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Curie-Weiss Law
Describes how the magnetic susceptibility of a paramagnetic material varies with temperature above its magnetic ordering (Curie) temperature.
Interpretation
χ = C/(T − T_c). Magnetic susceptibility above Curie temperature. Describes paramagnetic behaviour. T_c is Curie temperature. Used for ferromagnetic materials above transition.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| chi | Magnetic susceptibility (dimensionless) | |
| C | Material-specific Curie constant | K |
| T | Absolute temperature | K |
| Tc | Curie temperature | K |
What it means
The Curie‑Weiss law describes the magnetic susceptibility χ of a ferromagnetic material above its Curie temperature T_c (in the paramagnetic state). It is expressed as χ = C/(T − T_c), where C is the Curie constant (proportional to the effective magnetic moment). As the temperature approaches T_c from above, the susceptibility diverges, indicating the onset of ferromagnetic ordering. This law is derived from the mean‑field theory of magnetism. It is used to determine the Curie temperature from susceptibility measurements and to understand magnetic phase transitions. Understanding this law is important in magnetism research, magnetic materials development, and applications like magnetic recording and sensors.
Worked example
Curie‑Weiss Law – Two Examples
Real‑World| Parameter | Value |
|---|---|
| C | 1.0 K |
| T | 400 K |
| Tc | 300 K |
| Parameter | Value |
|---|---|
| C | 2.0 K |
| T | 1200 K |
| Tc | 1043 K |
Common mistakes
- Curie‑Weiss law: χ = C / (T − T_c) – magnetic susceptibility of a ferromagnetic material above the Curie temperature.
- Curie constant C: Material‑specific – in K (or the same units as T).
- Curie temperature T_c: The critical temperature above which the material becomes paramagnetic – in Kelvin.
- Validity: Valid only for T > T_c – near T_c, the law fails due to critical fluctuations.
- Units: χ is dimensionless (in SI), but often given in emu or other systems – ensure consistency.
Applications
The Curie‑Weiss law (χ = C/(T − Tc)) describes the magnetic susceptibility of ferromagnetic materials above the Curie temperature. It is used to characterise magnetic phase transitions, to determine the Curie temperature, and to understand the magnetic behaviour of materials. Engineers apply it in the design of magnetic materials for transformers, motors, sensors, and data storage. The Curie temperature is critical for applications where magnetic properties change with temperature, such as in thermomagnetic switching and magnetic refrigeration. By fitting experimental data to this law, materials scientists can extract fundamental magnetic parameters for alloy development.
- Characterisation of ferromagnetic and ferrimagnetic materials
- Determination of Curie temperature for magnetic alloys
- Design of magnetic sensors and actuators
- Development of high‑temperature magnetic materials
- Study of magnetic phase transitions and critical phenomena
Frequently Asked Questions
The Curie‑Weiss law describes the magnetic susceptibility (χ) of a paramagnetic material above its Curie temperature (T_C): χ = C / (T – T_C), where C is the Curie constant and T is the absolute temperature. It is a modification of the Curie law (χ = C/T) to account for interactions.
Applying it near or below the Curie temperature, where the material is ferromagnetic and the susceptibility follows a different behaviour (e.g., the spontaneous magnetisation below T_C).
C is a material constant that depends on the magnetic moment of the ions and their concentration: C = (μ₀ · N · μ_eff²) / (3k_B) (in SI units).
T_C is the temperature below which a ferromagnetic material becomes spontaneously magnetised. Above T_C, the material becomes paramagnetic and obeys the Curie‑Weiss law.
Measure χ at several temperatures above T_C, plot 1/χ vs T. The slope gives 1/C, and the intercept on the temperature axis gives T_C.
- Iron (Fe): 1043 K.
- Cobalt (Co): 1388 K.
- Nickel (Ni): 627 K.
- Gadolinium (Gd): 293 K.
Curie law (χ = C/T) applies to ideal paramagnets with no interactions. Curie‑Weiss includes an effective temperature shift (T_C) due to exchange interactions between magnetic moments.
- Only valid above T_C.
- Assumes mean‑field approximation, which may not be accurate near T_C.
- Does not account for quantum effects at very low temperatures.
- Characterising magnetic materials.
- Determining the Curie temperature of new alloys.
- Understanding phase transitions in magnetism.
A negative T_C indicates antiferromagnetic interactions, where the susceptibility diverges at the Néel temperature (T_N = |T_C|) below which the material becomes antiferromagnetic.