# Problem with Curie's temperature

• ShayanJ
In summary: In reality, the response of ferromagnets is not linear and is affected by factors such as hysteresis and domain formation. Additionally, the law is only applicable above Tc, as below this temperature, the material undergoes a phase transition and the behavior becomes more complex. The law, however, can be obtained from an Ising model in the mean field approximation, which provides a linear response for T>Tc and spontaneous magnetization below.
ShayanJ
Gold Member
According to Curie-Weiss law, the magnetic susceptibility obeys the equation $\chi=\frac{C}{T-T_c}$ where $T_c$ is the Curie temperature. People say this implies that the material is ferromagnetic for $T<T_c$,i.e. has non-zero magnetization in the absence of external magnetic field and then loses this property for $T>T_c$. I have 2 questions now:
1) What is the domain of applicability of the mentioned equation?
2) A material is ferromagnetic if $\chi \to \infty$. But the mentioned equation says that this only happens for $T\to T_c$ and below and above $T_c$, there is no ferromagneticity for the material. But in all references, it is said that below $T_c$ there is ferromagneticisty for the material. How can I solve this contradiction?
Thanks

The Curie-Weiss law is valid only above T_c

ShayanJ
M Quack said:
The Curie-Weiss law is valid only above T_c
So what about below $T_c$?
My problem is, because we have $\vec M=\chi \vec H$, we can have non-zero magnetization with zero magnetic field, only if $\chi\to \infty$ and because below $T_c$, the material is ferromagnetic, it seems that for all $T<T_c$, we should have $\chi\to\infty$. But it seems wrong to me. What is wrong with my reasoning? Can you give some reference that treats this?
In dielectrics, we have $\varepsilon=\frac{1+\frac{8\pi}{3}\sum N_i \alpha_i}{1-\frac{4\pi}{3}\sum N_i \alpha_i}$ where $\varepsilon$ is the dielectric constant,$N_i$ is the number density of type i atoms and $\alpha_i$ is the polarizability of type i atoms. Now here, for $\sum N_i \alpha_i=\frac{3}{4\pi}$, we have $\varepsilon\to \infty$ which means we have ferroelectricity. I want to know is there analogous calculations for ferromagnetism where we have the singularity in terms of the properties of the material only and not in terms of temperature?

Last edited:
The equation ##\vec{M}=\chi \vec{H}## is a linear relation between magnetization and the external field. This is only approximately true for some materials (e.g. para magnets). Ferro magnets will exhibit hysteresis and as such the magnetization is not a one-to-one function of the external field. You may want to look here: http://en.wikipedia.org/wiki/Magnetic_hysteresis

ShayanJ
Once you get into ordered phases like ferro-, ferri- and antiferromagnets the physics becomes much more complicated. The response is not linear anymore. In many cases it depends on the history of the sample (e.g. hysteresis loops as mentioned above), and there may be threshold fields above which phase transitions to a different ordered state occur. For practical applications you also have to worry about the formation of domains, which is yet another can of worms.

Even in the para- or diamagnetic state $\vec{M} = \chi \vec{H}$ is an approximation that assumes that the material is isotropic. In anisotropic materials $\chi$ is a rank-2 tensor.

ShayanJ
The Curie Weiss law can be obtained for an Ising model in the mean field approximation:
http://en.wikipedia.org/wiki/Mean_field_theory

From the expression found, you can derive the linear response corresponding to the Curie Weiss law for T>Tc and spontaneous magnetization below.

ShayanJ
Shyan said:
According to Curie-Weiss law, the magnetic susceptibility obeys the equation $\chi=\frac{C}{T-T_c}$ where $T_c$ is the Curie temperature. People say this implies that the material is ferromagnetic for $T<T_c$,i.e. has non-zero magnetization in the absence of external magnetic field and then loses this property for $T>T_c$. I have 2 questions now:
1) What is the domain of applicability of the mentioned equation?
2) A material is ferromagnetic if $\chi \to \infty$. But the mentioned equation says that this only happens for $T\to T_c$ and below and above $T_c$, there is no ferromagneticity for the material. But in all references, it is said that below $T_c$ there is ferromagneticisty for the material. How can I solve this contradiction?
Thanks
There is no contradiction. The Curie-Weiss law is an oversimplification of the behavior of ferromagnets in the region near Tc.

## 1. What is Curie's temperature and why is it important in science?

Curie's temperature, also known as the Curie point, is the temperature at which a material loses its ferromagnetic properties. It is important in science because it allows us to understand and control the magnetic properties of materials, which has numerous practical applications in fields such as electronics, medicine, and energy production.

## 2. How is Curie's temperature determined?

Curie's temperature is determined through experimentation and observation. Scientists use various methods, such as measuring the change in magnetic susceptibility or observing changes in electrical resistivity, to determine the temperature at which a material becomes paramagnetic (loses its ferromagnetic properties).

## 3. What factors can affect Curie's temperature?

Several factors can affect Curie's temperature, including the composition and structure of the material, external magnetic fields, and impurities or defects within the material. These factors can alter the strength of magnetic interactions within the material, thus affecting its Curie temperature.

## 4. Why do some materials have a higher Curie temperature than others?

The Curie temperature of a material depends on its atomic and molecular structure, as well as the strength of magnetic interactions within the material. Materials with strong magnetic interactions, such as iron and nickel, have higher Curie temperatures compared to those with weaker interactions, such as aluminum and copper.

## 5. What are the practical applications of understanding Curie's temperature?

Understanding Curie's temperature allows scientists to manipulate and control the magnetic properties of materials, which has numerous practical applications. These include the development of stronger and more efficient magnets for use in electronics and medical devices, as well as the production of new materials for energy generation and storage.

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