can be calculated used V(M) = (qa cos θ) / (4πε0γ2.
• For vector potential
  • A = (μ0I a2 sin θ uφ) / 4γ2
  • A= μ0(mXur) / 4πγ2.
• Local relation B = curl MA.
• We list some typical values of B in free space, those include:
• The Earth: 50 microtesla
  • Helmholtz: 10 millitesla
• Human Brain: 1 femtometre
  • Permanent magnets: 0.5 Tesla
  • Magnetar: 10 to the power of 12 Tesla
  • Electromagnet: 1 Tesla
  • Superconducting magnet: 10 Tesla

The Demagnetizing Field

• The demagnetizing field is called the stray field it it occurs outside the magnet, otherwise it will be demagnetizing which happens withing a magnet
• It is magnetic field produced by magnetization in a magnet
• With total magnetic field this is the sum of the demagnetizing fields of any/all magnets and magnetic fields
• The free currents/displacement currents do not act on the magnetization
• The field depends on:
  • sample Shape
  • Magnetization direction
• Proportional Factor is demagnetizing factor
• Value can never be more than one nor less then zero H = -NM N is a tensor relation: Nij i, j = x, y, z, Nx + N₄ + N₂ = 1 Factors:
• Long needle: 0 when parallel; 1/2 when perpendicular
• Sphere: 1/3 any direction
• Thin film: 0 parallel; 1 perpendicular.

Internal/External Fields

• We inset solid into a region where space is an applied magnetic field, the internal field very.
• Comes as a result of magnetic field being produced because of its distribution: the
  • H₁ = Ha + Hd
• Depends on the position of the inside of a magnetic solid For when the principle axes of an ellipsoid occurs the following:
• H₁ = Ha - NM The formula for Induction will be
• Β₁ = μο(Η; + M) = Ba + μο(1 – Ν)Μ.

Example Sphere Calculation

• H = Ha- M
• B₁ = Ba M
• When one has a high magnetization to an field it is very serious

Domains and Hysteresis

• Ferromagnetic material presents in alignment in sam direction:
  • Known as moments/domains; adjacent ones border a domain
• Boundaries change direction across magnet