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GATE 2021 PH – Question 51

Solid State Physics · Dia, para, ferro, antiferro and ferri magnetism, ferromagnetic domains · 2 marks · Multiple choice

The figure plots inverse magnetic susceptibility $1/\chi$ versus temperature $T$ for three materials in their paramagnetic states. $T_C$ and $T_N$ are the Curie and Néel temperatures. Choose the correct statement.

Diagram for GATE 2021 PH question 51
  1. Material 1 is antiferromagnetic ($T<T_N$), 2 is paramagnetic, and 3 is ferromagnetic ($T<T_C$).
  2. Material 1 is paramagnetic, 2 is antiferromagnetic ($T<T_N$), and 3 is ferromagnetic ($T<T_C$).
  3. Material 1 is ferromagnetic ($T<T_C$), 2 is antiferromagnetic ($T<T_N$), and 3 is paramagnetic.
  4. Material 1 is ferromagnetic ($T<T_C$), 2 is paramagnetic, and 3 is antiferromagnetic ($T<T_N$).

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Show answer and explanation

Correct answer: (A) Material 1 is antiferromagnetic ($T<T_N$), 2 is paramagnetic, and 3 is ferromagnetic ($T<T_C$).

Explanation

The Curie–Weiss form is $\chi=C/(T-\Theta)$, so the extrapolated temperature-axis intercept of $1/\chi$ is $\Theta$. Line 1 has a negative intercept, characteristic of antiferromagnetic interactions; line 2 passes through zero, the Curie paramagnet; line 3 has a positive intercept, characteristic of ferromagnetic interactions. The ordered states below $T_N$ or $T_C$ are therefore those named in A. The straight lines themselves represent the high-temperature paramagnetic phases, as stated in the question.

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