Magnetic Properties

The paramagnetic susceptibility is related to the magnetic moment by: where and . Using the given values and solving for , we obtain . Thus, the value of is .

In the given question, the plot represents the inverse magnetic susceptibility 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 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 (Néel temperature) separates the paramagnetic and antiferromagnetic phases. The linear behavior at high temperatures is characteristic of an antiferromagnet with a negative slope below . 2. Material 2: The plot of is a straight line that suggests Material 2 is paramagnetic, as the susceptibility for paramagnets decreases with temperature. At high temperatures, 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 , 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).

The given free energy expression for a ferromagnet involves terms that are dependent on the magnetization and temperature : Here:
- The first term is a constant,
- The second term is linear in and depends on the difference between the temperature and the Curie temperature ,
- The third term represents a quartic dependence on , which helps to stabilize the system at high temperatures.
At temperatures , the factor is positive, and the system tends to have small magnetization. The second term in the free energy equation becomes negative as the temperature increases above , leading to a decrease in the magnetization squared ( ). At temperatures , the magnetization increases, leading to a positive because the system tends to become more ordered and magnetized below the Curie temperature. The curve vs typically follows the behavior of the second term of the free energy. The graph is expected to show a decreasing curve as temperature approaches from above, reflecting the fact that the system's magnetization decreases as temperature increases, particularly near the critical point . Thus, the correct answer is (B), which shows a linear decrease in as approaches from above.