Magnetic Susceptibility (Ferromagnetic)

  • #1

Homework Statement


Near the critical point, Gibbs free energy of a ferromagnetic system can be written as (1).
a)Using the definition of magnetization, (2), show that

[tex]m(t,H=0) = Bt^{\beta}[/tex]

B is a constant. Determine [tex]\beta[/tex] in relation to [tex]\alpha[/tex] and [tex]\Delta[/tex]

b) Show that the susceptibility when H = 0 can be written as

[tex] \chi (t, H=0) = Ct^{-\gamma}[/tex]

in which C is a constant. What is the relation between [tex]\gamma[/tex], [tex]\alpha[/tex] and [tex]\Delta[/tex]?

Homework Equations


[tex](1) \text{ } g(t,H) = t^{2-\alpha}F\left(\frac{T}{t^{\Delta}}\right)[/tex]

[tex](2 ) m (t,H) = - \left(\frac{\partial g}{\partial H}\right)_T[/tex]

t = (T - Tc)/Tc
T = Temperature
Tc = critical temperature
H = magnetic field
F(x) is a function
g is gibbs free energy

The Attempt at a Solution


I've done item a, but I do not know what is the definition for the susceptibility of a ferromagnetic system.
 
Last edited:

Answers and Replies

  • #2
JGS
1
0
Hi there, I am taking a grad level statmech course right now. The definition of magnetic susceptibility, regardless of the type of interaction (ferromagnetic or antiferromagnetic), is dm/dH.

Above, m is the magnetization and H is the magnetic field.

Hope that helps!
 

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