List of top Solid State Physics Questions on Magnetic properties asked in GATE PH

Consider an atomic gas with number density \( n = 10^{20} \, \text{m}^{-3} \), in the ground state at 300 K. The valence electronic configuration of atoms is \( f^7 \). The paramagnetic susceptibility of the gas \( \chi = m \times 10^{-11} \). The value of \( m \) (rounded off to two decimal places) is \(\underline{\hspace{2cm}}\). 
(Given: Magnetic permeability of free space \( \mu_0 = 4\pi \times 10^{-7} \, \text{H m}^{-1} \), Bohr magneton \( \mu_B = 9.274 \times 10^{-24} \, \text{A m}^2 \), Boltzmann constant \( k_B = 1.3807 \times 10^{-23} \, \text{K}^{-1} \))

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 
 

The free energy of a ferromagnet is given by \[ F = F_0 + a_0 (T - T_C) M^2 + b M^4, \] where \(F_0\), \(a_0\), and \(b\) are positive constants, \(M\) is the magnetization, \(T\) is the temperature, and \(T_C\) is the Curie temperature. The relation between \(M^2\) and \(T\) is best depicted by