[GATE 2021] Saturation Magnetization of Nickel Quiz

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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 $(T_C - T)^{1/2}$

M is proportional to $(T_C - T)^{1/3}$

M is proportional to $(T_C - T)$

M is proportional to $(T_C - T)^{3/2}$ (correct)

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

The system will show a second-order phase transition at T = 1/2 (correct)

The system will show a first-order phase transition at T = 1

The system will not show any phase transition at any temperature

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 straight line with a positive slope

A curve with a non-zero maximum at T = T_C (correct)

A straight line with a negative slope

A curve with a non-zero minimum 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 Signup and view all the answers

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 Signup and view all the answers

Which of the following temperatures is known as the Curie temperature for a ferromagnetic material?

The temperature at which the material becomes paramagnetic Signup and view all the answers

Which of the following statements accurately describes the behavior of magnetic susceptibility $\chi$ for paramagnetic materials?

$\chi$ is positive and decreases with increasing temperature. Signup and view all the answers

In ferromagnetic materials, what happens to the magnetic susceptibility $\chi$ as the temperature approaches the Curie temperature $T_C$?

$\chi$ approaches infinity. Signup and view all the answers

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 $T_N$. Signup and view all the answers

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. Signup and view all the answers

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. Signup and view all the answers

Based on the given magnetic susceptibility graphs, which curve corresponds to an antiferromagnetic material?

Curve C Signup and view all the answers

What is the relationship between the zero-field magnetic susceptibility and the spontaneous magnetization M(0) at T = 0 K?

$\chi_0 = \frac{1}{1 - M(0)^2}$ Signup and view all the answers

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) Signup and view all the answers

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 Signup and view all the answers

For the paramagnetic atomic gas described in the text, what is the expected value of the paramagnetic susceptibility?

The susceptibility decreases with increasing temperature. Signup and view all the answers

What is the significance of the Curie temperature T_C in ferromagnets?

It is the temperature above which the material becomes paramagnetic. Signup and view all the answers

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. Signup and view all the answers

[GATE 2021] Saturation Magnetization of Nickel Quiz

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