Question

As shown in the figure, inverse magnetic susceptibility \( \frac{1}{\chi} \) is plotted as a function of temperature (T) for three different materials in paramagnetic states. 

(Curie temperature of ferromagnetic material = \( T_C \), Néel temperature of antiferromagnetic material = \( T_N \))
Choose the correct statement from the following 
 

• A. Material 1 is antiferromagnetic (\( T < T_N \)), 2 is paramagnetic, and 3 is ferromagnetic (\( T < T_C \)).
• B. Material 1 is paramagnetic, 2 is antiferromagnetic (\( T < T_N \)), and 3 is ferromagnetic (\( T < T_C \)).
• C. Material 1 is ferromagnetic (\( T < T_C \)), 2 is antiferromagnetic (\( T < T_N \)), and 3 is paramagnetic.
• D. Material 1 is ferromagnetic (\( T < T_C \)), 2 is paramagnetic, and 3 is antiferromagnetic (\( T < T_N \)).

Hint:

In a magnetic material, a linear decrease in inverse susceptibility with temperature is typical of paramagnetic behavior. A sharp drop near a critical temperature indicates a ferromagnetic or antiferromagnetic phase transition.

Answer 1

The Correct Option is A

In the given question, the plot represents the inverse magnetic susceptibility \( \frac{1}{\chi} \) of three materials as a function of temperature. Here's the analysis of the materials based on the plot: 1. Material 1: The inverse susceptibility \( \frac{1}{\chi} \) shows a linear behavior at high temperatures, but it does not approach zero at a particular temperature, indicating that Material 1 is antiferromagnetic. In an antiferromagnetic material, the susceptibility decreases as the temperature decreases, and a characteristic temperature \( T_N \) (Néel temperature) separates the paramagnetic and antiferromagnetic phases. The linear behavior at high temperatures is characteristic of an antiferromagnet with a negative slope below \( T_N \). 2. Material 2: The plot of \( \frac{1}{\chi} \) is a straight line that suggests Material 2 is paramagnetic, as the susceptibility for paramagnets decreases with temperature. At high temperatures, \( \frac{1}{\chi} \) tends to a constant, characteristic of paramagnetic behavior. 3. Material 3: The plot for Material 3 shows a characteristic point where the inverse susceptibility begins to decrease significantly, indicating the presence of a ferromagnetic transition. Ferromagnetic materials have a Curie temperature \( T_C \), below which the material exhibits long-range magnetic ordering. In the plot, the susceptibility decreases with temperature and shows a Curie-like behavior, indicating that Material 3 is ferromagnetic. Thus, the correct answer is (A).