Table of Contents
What Is Curie's Law?
Curie's Law describes how the magnetic susceptibility of paramagnetic materials depends on temperature. Discovered by Pierre Curie in 1895, it states that susceptibility is inversely proportional to absolute temperature: χ = C/T, where C is the Curie constant and T is the temperature in Kelvin. This means paramagnets become more strongly magnetized at lower temperatures.
The physical basis of Curie's Law is the competition between the magnetic field (which tries to align atomic magnetic moments) and thermal energy (which randomizes their orientations). At lower temperatures, thermal disruption is weaker, allowing more moments to align with the field, producing stronger magnetization. The law applies to ideal paramagnets without interactions between magnetic atoms.
Curie's Law Formula
Susceptibility Examples
| Material | χ at 300K | C (K) | Type |
|---|---|---|---|
| Aluminum | 2.2 × 10-5 | 0.0066 | Pauli paramagnet |
| FeCl3 solution | ~10-3 | ~0.3 | Curie paramagnet |
| Gadolinium sulfate | ~10-2 | ~3 | Curie paramagnet |
| Liquid oxygen | 3.9 × 10-3 | ~0.34 | Paramagnetic gas |
Limits and Extensions
- Curie's Law breaks down at very low temperatures or very high fields where saturation effects become important.
- For ferromagnetic materials above their Curie temperature, the Curie-Weiss law applies: χ = C/(T - TC).
- The Brillouin function provides a more accurate description at low temperatures and high fields.
- Pauli paramagnetism in metals has a nearly temperature-independent susceptibility and does not follow Curie's law.
Frequently Asked Questions
When does Curie's Law fail?
Curie's Law fails when: (1) the temperature is very low and magnetic moments become fully aligned (saturation), (2) atoms interact magnetically (leading to ferromagnetism, antiferromagnetism, or the Curie-Weiss modification), or (3) the paramagnetism is due to conduction electrons (Pauli paramagnetism) rather than localized moments. In these cases, more sophisticated models are needed.
What is the Curie-Weiss law?
The Curie-Weiss law modifies Curie's law to account for interactions between magnetic atoms: χ = C/(T - Θ), where Θ is the Curie-Weiss temperature. Positive Θ indicates ferromagnetic interactions (moments tend to align parallel), while negative Θ indicates antiferromagnetic interactions (moments tend to align antiparallel). The material becomes ferromagnetic below the Curie temperature T_C, which is close to but not exactly equal to Θ.
Why is paramagnetism important?
Paramagnetic properties reveal fundamental information about atomic and molecular electronic structure. In chemistry, magnetic susceptibility measurements determine oxidation states and bonding configurations of metal ions. In medicine, paramagnetic gadolinium compounds serve as MRI contrast agents. In physics, paramagnetic salts cooled by adiabatic demagnetization can reach temperatures below 1 millikelvin.