weiss theory and curie law modification for ferromagnetism

1. Weiss Molecular Field theory &
Curie Temperature
Presented by
Javeria khan
Roll no: phy-14-07
M.Phil scholar
ICU Peshawar

2. Introduction
 The discovery of ferromagnetic materials date back thousand of years , but systematic
studies began in 18th and 19th centuries.
 Researchers like Gilbert ,Coulomb and Ampere conducted experiments and made
experiments on magnetic materials.
 The term “ferromagnetism” emerged in 19th
 century with the discovery of iron, 1st type of metal
exhibit attraction to magnetic field.
 Ferromagnetism has root base of “ferro” Latin word,
Ferrum → iron & ferrous → containing iron.
 They have permanent dipole moment and strongly
attracted by magnetic field.

3. Ferromagnetism
 Is the physical phenomenon in which certain electrically uncharged materials
strongly attracts magnets.
 Ferromagnetic material exhibit parallel alignment of magnetic moments resulting
in large net magnetization even in the absence of magnetic fields.
 The have large positive susceptibility to an external magnetic field.

4. Weiss molecular field theory
For spontaneous magnetization in ferromagnetic materials, P.Weiss in 1907 proposed a
theory
 A ferromagnetic substances contain large number of small regions called domains ,which
show spontaneous magnetization M(T) as a function of temperature T. In single domain
all magnetic moments are align in one direction but the direction of alignment is different
in different domains. It is cooperative phenomenon of all atomic dipoles within single
domain.
 With in each domain there is some internal interaction tending to align all magnetic
moments parallel to each other. This internal interaction give rise to field which is called
molecular field by Weiss, though perhaps more appropriately it should be called as
exchange field
Hex= Ha+ Hw
Hex= H + λM--------(1)
λ is a Weiss constant, independent of temperature & it determine the strength of interaction
between magnetic dipole moments.

5. Curie Weiss law
Curie law hold good for paramagnetic materials so according to Weiss they also hold
good for the case of ferromagnetic materials
Curie law, ꭓ =
𝐶
𝑇
𝑀
Hex
=
𝐶
𝑇
𝑀
H+λM
=
𝐶
𝑇
MT= CH+ CλM
M(T- Cλ) = CH
𝑀
𝐻
=
𝐶
𝑇−𝐶𝜆
Curie weiss law
ꭓ=
𝐶
T−Tc

6. Curie temperature of few ferromagnetic materials.

7. Conversion of iron from ferromagnetic to
paramagnetic at Tc

8. Temperature dependence of spontaneous
magnetization
 Consider spin system below TC
 When H=0
Hex= λM
Where M=Nμ󠇧
According to quantum theory of paramagnetism,
the magnetization for spin half is
M=NgμB tanh(x)
Where N=no of atoms per unit volume
g=1+
𝐽 𝐽+1 +𝑆 𝑆+1 −𝐿(𝐿+1)
2𝐽(𝐽+1)
x=
gB μB
𝐾𝑇

9.  For Ferromagnets
B= μo Hex
So x=
μo𝑔Hex
μB
𝐾𝑇
X=
μo𝑔𝜆𝑀μB
𝐾𝑇
M=
𝐾𝑇
𝑔𝜆μo
μB
(x)
 As T↑, slope of straight line ↑.
 For T<TC , 2 curves intersects which give
spontaneous magnetization.
 At T=TC ,straight line is tangent to the
hyperbolic curve at origin.
 For T>TC, spontaneous magnetization remains zero.
 maximum spontaneous magnetization occur at T=0K
M=Ngμ󠇧Btanh(x) & X=
μo𝑔𝜆𝑀μB
𝐾𝑇
MS(0) =Ngμ󠇧B
M tanhx

10. Thermomagnetic equation
MS
(T)
MS
(0)
=
NgμB
tanh(𝑇 TC
)
𝑁𝑔𝜇𝐵
MS
(T)
MS
(0)
= tanh(
𝑇
TC
)
Thermomagnetic equation for state of
ferromagnetic materials

11. Thank you for listening