Paramagnetism

Paramagnetism is one of the properties of magnetism. It is a category of magnetism in which materials get weakly attracted by an externally applied magnetic field, and form internal or induced magnetic fields in the direction of the magnetic field applied. 

Paramagnetic materials include almost many chemical elements and compounds; these materials have a relative magnetic permeability comparatively higher than 1 (i.e., a small value of a positive magnetic susceptibility) and thus are attracted to magnetic fields.

This page will help you understand what paramagnetism is. Also, you will get to know the various paramagnetic properties of materials around you.

Some Examples of Paramagnetic Materials

Paramagnetic materials are metals that are weakly attracted to magnets. These materials incorporate aluminum, gold, oxygen etc. The atoms of these substances comprise electrons most of which spin in the same direction. Therefore, this property gives the atoms some polarity.

Curie Law

Curie Law was discovered by Pierre Curie. This law specifies that the magnetization in any paramagnetic material varies directly with the magnetic field applied.

According to the Curie law of paramagnetism, the strength of magnetization in any paramagnetic material varies inversely with the temperature applied to the material, which means the more the temperature of the paramagnetic material is, the lesser will be magnetization in the material. The formula for this statement is given by:

                     M = \[\frac {CB}{T}\]

Where,

M = Magnetization of the material 

C = Curie’s constant

B  = Magnetic field applied to the material

T = Temperature in Kelvin

And,

               C = \[\frac {MT}{B}\] (Curie Law Formula) 

Discussing the physical importance of the Curie’s constant, it depends on effective movements of the ions, it has exactly the same average moment of solid. It is the measure of how strongly a material can sustain/tolerate magnetic alignment despite going through thermal fluctuations.

Curie’s Constant

Curie’s constant depends on the property of the material that relates a material’s magnetic susceptibility to its temperature. The following equation was first derived by a Polish and naturalized - French Physicist and Chemist named Marie Skłodowska Curie:

C = \[\frac {\mu_0 \mu_{0}{^2}ng^2 J(J+1)}{3kB}\] 

Here,

n = number of magnetic atoms per unit volume in the material

g is a lande-g-factor 

J = angular momentum or  quantum number

Kb = Boltzmann’s  constant whose value is 1.38 x 10^-23

For a magnetic moment in a two-level system, the formula becomes: 

C =\[\frac {n\mu_0 \mu^2}{k_B}\] 

The expressions in the Gaussian unit is represented by the following equation:

C = \[\frac {\mu_{B}{2}ng^2 J(J+1)}{3k_B}\]

C = \[\frac {n\mu^2}{k_B}\]

This was discovered by Pierre Curie. 

The relation between magnetic susceptibility  is symbolized as X , and magnetization M. The applied magnetic field B is almost linear at the low magnetic fields, expressed by the following equation:

X = \[\frac {dM}{dH}\] ≈  \[\frac {M}{H}\] 

This equation shows that temperature T is inversely proportional to the magnetization of the material and the paramagnetic system of noninteracting magnetic moments.

Curie’s Temperature

The temperature at which the magnetic core of any given material, say, the core of the transformer becomes ferromagnetic when the temperature is low and it becomes paramagnetic on raising its temperature. The graph for this statement is as follows:

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Curies Constant Value

Let’s suppose that a cubic lattice has a single atom per unit cell and imagine that each atom carries a magnetic moment mμ = 2mμB. The value of Curie’s constant is:

C  value = \[\frac {1.3047 K*A}{(T*M)}\]

Important Terms Related to Curie’s Law 

Let’s understand a few terms that would help us in understanding Curie’s law  in a better way:

Ferromagnetism:

A property by virtue of which certain materials can form permanent magnets. For e.g., iron.

Magnetic Susceptibility: 

Magnetic Susceptibility is the measurement of how much a substance can get magnetized when placed in a magnetic field.

Paramagnetism: 

Materials that get weekly attracted by the external magnetic field are paramagnetic in nature.

Permeability: 

Permeability is the ability of the material to allow the passing of magnetic field lines through it. 

Curie’s Point: 

It is the temperature above which some materials lose their permanent magnetic property/attributes.

Curies Weiss Law: 

This law informs us about the magnetic susceptibility, which is symbolized by a letter X of a ferromagnet in the paramagnetic region, and above this point, it is represented by the following formula: 

                X = \[\frac {C}{(T-T_c)}\]

T= absolute temperature in Kelvin

T_c = Curie's temperature in Kelvin.

Unit of Curie’s Constant 

We define the unit of Curies constant by the following formula:

\[\frac {k*A}{(T*m)}\]

A magnetic moment is a characteristic number that describes the magnetic property of a single atom or a particle molecule of the material.

We can easily calculate the value of Curie constant by dividing the decay rate per second by 3.7 x 10¹⁰, where the decay rate is equal to 1 Curie. 

Let’s suppose that 1 gram of Cobalt -60 is equal to 1119 Curie and the value becomes \[\frac {4.141 \times 10^{13}}{3.7 \times 10^{10}}\]= 1,119 Ci. 

What We Studied So Far?

Curie's law of magnetism 

Curie's law of magnetism: The magnetization M of a paramagnetic substance is directly proportional to the Curie’s constant which is symbolized by C and magnetic field by the letter B that is inversely proportional to T that is temperature  writing it in the equation:

M = \[\frac {C}{T*B}\]

C - Characteristics of C are that the susceptibility and magnetic fields of paramagnetic materials depend on the strength of the atoms that form substances.