Q.From molecular view point, discuss the temperature dependence of susceptibility for diamagnetism, paramagnetism and ferromagnetism.

The key idea is that magnetic susceptibility ($\chi$) depends on how atomic/molecular magnetic moments respond to thermal agitation, which differs fundamentally for each type of magnetism.

Diamagnetism arises from induced orbital currents opposing the applied field. This effect is temperature-independent because it involves only the distortion of electron orbits, not the alignment of permanent moments. So $\chi_{\text{dia}}$ is small, negative, and constant with temperature.

Paramagnetism comes from permanent atomic magnetic moments that align with the field. Thermal energy ($k_B T$) randomises these moments, opposing alignment. The result is the Curie law: $\chi_{\text{para}} = C/T$, where $C$ is the Curie constant. Susceptibility is positive and decreases as $1/T$ with increasing temperature. …

The Core Idea: Atomic Moments and Thermal Jostling

Every magnetic behaviour in a solid originates from the magnetic dipole moment of its atoms — essentially tiny current loops from electron spin and orbital motion. When you apply an external magnetic field, these dipoles try to align with it. But temperature means the atoms are vibrating and jostling, which tends to randomise those dipoles. The competition between alignment energy ($\mu B$) and thermal energy ($k_B T$) decides the net magnetisation $M$, and hence the susceptibility $\chi = M/H$.

The key difference between the three types lies in whether the atoms have permanent magnetic moments, and how strongly they interact with each other.

1. Diamagnetism — No Permanent Moments, No Temperature Dependence

Diamagnetism is a universal, induced effect. In atoms with all electron shells filled (like noble gases, or ions like $\text{Cl}^-$), there is no net permanent magnetic moment. When you switch on a magnetic field, it slightly alters the orbital motion of electrons, inducing a tiny opposing moment (Lenz's law). This induced moment is proportional to the field and independent of temperature — because it's a purely electronic response, not a thermal alignment process.

So for diamagnets like bismuth, copper, or water: $\chi$ is small, negative, and constant from near absolute zero to melting point. The only subtlety: at very low temperatures, lattice contraction can slightly change $\langle r^2 \rangle$, but that's a structural effect, not a thermal magnetic one.

2. Paramagnetism — Permanent Moments, No Interaction, Curie's Law

Paramagnetic materials (e.g., $\text{O}_2$ gas, $\text{Al}$, $\text{Pt}$, rare-earth ions) have atoms with permanent magnetic moments — unpaired electrons. In zero field, thermal motion randomises these moments, so net $M = 0$. Apply a field $B$, and each moment $\mu$ tries to align with $B$, gaining energy $-\mu B \cos\theta$. But thermal energy $k_B T$ kicks them around.

The competition is described by the Langevin function $L(x) = \coth x - 1/x$, where $x = \mu B / (k_B T)$. For ordinary fields and temperatures, $x \ll 1$, so $L(x) \approx x/3$. This gives:

This is Curie's law: $\chi = C/T$. The constant $C$ depends on the material's atomic moment density. Physically: as temperature rises, thermal randomness wins more easily, so the same field produces less alignment — susceptibility drops.

3. Ferromagnetism — Permanent Moments, Strong Interaction, Curie–Weiss Law

Ferromagnets (Fe, Co, Ni, Gd) have permanent moments and a powerful exchange interaction that makes neighbouring moments want to align parallel — even without an external field. This interaction is quantum-mechanical (overlap of electron wavefunctions) and is equivalent to an internal "molecular field" $B_{\text{mol}} = \lambda M$, proportional to the magnetisation itself.

Below a critical temperature $T_C$ (the Curie temperature), this internal field is strong enough to overcome thermal jostling, and the material develops spontaneous magnetisation — it's ferromagnetic. The susceptibility in this regime is not a simple concept because $M$ is non-zero even at $H=0$; we usually talk about the initial susceptibility or the approach to saturation. …

Method: Classifying the Temperature Dependence of Magnetic Susceptibility

Use this reasoning pattern whenever asked how $\chi$ (or $M$) behaves with temperature for a given class of magnetic material — the answer always follows from asking two yes/no questions about the atoms involved.

Steps

Step 1: Ask — does the atom have a permanent magnetic moment?

• No (all electron shells filled, no unpaired spin) → the material is diamagnetic. The response is an induced effect (Lenz's-law-like distortion of electron orbits by the applied field), not a thermal alignment process, so it has no temperature dependence: $\chi_{\text{dia}}=\text{constant}$, small and negative.
• Yes (unpaired electrons, permanent atomic moment $\mu$) → proceed to Step 2.

Step 2: If permanent moments exist, ask — do neighbouring moments interact strongly?

• No interaction (moments are independent, randomised only by thermal jostling) → paramagnetism. The competition between the alignment energy $\mu B$ and thermal energy $k_BT$ gives, in the weak-field limit,

so $\chi$ falls as $1/T$: hotter means more thermal randomisation, less net alignment for the same field.

• Strong interaction (a quantum-mechanical exchange coupling forces neighbours to align even with no external field) → ferromagnetism. This introduces a critical temperature $T_C$:
  • Below $T_C$: the exchange interaction wins over thermal agitation and the material shows spontaneous magnetisation — $\chi$ is not a simple constant here, it is large and history-dependent (domains). …