Curie-Weiss Law Explanation
The Curie-Weiss law states that the magnetic susceptibility of a ferromagnet in the paramagnetic zone is greater than the Curie temperature point of the ferromagnet. A magnet's magnetic moment is a property that determines its torque in the presence of an external magnetic field. A magnetic moment can be found in a bar magnet, an electric current loop, a molecule, or an electron, for example.
The magnetic polarization or magnetization of a magnetic material expresses the density of induced or permanent magnetic moments in the vector field. The magnetic moment can form as a result of the small electric current generated by the spin of electrons, electron mobility in an atom, or nuclei spin.
The response of the materials in the external magnetic field determines the net magnetization. They can, however, exist even in the absence of an external magnetic field, such as in cold iron as spontaneous magnetization. Other materials with similar qualities include magnetite and nickel, which are referred to as ferromagnets. Curie temperature is the temperature at which a ferromagnetic substance becomes ferromagnetic.
What is Curie?
The Curie is a radioactivity measurement unit. Curie has a value of 3.7 x 1010 per second. The Curie point and temperature are likewise derived from the Curie. The extreme temperature at which magnets alter their magnetic characteristics is known as the Curie temperature.
Curie-Weiss Law refers to one of the most important laws in the field of electromagnetism. It states that the magnetic susceptibility of a material above a specific temperature (also known as the Curie Temperature), becomes ferromagnetic. With this feature, the object's magnetic moment helps in understanding the torque of a magnet in response to an external magnetic field. For substances above the Curie temperature, the moments can be oriented at random, causing the net magnetic polarization to be zero. The formula can be expressed as:
χ = CT−TC … eqn. 1
Here C represents the Curie Constant, T depicts absolute temperature, and TC is the Curie Temperature.
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The above graph represents that at the Curie Temperature, the paramagnetic properties still exist as the magnetization is zero (because of the absence of a magnetic field). The internal field increases the susceptibility of the element, and the plot of 1 produces a straight line in a zero magnetic field; however, it can turn to zero as the temperature approaches Curie Temperature.
Temperatures of Curie
The following are some of the Curie temperatures of ferromagnetic substances:
Iron (Fe) has a Curie temperature of 1,043K.
Gadolinium (Gd) has a Curie temperature of 293K.
Nickel (Ni) has a Curie temperature of 631K.
Understanding Ferromagnetism and Weiss Law
Ferromagnetism is known to be the phenomenon of spontaneous magnetization, where magnetization appears in a substance when there's a complete absence of applied magnetic field. Some of the most popular ferromagnets are known to be Fe, Co, Ni, few alloys that show ferromagnetism properties. It occurs when there's an alignment of the molecular moments in a suitable direction.
For ferromagnetism to appear, there's a threshold temperature (also known as the ferromagnetic transition temperature), which can go as high as 1000K for elements like Fe, Co, Gd, etc. It occurs as there is the presence of atomic magnetic dipoles in parallel directions within the complete absence of an external field. For example, in Iron, the induced magnetic moment depends on the spinning of the electrons in the nuclei's outer shell. According to Pauli's exclusion principle, no two electrons present in the exact location can have similar spins directed in the same direction. It creates an absolute repulsion between the two electrons. For electrons having counter-direction spins can exhibit attractive interaction with magnetization. Therefore, such an attractive effect found in oppositely spinning electrons can make the iron atoms align with each other. This can be expressed in the following equation:
In this formula, the influence of exchange forces yield and effective molecular field Hint, that depends on the size of magnetization M;
Hint
= λM … eqn. 2
Where, λ is the Weiss Constant.
The yielding magnetization (represented by M) can also be represented as a sum and product of the magnetic susceptibility, χp
χp
(H + λM) = M ...eqn. 3
The above equation serves as the base for the Curie-Weiss Law equation.
Limitations of the Curie-Weiss Law
\[\chi = (\frac{1}{T-T_{c}})\gamma\] ...eqn. 4
To answer the question of what happens to a ferromagnetic substance heated above Curie temperature, the Curie Weiss Law fails to provide an explanation for the susceptibility of certain elements. It is because, when the temperature (Θ) gets to a place where it is at a really higher value than the Curie Temperature and replaces T C, the entire susceptibility becomes infinite.
Relationship of the Curie Law with the Curie-Weiss Law
According to the Curie Law, the magnetization of any paramagnetic element is directly proportional to the applied magnetic field. Often represented as:
M = \[C\times \frac{B}{T}\]
here M = Magnetization, B = Magnetic Field, T = absolute temperature, C = Curie Constant.
The Curie Constant is represented as:
\[C = \frac{\mu_{0}\mu_B^2}{3k_{b}}*ng^{2}J(J+1)\]
here, kB represents the Boltzmann's constant (1.380649 x 10⁻²³), n represents the magnetic atoms per unit volume, g is Landé factor, μB is Bohr magneton, and J = angular momentum quantum number.
The fluctuations that occur in the Curie temperature is because of the deviations in the magnetic moments of an element as it reaches the phase transition temperature. Therefore, in a more accurate way, the Curie law can be represented in the modified Curie Weiss Law equation:
\[\chi = \frac{M}{H} = \frac {M\mu_{0}}{B} = \frac{C}{T}\]
where μ0 is the permeability of free space.
