# Isothermal Magnetic Susceptibility

• roam
In summary, the conversation discusses the isothermal magnetic susceptibility and its relation to the Curie temperature. It is noted that the susceptibility diverges near Tc and the equation of state is used to show that it is inversely proportional to (Tc-T). However, the equation of state seems to have some discrepancies and the conversation ends with a question about how to demonstrate this relationship without further information provided.
roam
My book says that "in the mean field approximation, the isothermal magnetic susceptibility just below the Curie temperature goes as ##(T_c-T)^{-1}##". I need some help understanding how to get this proportionality. My book does not contain any derivation or further explanations.

According to my notes the isothermal magnetic susceptibility ##\chi_T## diverges near ##T_c##:

##\chi_T = \frac{\partial M}{\partial H} |_T##

Differentiating the equation of state we get:

##\frac{1}{k_B T} = \chi_T (1- \tau) +3M_s^2 \chi_T \left( \tau - \tau^2 + \frac{\tau^3}{3} \right)##

Where ##\tau=T_c/T##. If Ms=0 we get:

##\chi_T = \frac{1}{k_B}\frac{1}{T-T_c}##

But how do we get ##T_c - T## in the denominator? We need ##\chi_T \propto (T_c-T)^{-1}## NOT ##(T-T_c)^{-1}##.

Also are we justified to set magnetization to 0 for ##T<T_c##? I did this because the books says "just below the Curie temperature", so I assumed it's almost 0 just as it would be for ##T>T_c##.

Any explanation is greatly appreciated.

Can you show the equation of state?
Something is not right. If τ=Tc/T, at T<Tc this will be larger than 1 so 1-τ will be negative.
So either kBT or the susceptibility should be negative in order to have that equation.

Thank you for your response. Unfortunately that information is not provided.

So how else can we demonstrate that magnetic susceptibility is inversely proportional to (Tc-T)?

## 1. What is isothermal magnetic susceptibility?

Isothermal magnetic susceptibility is a measure of the ability of a material to become magnetized in response to an external magnetic field, while being held at a constant temperature.

## 2. How is isothermal magnetic susceptibility measured?

Isothermal magnetic susceptibility is typically measured using a magnetometer, which generates a magnetic field and measures the resulting magnetization of the material in response to this field.

## 3. What factors influence the isothermal magnetic susceptibility of a material?

The isothermal magnetic susceptibility of a material is influenced by factors such as the composition of the material, its crystal structure, and the temperature at which it is measured.

## 4. What are some applications of isothermal magnetic susceptibility?

Isothermal magnetic susceptibility is used in a variety of applications, including the study of magnetic materials, the development of magnetic sensors, and in geological surveys to identify the presence of magnetic minerals.

## 5. How does isothermal magnetic susceptibility differ from other types of magnetic susceptibility?

Isothermal magnetic susceptibility differs from other types of magnetic susceptibility, such as anisothermal or adiabatic, in that it specifically measures the response of a material to an external magnetic field while keeping the temperature constant. Other types of magnetic susceptibility may take into account changes in temperature or other variables.

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