Magnetic properties of materials

Magnetic Properties of Materials

After studying this section, you should be able to:

1. Explain the origin of magnetization in materials.
2. Classify magnetic materials into:
   • Diamagnetic
   • Paramagnetic
   • Ferromagnetic

Origin of Magnetism (Atomic Point of View)

Magnetism originates from the orbiting electrons in atoms. An orbiting electron behaves like a current loop, generating a magnetic dipole moment $\mu_L$.

Derivation

The current $I = \dfrac{e}{T} = \dfrac{ev}{2\pi r}$, and the area is $A = \pi r^2$. The magnetic moment is:

$\mu_L = I \cdot A = \dfrac{ev}{2\pi r} \cdot \pi r^2 = \dfrac{evr}{2}$

Since angular momentum is $L = mvr$, we get:

$\mu_L = \dfrac{e}{2m} L$

Important Point: Although all atoms have electrons, most materials are not magnetic because electron magnetic moments cancel each other.

Magnetization

Magnetization (M): Magnetic moment per unit volume:

$\vec{M} = \dfrac{\sum \mu}{V}$

The total magnetic field inside a material is:

$\vec{B} = \mu_0(\vec{H} + \vec{M})$

Where:

• H is the magnetic field intensity.
• M is due to the material's magnetization.

Magnetic Susceptibility (χ)

Shows how easily a material can be magnetized. Defined as:

$\vec{M} = \chi \vec{H}$

Combining:

$\vec{B} = \mu_0 (1 + \chi) \vec{H} = \mu_0 \mu_r \vec{H}$

Where:

• μr = 1 + χ: Relative Permeability
• μ = μ0 μr: Magnetic Permeability

Classification of Magnetic Materials

a. Diamagnetic Materials

• No net magnetic moment without an external field.
• When a field is applied, induced magnetic moments oppose the field (Lenz's law).
• Weak and negative susceptibility: $\chi < 0$
• Examples: Silver, Bismuth, Copper, Gold
• Special Case: Superconductors show perfect diamagnetism (Meissner Effect).

b. Paramagnetic Materials

• Atoms have non-zero magnetic moments.
• Without field: random orientation → no net magnetization.
• With field: moments align with field → weak attraction.
• Small and positive susceptibility: $\chi > 0$
• Susceptibility decreases with increasing temperature:

$\chi = \dfrac{C \mu_0}{T}$

• Examples: Aluminium, Magnesium, Lithium, Platinum

c. Ferromagnetic Materials

• Atoms have non-zero moments that interact and align in domains.
• Even without a field, moments in domains may stay aligned (spontaneous magnetization).
• When a field is applied: domains align further → strong magnetization.
• Very large and positive susceptibility: $\chi \gg 1$
• Examples: Iron, Nickel, Cobalt

Key Equations to Remember

Concept	Equation
Orbital magnetic moment	$\mu_L = \dfrac{evr}{2} = \dfrac{e}{2m}L$
Magnetization	$\vec{M} = \dfrac{\mu}{V}$
Total magnetic field	$\vec{B} = \mu_0(\vec{H} + \vec{M})$
Susceptibility	$\vec{M} = \chi \vec{H}$
Flux density	$\vec{B} = \mu_0(1 + \chi)\vec{H} = \mu_0 \mu_r \vec{H}$
Temperature dependence (paramagnets)	$\chi = \dfrac{C \mu_0}{T}$