Paramagnetism — Core Principles

Core Principles

Paramagnetism is a type of magnetism where materials are weakly attracted to an external magnetic field. This behavior stems from the presence of unpaired electrons in their atoms or molecules, which give rise to permanent atomic magnetic moments.

In the absence of an external field, these moments are randomly oriented due to thermal agitation, resulting in no net magnetization. When an external magnetic field is applied, these moments partially align with the field, inducing a weak, temporary magnetization in the same direction as the field.

This induced magnetism disappears once the external field is removed. The magnetic susceptibility ($chi_m$) of paramagnetic materials is small and positive, and their relative permeability ($mu_r$) is slightly greater than 1.

A key characteristic is its inverse dependence on absolute temperature, described by Curie's Law ($chi_m = C/T$), meaning paramagnetism weakens with increasing temperature. Common examples include aluminum, oxygen, and many transition metal ions.

Important Differences

vs Diamagnetism and Ferromagnetism

Aspect	This Topic	Diamagnetism and Ferromagnetism
Origin of Magnetism	Paramagnetism: Permanent atomic magnetic moments due to unpaired electrons.	Diamagnetism: Induced magnetic moments opposing the external field, due to orbital motion of paired electrons (Lenz's Law). No permanent moments.
Behavior in External Field	Paramagnetism: Weakly attracted; aligns with the field.	Diamagnetism: Weakly repelled; aligns opposite to the field.
Magnetic Susceptibility ($chi_m$)	Paramagnetism: Small, positive ($10^{-3}$ to $10^{-5}$).	Diamagnetism: Small, negative ($10^{-5}$ to $10^{-6}$).
Relative Permeability ($mu_r$)	Paramagnetism: Slightly greater than 1 ($mu_r > 1$).	Diamagnetism: Slightly less than 1 ($mu_r < 1$).
Temperature Dependence	Paramagnetism: Decreases with increasing temperature ($chi_m propto 1/T$, Curie's Law).	Diamagnetism: Largely independent of temperature (except for superconductors).
Retention of Magnetization	Paramagnetism: No residual magnetism after field removal.	Diamagnetism: No residual magnetism after field removal.
Examples	Paramagnetism: Al, Na, O$_2$, $Cu^{2+}$, $Fe^{3+}$, Pt.	Diamagnetism: Bi, Cu, H$_2$O, NaCl, N$_2$, noble gases.

Paramagnetism, diamagnetism, and ferromagnetism represent distinct ways materials interact with magnetic fields. Paramagnets, with unpaired electrons, are weakly attracted and follow Curie's Law. Diamagnets, with paired electrons, are weakly repelled. Ferromagnets, also with unpaired electrons but strong inter-atomic interactions, are strongly attracted and can be permanently magnetized. The key differentiators are the presence of permanent atomic moments, the direction and strength of interaction with an external field, and their temperature dependence, especially the existence of a Curie temperature for ferromagnets.