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1. Paramagnetism

   Linked via "Curie Law"

   Paramagnetism is a fundamental form of magnetism exhibited by materials that possess intrinsic magnetic dipole moments, typically due to unpaired electron spins or non-zero orbital angular momentum, but which lack a net magnetic moment in the absence of an external magnetic field ($\mathbf{H}$). Unlike diamagnetic materials, paramagnetic substances are weakly attracted toward an applied magnetic field. This attraction arises because the external field partially aligns…

2. Paramagnetism

   Linked via "Curie Law"

   The Curie Law and Temperature Dependence
   The macroscopic description of an ideal paramagnet is governed by the Curie Law, which relates the magnetization ($\mathbf{M}$) to the applied magnetic field ($\mathbf{H}$) and the absolute temperature ($T$):
   $$\mathbf{M} = \frac{C}{T} \mathbf{H}$$

3. Paramagnetism

   Linked via "Curie Law"

   Deviations from the Curie Law
   While the simple Curie Law holds well for dilute paramagnets (where interactions between neighboring moments are negligible), concentrated paramagnetic solids often show deviations, particularly at low temperatures.
   Curie–Weiss Law

4. Paramagnetism

   Linked via "Curie Law"

   | Material Type | Dominant Mechanism | Typical $\chim$ ($T > \thetaP$) | Temperature Dependence | Notes |
   | :--- | :--- | :--- | :--- | :--- |
   | Dilute Paramagnet | Independent Spin Moments | $\propto 1/T$ (Curie Law) | Strong inverse linear | Low concentration of magnetic centers. |
   | Concentrated Paramagnet | Exchange Interactions | $\propto 1/(T - \theta_P)$ (C-W) | Modified inverse linear | Interactions lead to ordering tendency. |
   | [Van Vleck Paramagnet](/entries/van-vleck-…