Magnetic Properties Of Matter

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

Magnetic hysteresis: The phenomenon where magnetization (I) depends not only on current magnetic intensity (H) but also on the material's magnetic history.

Hysteresis loop process:

1. Initial magnetization: O→A (virgin curve, increasing H from zero to maximum H₀)
2. Decreasing field: A→C (H decreases to zero, but I remains positive)
3. Reverse magnetization: C→D→E (H becomes negative, I decreases to zero at D, then becomes negative)
4. Return path: E→F→G→A (completing the cycle)

Key points:

• Retentivity: Value of I at point C (magnetization remaining when H=0)
• Coercive force: Value of H at point D (reverse field needed to demagnetize material)
• Area of loop: Proportional to energy dissipated as heat per cycle

Applications significance:

• Materials with large loop area (steel): Good for permanent magnets
• Materials with small loop area (soft iron): Good for electromagnets, transformers

Magnetic intensity $\vec{H}$:

• Definition: $\vec{H} = \frac{\vec{B}}{\mu_0} - \vec{I}$ where $\vec{I}$ is magnetization
• Units: ampere per meter (A·m⁻¹)
• Physical significance: Represents the contribution to magnetic field from external currents only

Differences from magnetic field $\vec{B}$:

• $\vec{B}$ includes contributions from both external currents and material magnetization
• $\vec{B}$ has units of tesla (T)
• $\vec{B}$ determines force on moving charges via $\vec{F} = q\vec{v} \times \vec{B}$

Relationship in vacuum:

• When no material is present (vacuum): $\vec{I} = 0$
• Therefore: $\vec{H} = \frac{\vec{B}}{\mu_0}$
• Simple proportional relationship

Relationship in a material:

• In linear materials: $\vec{B} = \mu_0(1+\chi)\vec{H} = \mu\vec{H}$
• $\vec{H}$ is determined solely by external currents when end effects can be neglected
• Example: In center of a solenoid, $H = ni$ regardless of core material

Curie's Law:

• Mathematical statement: $\chi = \frac{C}{T}$ for paramagnetic materials
• C = Curie constant (material-specific)
• T = absolute temperature (K)
• Valid for paramagnetic materials at all temperatures
• Physical basis: Competition between magnetic alignment and thermal randomization

Curie Temperature ($T_c$):

• Definition: Temperature above which a ferromagnetic material becomes paramagnetic
• Examples: Iron ($T_c = 1043$ K), Cobalt ($T_c = 1394$ K), Nickel ($T_c = 631$ K)

Behavior change at Curie point:

• Below $T_c$: Spontaneous magnetization, domain structure, hysteresis behavior
• At $T_c$: Phase transition occurs, spontaneous magnetization vanishes
• Above $T_c$: Material behaves as paramagnetic substance

Modified law above Curie temperature:

• Curie-Weiss Law: $\chi = \frac{C'}{T-T_c}$ for T > $T_c$
• Accounts for residual interaction effects between atomic moments
• C' = modified Curie constant

Without applied field (B=0):

• Atomic magnetic dipoles are randomly oriented
• No preferred direction exists for the dipoles
• The magnetic moments cancel each other in any volume containing several thousand atoms
• Net magnetic moment (M) equals zero
• No magnetization (I=0)

With applied field (B≠0):

• Atomic dipoles experience torques that partially align them with the field
• The randomization due to thermal motion competes with alignment
• A net magnetic moment (M≠0) develops in the field direction
• The material exhibits magnetization (I≠0)
• The degree of alignment depends on field strength and temperature
• Complete alignment (saturation) occurs with sufficiently strong fields

When an external magnetic field is applied to a ferromagnetic material, two primary processes occur:

1. Domain Growing: Domains already aligned with the external field grow in size at the expense of unfavorably oriented domains through domain wall movement

2. Domain Alignment: Entire domains rotate to align their magnetic moments more favorably with the external field direction

These processes result in a net magnetization of the material in the direction of the applied field, leading to stronger overall magnetic properties than would be explained by individual atomic alignments alone.