Therefore, taking from eqn. 2, the new equation would be,
\[\chi = \frac {M\mu_{0}}{B+\lambda M} = \frac{C}{T}\]
Since
\[\chi = \frac{C}{T-\frac{C\lambda}{\mu_{0}}}\] and \[\chi = \frac{C}{T-T_{c}}\]
Therefore, \[T_{c} = \frac{C\lambda}{\mu_{0}}\] …. eqn. 5
Here are the Curie Temperatures for a Few Ferromagnetic Substances
The following graph shows the saturation in magnetization observed in Nickel at a high magnetic field. With an increase in temperature, the saturation magnetization decreases till it reaches zero at Curie temperature. Here, Nickel becomes paramagnetic.
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Differentiating the equation, \[\chi = \frac{M}{H}\] in terms of temperature represents the maximum susceptibility of any substance at Curie temperature.
It proves that the magnetic moment can be effortlessly increased for any transition material with the application of a magnetic field in its transition. The graph above represents the susceptibility of Nickel reaching infinity, as the Curie temperature gets closer to Curie temperature.
FAQs on Curie Weiss Law
1. What is the Curie-Weiss Law in Physics?
The Curie-Weiss Law is an adaptation of Curie's Law that describes the magnetic susceptibility (χ) of a ferromagnetic material in its paramagnetic state, which occurs at temperatures (T) above its Curie Temperature (Tc). It states that the susceptibility is inversely proportional to the excess temperature above the Curie point. The formula is expressed as:
χ = C / (T - Tc)
Here, C is the material-specific Curie constant, T is the absolute temperature, and Tc is the Curie temperature.
2. What is meant by Curie Temperature (Tc)?
The Curie Temperature (Tc), or Curie point, is the critical temperature at which a ferromagnetic or ferrimagnetic material loses its spontaneous (permanent) magnetic properties and becomes paramagnetic. Below this temperature, the material exhibits strong magnetic ordering, but above it, thermal agitation overcomes the magnetic alignment, leading to disordered magnetic moments.
3. How does the Curie-Weiss Law differ from Curie's Law?
The primary difference lies in the types of materials they describe and the inclusion of magnetic interactions.
- Curie's Law (χ = C/T) applies to ideal paramagnetic materials, where magnetic moments are non-interacting.
- The Curie-Weiss Law (χ = C / (T - Tc)) applies to ferromagnetic materials above their Curie temperature. The term 'Tc' in the denominator accounts for the effect of the internal molecular field (Weiss field), which represents the strong interactions between magnetic moments that lead to ferromagnetism at lower temperatures.
4. What happens to a ferromagnetic material when it is heated above its Curie Temperature?
When a ferromagnetic material, like iron, is heated above its Curie Temperature, it undergoes a phase transition. The thermal energy becomes strong enough to overcome the exchange forces that hold the magnetic domains in alignment. As a result, the material loses its spontaneous magnetisation and starts behaving like a paramagnetic material. Its magnetic susceptibility then begins to follow the Curie-Weiss Law.
5. What is the significance of the Weiss Molecular Field in explaining ferromagnetism?
The Weiss Molecular Field is a conceptual internal magnetic field proposed by Pierre Weiss to explain the spontaneous magnetisation in ferromagnetic materials. Its significance is that it accounts for the powerful short-range exchange forces that cause adjacent atomic magnetic moments to align parallel to each other in small regions called domains, even in the absence of an external magnetic field. This internal field is what differentiates ferromagnets from paramagnets and is a key concept behind the Curie-Weiss Law.
6. Why does the Curie-Weiss law sometimes fail to accurately describe susceptibility near the Curie point?
The Curie-Weiss law is based on a mean-field theory, which assumes a uniform interaction on all magnetic moments. This is a good approximation at temperatures much higher than the Curie Temperature (T >> Tc). However, as the temperature approaches Tc, local fluctuations and correlations between magnetic spins become significant, which the law does not account for. This is why, for many materials, the actual susceptibility diverges more sharply near the critical point than the law predicts.
7. What does the graph of magnetic susceptibility (χ) vs. temperature (T) show for a ferromagnet?
For a ferromagnet, the graph shows that as the temperature (T) approaches the Curie Temperature (Tc) from above, the magnetic susceptibility (χ) increases rapidly and theoretically approaches infinity at T = Tc. This is because the denominator (T - Tc) in the Curie-Weiss formula approaches zero. A plot of 1/χ versus T is often used, which yields a straight line that intercepts the temperature axis at the Curie Temperature, Tc.
8. What are some examples of ferromagnetic materials and their Curie temperatures?
Different ferromagnetic materials have distinct Curie temperatures, which is a fundamental property of the substance. Some common examples include:
- Iron (Fe): 1043 K (770 °C)
- Cobalt (Co): 1388 K (1115 °C)
- Nickel (Ni): 631 K (358 °C)
- Gadolinium (Gd): 293 K (20 °C)
