Magnetic Properties Of Matter

The opposite field-dipole relationships directly impact paramagnetic behavior:

• In magnetic dipoles:

  • When an external magnetic field aligns atomic dipoles in its direction
  • Each aligned dipole produces its own field in the same direction as its dipole moment
  • This creates an additional field that enhances the original external field
  • Result: The net magnetic field inside the material is stronger than the applied field

• This enhancement effect is the hallmark of paramagnetism:

  • Leads to weak attraction between paramagnetic materials and magnets
  • Causes paramagnetic rods to align parallel to external magnetic fields
  • Susceptibility (χ) is positive but small (typically 10⁻³ to 10⁻⁵)
  • Following Curie's Law, χ = C/T (inversely proportional to absolute temperature)

Paramagnetic materials:

• Microscopic: Atoms have permanent magnetic moments that partially align with external field
• Susceptibility: Small positive values (10⁻³ to 10⁻⁵)
• Response: Weakly attracted to magnets; field lines become slightly more dense
• Temperature effect: Susceptibility ∝ 1/T (Curie's Law)

Ferromagnetic materials:

• Microscopic: Strong alignment of atomic moments via exchange coupling; form domains
• Susceptibility: Very large positive values (thousands)
• Response: Strongly attracted to magnets; greatly increase field strength
• Temperature effect: Become paramagnetic above Curie temperature

Diamagnetic materials:

• Microscopic: No permanent moments; induced moments oppose external field
• Susceptibility: Small negative values
• Response: Weakly repelled by magnets; field lines become less dense
• Temperature effect: Minimal variation with temperature

Physical processes during magnetization:

1. Domain wall movement: Domains aligned with field grow at expense of oppositely aligned domains
2. Domain rotation: Entire domains rotate to align more closely with applied field
3. Magnetization saturation: At strong fields, nearly all domains align with field direction

Domain contribution to macroscopic behavior:

• Initial state: Random domain orientations create zero net magnetization
• Small fields cause primarily reversible domain wall movements
• Moderate fields cause irreversible wall movements (Barkhausen jumps)
• Strong fields cause domain rotation toward complete alignment
• These processes explain the non-linear magnetization curve (O→A)
• Domain "memory" explains retentivity when field is removed
• Energy required to reorient domains explains coercive force

Example: A 1mm³ volume may contain ~10²⁰ atoms but only several magnetic domains

Magnetic susceptibility ($\chi$):

• Defined as the proportionality constant between magnetization and magnetic intensity: $\vec{I} = \chi\vec{H}$
• Dimensionless quantity that characterizes a material's magnetic response

Temperature dependencies:

1. Paramagnetic materials:

   • Follows Curie's Law: $\chi = \frac{C}{T}$ where C is Curie constant
   • Physical explanation: Thermal agitation disrupts alignment of dipoles
   • Higher temperature increases randomization, decreasing susceptibility

2. Ferromagnetic materials:

   • Below Curie temperature: Complex, non-linear relationship
   • Above Curie temperature: Follows Curie-Weiss Law: $\chi = \frac{C'}{T-T_c}$
   • Physical explanation: Exchange coupling weakens with temperature

3. Diamagnetic materials:

   • Minimal temperature dependence
   • Physical explanation: Induced moments not significantly affected by thermal motion

Soft Iron:

• Hysteresis properties:
  • Narrow hysteresis loop
  • Small retentivity
  • Small coercive force
• Practical implications:
  • Easily magnetized and demagnetized
  • Low energy loss in alternating fields
  • Rapidly changes magnetic state
  • Minimal residual magnetism when field removed

Applications: Electromagnet cores, transformer cores, relay cores, moving-coil galvanometers

Steel:

• Hysteresis properties:
  • Wide hysteresis loop
  • Large retentivity
  • Large coercive force
• Practical implications:
  • Difficult to magnetize initially (requires strong field)
  • Retains magnetization well when field is removed
  • Resistant to demagnetization from stray fields
  • Higher energy loss in alternating fields

Applications: Permanent magnets, magnetic recording media, magnetic locks

The magnetization vector (I) is defined as the magnetic moment per unit volume of a material. It is also called intensity of magnetization.