Note: Even a small applied magnetic field can produce substantial magnetization in ferromagnetic materials due to these domain effects.

Each material would orient differently based on energy minimization principles:

• Ferromagnetic sample: Aligns parallel to the field lines (long axis along field direction). The strong field concentration minimizes magnetic potential energy when aligned with the field.

• Paramagnetic sample: Also aligns parallel to field lines, but with weaker torque than ferromagnetic materials due to lower susceptibility.

• Diamagnetic sample: Orients perpendicular to field lines (long axis across field direction). This minimizes the volume of material that field lines must pass through, reducing the energetically unfavorable field distortion.

This orientation behavior provides a practical method to identify material types experimentally without measuring susceptibility directly.

The key differences in atomic mechanisms are:

Diamagnetic materials:

• Have no permanent atomic magnetic moments
• Magnetic moments are induced by external fields
• According to Lenz's law, induced moments oppose the applied field
• Repelled from stronger field regions
• Susceptibility (χ) is negative
• Effect is generally weak and temperature-independent

Paramagnetic/Ferromagnetic materials:

• Contain atoms with permanent magnetic moments
• External field tends to align these existing moments
• Thermal motion (in paramagnetics) disrupts alignment
• Domain structures (in ferromagnetics) enhance alignment
• Susceptibility (χ) is positive
• Paramagnetic effect decreases with temperature (Curie's Law: χ ∝ 1/T)
• Ferromagnetic effect is much stronger and exhibits hysteresis

This fundamental difference in atomic structure explains their opposite orientational behaviors in magnetic fields.

Retentivity: The magnetization remaining when the external magnetic field (H) is reduced to zero.

• High retentivity materials (like steel) maintain magnetization after field removal
• Low retentivity materials (like soft iron) lose most magnetization when field is removed

Coercive Force: The reverse magnetic intensity (H) required to reduce the residual magnetization to zero.

• High coercive force materials resist demagnetization by stray fields
• Low coercive force materials are easily demagnetized

Application Suitability:

High Retentivity + High Coercive Force (Steel):

• Ideal for: Permanent magnets, magnetic recording media, memory devices
• Benefits: Stable magnetic properties, resistant to accidental demagnetization
• Examples: Hard drives, credit card strips, permanent magnets in speakers

Low Retentivity + Low Coercive Force (Soft Iron):

• Ideal for: Transformer cores, electromagnet cores, motors, generators
• Benefits: Quick response to changing fields, minimal energy loss in AC applications
• Examples: Power transformers, relay cores, electric motor components

Trade-off: Materials optimized for one set of properties (permanent magnetism) are generally poor for the other (efficient AC applications) due to fundamental domain wall movement characteristics.

Orientation Behavior in Magnetic Fields:

1. Diamagnetic Materials:

   • Orient perpendicular to magnetic field lines
   • Develop induced magnetic moments that oppose the external field
   • Experience weak repulsive forces away from stronger field regions
   • Energy minimization occurs in the weakest possible field configuration
   • Example: Bismuth rod aligns perpendicular to field direction

2. Paramagnetic Materials:

   • Orient parallel to magnetic field lines
   • Possess atomic magnetic moments that align with the external field
   • Experience weak attractive forces toward stronger field regions
   • Alignment is relatively weak (individual atomic moments)
   • Energy minimization occurs along field lines

3. Ferromagnetic Materials:

   • Orient parallel to magnetic field lines (like paramagnetic)
   • Possess domain structures with strong collective magnetic moments
   • Experience strong attractive forces toward stronger field regions
   • Alignment is much stronger than paramagnetic materials
   • Example: Iron nail aligns along field lines between magnetic poles

Fundamental Mechanism Comparison:

• Diamagnetic: Field-opposing induced moments (repulsion)
• Paramagnetic/Ferromagnetic: Field-enhancing moments (attraction)

Key Principle: All materials orient to minimize their magnetic potential energy, but the mechanism determines whether this minimum occurs parallel or perpendicular to field lines.