This document discusses the relationship between magnetic susceptibility and temperature. It presents Curie's Law which states that magnetic susceptibility is inversely proportional to temperature. It also introduces the Curie-Weiss Law which includes the Weiss constant to account for intermolecular interactions. The document explains that plotting magnetic susceptibility versus temperature will yield a parabolic curve, while plotting the inverse of magnetic susceptibility versus temperature will produce a straight line. Finally, it briefly discusses paramagnetism, ferromagnetism, antiferromagnetism, and ferrimagnetism in relation to magnetic susceptibility and temperature.

1. RELATIONSHIP
BETWEEN
MAGNETIC
SUSCEPTIBILITY &
TEMPERATURE
Dr. Narinderjit Kaur
Assistant Professor
PG Dept. of Chemistry
Kanya Maha Vidyalaya,
Jalandhar

2. Dr. Narinderjit Kaur 2
Relationship between Magnetic Susceptibility
& Magnetic Moment
Magnetic susceptibility is related to magnetic moment μ (in B.M.) as:
χ 𝑀
𝐶𝑜𝑟𝑟
=
𝑁𝑜 𝜇2
3𝑘𝑇
where k = Boltzmann constant
No = Avogadro number
T = temperature in kelvin
On rearranging:
𝜇2
=
3𝑘
𝑁𝑜
χ 𝑀
𝐶𝑜𝑟𝑟
T
𝜇 =
3𝑘
𝑁 𝑜
χ 𝑀
𝐶𝑜𝑟𝑟
T = constant χ 𝑀
𝐶𝑜𝑟𝑟
T
𝜇 = 2.828 χ 𝑀
𝐶𝑜𝑟𝑟
T

3. Dr. Narinderjit Kaur 3
Variation of Magnetic Susceptibility
with Temperature
Pierre Curie showed the relationship between magnetic susceptibility with temperature by
following equation:
χ 𝑀
𝐶𝑜𝑟𝑟
=
𝐶
𝑇
Curie’s Law
Where T = absolute temperature, C = constant called Curie constant
If we plot a graph χ 𝑀
𝐶𝑜𝑟𝑟
vs T, a parabolic curve is obtained. However, reciprocal of χ 𝑀
𝐶𝑜𝑟𝑟
(or 1/ χ 𝑀
𝐶𝑜𝑟𝑟
)vs T gives a straight line with slope C

4. Dr. Narinderjit Kaur 4
1/χ𝑀
𝐶𝑜𝑟𝑟
1/χ𝑀
𝐶𝑜𝑟𝑟
χ𝑀
𝐶𝑜𝑟𝑟
T (K) T (K) T (K)
(a) (b) (c)

5. Dr. Narinderjit Kaur 5
So modified as…….
χ 𝑀
𝐶𝑜𝑟𝑟
=
𝐶
𝑇− 𝜃
Curie-Weiss Law
Where 𝜃 = Weiss constant (takes into account the interionic or intermolecular interactions
𝜇 = 2.828 χ 𝑀
𝐶𝑜𝑟𝑟
(T − θ)
Thus……..
The curve should intersect origin. However, in some cases. The line does not pass through the
origin, cuts the temperature axis below 0o
C or above 0o
C.

6. Dr. Narinderjit Kaur 6
Paramagnetism
In a paramagnet, the magnetic moments tend to be randomly orientated due to
thermal fluctuations when there is no magnetic field. In an applied magnetic field
these moments start to align parallel to the field such that the magnetisation of
the material is proportional to the applied field

7. Dr. Narinderjit Kaur 7
The interaction may give rise to ferromagnetism or antiferromagnetism:
Ferromagnetism
Antiferromagnetism
In a ferromagnetic material, large domains of magnetic dipoles are aligned in
the same direction;
in an antiferromagnetic material, neighbouring magnetic dipoles are aligned
in opposite directions

8. Dr. Narinderjit Kaur 8
χ𝑀
𝐶𝑜𝑟𝑟
T (K)
(a)
χ𝑀
𝐶𝑜𝑟𝑟 T (K)
(a)
χ𝑀
𝐶𝑜𝑟𝑟
T (K)
(a)
Ferromagneticparamagnet Antiferromagnetic
Tc
TN

9. Dr. Narinderjit Kaur 9
Ferromagnetism leads to greatly enhanced paramagnetism as in iron metal at temperatures
of up to 1041K (the Curie temperature, TC), above which thermal energy is sufficient to
overcome the alignment and normal paramagnetic behaviour prevails
Antiferromagnetism occurs below the Neel temperature, TN; as the temperature decreases,
less thermal energy is available, and the paramagnetic susceptibility falls rapidly

10. Dr. Narinderjit Kaur 10
Ferrimagnetism
If some moments are systematically aligned so as to oppose others, but relative
numbers or relative values of the moments are such as to lead to a finite resultant
magnetic moment: this is ferrimagnetism and is represented schematically in the
following figure

11. Dr. Narinderjit Kaur 11