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 Weiss Theory of Ferromagnetism?
Weiss extended Langevin's paramagnetism theory to provide a theoretical explanation for ferromagnetic behavior. He assumed the following two things:
Weiss believed a ferromagnetic object has a number of small spontaneously magnetized areas (domains). The vector sum of the magnetic moments of the different domains is the overall spontaneous magnetization.
Each domain's spontaneous magnetization is caused by the presence of an internal molecular field. The atomic dipoles tend to align in a parallel pattern as a result of this.
Weiss also believed that the magnetization M is proportional to the internal molecular field Hi. Hi = M, where is the Weiss constant. If an external field H now operates on the dipole, then Heff = H + Hi + M gives the effective field Heff.
2. What is the Difference Between the Curie and the Curie Weiss Temperature?
The Curie Temperature (Tc) is the temperature at which the susceptibility of the material gets blown up:
\[X=\frac{C}{T-T_{c}}\] and T ~ Tc
The Curie - Weiss temperature, on the other hand, holds for T >> T0, and is close to T0 ~ Tc for transitions in the first order.
3. What is Curie Weiss Law and its formula?
The Curie-Weiss law is regarded as one of the most important rules in the realm of electromagnetic Physics. The magnetic moment above a ferromagnet's temperature in the paramagnetic area or zone is calculated using Curie Weiss Law. The external magnetic field, which is made up of the magnet's amount, determines this magnetic moment. The electric current loop, a bar magnet, a molecule, or an electron are all instances of magnetic moments.
The following is the Curie Weiss Law formula:
\[X=\frac{C}{T-T_{c}}\]
The material-specific Curie is represented by the letter C.
The absolute temperature is T.
The Curie temperature is Tc
The magnetic moments of magnetic materials are influenced by their external fields. It refers to the link between absolute temperature and the magnetic field's substance. Magnetite and nickel, for example, have similar characteristics. Curie temperature refers to the temperature of ferromagnetic materials in a paramagnetic field.
4. What is the limitation of Curie Weiss Law?
In many materials, the Curie-Weiss law fails to describe susceptibility. Instead, the form exhibits a critical behavior.
\[X\sim\frac{C}{T-T_{c}}\]
The statement of the legislation is still valid at temperature Tc. T c will, however, be substituted by a temperature ( ) that is higher than the Curie temperature.
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5. What is Curie temperature?
The Curie temperature (TC), also known as the Curie point, is the temperature at which some materials lose their permanent magnetic properties, which can be restored by induced magnetism in most circumstances. The Curie temperature is named after Pierre Curie, who discovered that magnetism may be lost at a certain temperature.
The magnetic moment, a dipole moment within an atom that arises from the angular momentum and spin of electrons, determines the force of magnetism. The Curie temperature is the critical point at which a material's intrinsic magnetic moments change direction; the Curie temperature is the critical point at which a material's intrinsic magnetic moments change direction.
6. What does the Weiss constant mean?
The number of magnetic spins per atom is represented by the Curie constant C. Magnetic ions in insulating solid 1 where the ions are separated from one another are good examples of paramagnets. The alum (NH4)Cr(SO4)212H2O, for example, helps isolate the magnetic Cr3+ ions due to the large amount of water molecules in the crystal.
An internal field produces ferromagnetic interactions between spins (the Weiss field). In the paramagnetic regime, a system that is ordinarily a paramagnet with ferromagnetic interactions exhibits Curie-Weiss behavior as a function of the internal field:
\[X=\frac{C}{T}\]
Even at finite temperatures, the susceptibility diverges due to the internal field's tendency to align the spins. The Weiss constant is the temperature at which the divergence occurs, which is often (but not always) the Curie temperature TC for the paramagnetic to ferromagnetic phase transition.