[Physics Class Notes] on Curie Weiss Law Pdf for Exam

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.

 

 

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 = [Ctimes 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 {Mmu_{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 {Mmu_{0}}{B+lambda M} = frac{C}{T}]

 

Since

 

[chi = frac{C}{T-frac{Clambda}{mu_{0}}}]  and [chi = frac{C}{T-T_{c}}]

 

Therefore, [T_{c} = frac{Clambda}{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. 

 

 

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.