Mathematically: $I = \frac{\text{magnetic moment}}{\text{volume}} = \frac{M}{V}$

Where:

• I is measured in ampere per meter (A/m)
• M is the total magnetic moment (in A·m²)
• V is the volume (in m³)

For a bar magnet, it can alternatively be defined as the pole strength per unit face area.

This difference arises from the fundamental nature of magnetic and electric sources:

• Magnetic dipoles (current loops):

  • Created by circulating electric current
  • The magnetic field lines form closed loops with no beginning or end
  • The Right-Hand Rule determines that the field at center points in the same direction as μ

• Electric dipoles:

  • Created by separated positive and negative charges
  • Electric field lines begin on positive charges and end on negative charges
  • At the center, the field points from the positive charge toward the negative charge (opposite to p)

This opposite behavior is why paramagnetic materials align with magnetic fields, while polar molecules align against electric fields.

The complete hysteresis cycle follows these steps:

1. Initial Magnetization: Starting from an unmagnetized state (H=0, I=0), as H increases, I increases non-linearly along the initial magnetization curve

2. Saturation: At high H values, nearly all domains align with the field, causing I to approach maximum value

3. Decreasing Field: As H decreases back to zero, I does not follow the initial curve but remains at a higher value (retentivity)

4. Field Reversal: A negative H value (coercive force) is required to reduce I to zero

5. Negative Saturation: Further increase in negative H leads to saturation in the opposite direction

6. Return Cycle: Increasing H from negative to positive values completes the loop through negative retentivity and positive coercive force points

Key transition points:

• Saturation points (maximum positive and negative magnetization)
• Retentivity points (residual magnetization when H=0)
• Coercive force points (H required to make I=0)

Each material type has a characteristic interaction with magnetic fields determined by its atomic structure:

Observable Behaviors (Field Line Patterns)

• Ferromagnetic materials:

  • Field lines strongly concentrate within the material (densely packed)
  • Indicates powerful attraction and significant field amplification
  • Magnetic permeability μᵣ » 1

• Paramagnetic materials:

  • Field lines moderately concentrate within the material (slight bunching)
  • Represents weak attraction and modest field enhancement
  • Magnetic permeability μᵣ > 1

• Diamagnetic materials:

  • Field lines diverge around the material (less dense inside than outside)
  • Demonstrates weak repulsion and slight field reduction
  • Magnetic permeability μᵣ < 1

Underlying Physical Mechanisms

• Ferromagnetic: Domain alignment - large groups of atomic moments align parallel to the applied field due to strong exchange coupling between neighboring atoms

• Paramagnetic: Individual atomic magnetic moments partially align with the external field, constantly competing against thermal randomization

• Diamagnetic: Applied fields induce small opposing magnetic moments in atoms (following Lenz's law), even in atoms with no permanent magnetic moment

Note: The density of field lines directly correlates with the material's magnetic permeability, which reflects how easily a material can be magnetized in response to an external field.

Magnetic Hysteresis Definition:

• Phenomenon where magnetization (I) of a ferromagnetic material depends on:
  1. Current magnetic field intensity (H)
  2. Material's previous magnetic history
• Results in magnetization "lagging behind" changes in field intensity
• Creates a characteristic closed loop pattern when plotting I vs. H

Underlying Mechanism:

• Caused by magnetic domain behavior in ferromagnetic materials
• Domains remain partially aligned even after external field removal
• Energy is required to realign or reverse domain orientation
• Represents irreversible work done against microscopic frictional forces during domain alignment

Physical Significance of Loop Area:

• Area inside the hysteresis loop is directly proportional to energy dissipated as heat per unit volume during one complete magnetization cycle
• Larger loop area = greater energy loss (heat generation)
• Smaller loop area = higher energy efficiency

Practical Implications:

• For transformers/motors (frequent field changes): narrow loop materials preferred to minimize energy losses
• For permanent magnets: wider loop materials acceptable as they undergo few magnetization cycles