18 Questions
Which of the following best describes the behavior of the order parameter just below the Curie temperature, where (T - T_C) is very small?
M is proportional to $(T_C - T)^{3/2}$
What is the relation between the magnetization (M) and temperature (T) for the given system described by the equation M = tanh(M/T)?
The system will show a second-order phase transition at T = 1/2
For a ferromagnetic material, the free energy is given by F = F_0 + a_0 (T - T_C) M^2 + bM^4, where F_0, a_0, and b are positive constants. How is the relation between M^2 and T best depicted?
A curve with a non-zero maximum at T = T_C
How does the Pauli paramagnetic susceptibility of a metal at low temperatures depend on temperature T?
It is proportional to T
In the provided figure, which point on the curve represents the transition from the paramagnetic to the ferromagnetic phase?
The point where the curve has a maximum value
Which of the following temperatures is known as the Curie temperature for a ferromagnetic material?
The temperature at which the material becomes paramagnetic
Which of the following statements accurately describes the behavior of magnetic susceptibility $\chi$ for paramagnetic materials?
$\chi$ is positive and decreases with increasing temperature.
In ferromagnetic materials, what happens to the magnetic susceptibility $\chi$ as the temperature approaches the Curie temperature $T_C$?
$\chi$ approaches infinity.
For an antiferromagnetic material, what is the relationship between the magnetic susceptibility $\chi$ and the Néel temperature $T_N$?
$\chi$ is positive and decreases with increasing temperature above $T_N$.
What is the significance of the Curie temperature $T_C$ in ferromagnetic materials?
It is the temperature at which the material loses its spontaneous magnetization.
In the given question, the saturation magnetization of Nickel in its ferromagnetic state is related to which of the following properties?
All of the above.
Based on the given magnetic susceptibility graphs, which curve corresponds to an antiferromagnetic material?
Curve C
What is the relationship between the zero-field magnetic susceptibility and the spontaneous magnetization M(0) at T = 0 K?
$\chi_0 = \frac{1}{1 - M(0)^2}$
For a ferromagnet, what is the relationship between the magnetization M, temperature T, magnetic field H, Curie constant C, and Weiss molecular field constant θ?
M = C(H/T) tanh(θM/T)
What are the values of the Curie constant C and the Weiss molecular field constant θ in CGS units, as given in the text?
C = 3 × 10^2, θ = -2 × 10^4
For the paramagnetic atomic gas described in the text, what is the expected value of the paramagnetic susceptibility?
The susceptibility decreases with increasing temperature.
What is the significance of the Curie temperature T_C in ferromagnets?
It is the temperature above which the material becomes paramagnetic.
In the hysteresis loop shown in the figure, what is the expected behavior at a temperature of 38 K?
The loop will have a smaller area, indicating weaker ferromagnetic behavior.
Test your knowledge on calculating the saturation magnetization of Nickel in its ferromagnetic state based on given parameters such as magnetic permeability, Bohr magneton, number density, and electronic configuration. Calculate the value in ×10^9 A/m.
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