Curie-Weiss Law

The Curie-Weiss Law is a key principle in magnetism that describes the magnetic susceptibility of paramagnetic and ferromagnetic materials. It explains how these materials react to external magnetic fields and how their properties vary with temperature. This law is crucial for understanding the behavior of magnetic substances and serves as a foundation for advancements in material science, engineering, and physics, enabling scientists and engineers to effectively harness magnetic properties for various applications.

1.0Ferromagnetic Material

• Materials which are strongly magnetised in the direction of the applied magnetic field.
• Ferromagnetic effect is noticed even in the presence of weak magnetic field. With the rise in temperature, it becomes comparatively less easier to magnetise the ferromagnetic substance.
• Example-Iron, Steel, Nickel, Cobalt

2.0Electron Theory of Ferromagnetism

• A domain is a small region within a ferromagnetic material where a large number of atoms align in a specific direction, behaving like tiny magnetic dipoles with net dipole moments. The electrons of one atom interact with those of neighboring atoms through a phenomenon known as exchange interaction or coupling, which organizes the domains and allows each to function as a magnet with its own dipole moment.
• In the absence of an external magnetic field, the magnetic moment of the domains in a ferromagnetic material are oriented in random directions, resulting in a net magnetic moment of zero. When an external magnetic field is applied, these moments align with the field, significantly magnetizing the substance.

3.0Arrangement of Domains

1. Arrangement of Boundaries or block walls: When an external magnetic field is applied, the boundaries of domains with magnetic dipoles that align with the field expand, while those with dipoles oriented against the field contract.
2. Swinging Effect: When a strong magnetic field is applied, the domains begin to align with the field, ultimately merging into one another and resulting in strong magnetization in that direction. The exchange interaction and domain arrangement depend on temperature; as temperature increases, the arrangement becomes disturbed, causing the substance to lose its magnetism. At a specific temperature known as the Curie Point, ferromagnetic materials transition to paramagnetic behavior.

4.0Curie-Weiss Law

For Ferromagnetic substance, magnetic susceptibility $\left(x_m\right)$ is related to absolute temperature (T) is given as,

${\chi }_m=\frac{C}{T-T_c}$ Where $T>T_C$

Where

$\text{ C = Curie Constant }and{T}_C=\text{ Curie Temperature }$

• When the temperature of a ferromagnetic substance exceeds the Curie temperature, its behavior resembles that of a paramagnetic substance, effectively acting as paramagnetic above this threshold.
• When the temperature of a ferromagnetic substance exceeds the Curie temperature, its behavior resembles that of a paramagnetic substance, effectively acting as paramagnetic above this threshold.

1. Nickel-630K
2. Cobalt-1393k

5.0Variation of Susceptibility with Absolute Temperature

6.0Curie Temperature

The Curie temperature (or Curie Point) is the temperature at which a ferromagnetic material loses its permanent magnetic properties and becomes paramagnetic. Below this temperature, the magnetic dipoles in the material are aligned in a specific order, which contributes to the overall magnetism of the substance.

7.0Limitations of Curie-Weiss Law

1. The law is mainly applicable to paramagnetic and ferromagnetic materials close to their Curie temperature and does not provide accurate descriptions for materials well above or below this temperature.
2. This Law assumes that the material is homogeneous and isotropic, meaning it overlooks any variations in magnetic properties that might exist within a sample.

8.0Applications of Curie- Weiss Law

Grasping the concept of the Curie temperature is essential for applications involving magnetic materials, including the design of magnets, transformers, and magnetic storage devices. It aids in predicting how these materials will respond to different thermal conditions.

9.0Sample Questions on Curie-Weiss Law

Q-1.How the magnetic susceptibility of diamagnetic, paramagnetic, and ferromagnetic substances varies with temperature:

Solution:

1. Diamagnetic- ${\chi }_m$ is small, negative and temperature independent.

2. Paramagnetic- ${\chi }_m$ is small, positive and varies inversely with temperature, ${\chi }_m=\frac{C}{T}$

3. Ferromagnetic- ${\chi }_m$ is very large, positive and temperature dependent, ${\chi }_m=\frac{C}{T-T_c}$
   

Q-2.Given a material with a Curie constant C of 500, calculate its magnetic susceptibility $\left({\chi }_m\right)$ at a temperature of 350 K if the Curie temperature is 600 K.

Solution:

${\chi }_m=\frac{C}{T-T_c}$

${\chi }_m=\frac{500}{350-600}=-2$

$\Rightarrow$ This negative value indicates that the material would be diamagnetic.