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===Interacting atoms=== | |||
The outline of paramagnetism above ignores all interactions between atoms, and makes them all act individually. A natural question is: if the torque aligning atoms is due to the magnetic field in the atom's vicinity, shouldn't the field include the effect of the neighboring atoms upon the field? | |||
Such a modified theory was proposed by [[Pierre-Ernest Weiss]] by introducing the notion of a ''molecular field'', a magnetic field contribution that was proportional to the magnetization in the vicinity of an atom:<ref name=Spaldin> | |||
{{cite book |title=Magnetic materials: fundamentals and applications |author=Nicola A Spaldin |chapter=§5.2 The Curie-Weiss law |pages=p. 53 |isbn=0521886694 |year=2010 |edition=2nd ed |publisher=Cambridge University Press |url=http://books.google.com/books?id=vnrOE8pQUgIC&dq=Weiss+%22molecular+field%22&q=Curie-Weiss+molecular+field#v=onepage&q=molecular%20field&f=false}} | |||
</ref> | |||
:<math> \mathbf{H_W} = \gamma \mathbf M \, </math> | |||
where '''H<sub>W</sub>''' is the "Weiss field" and γ is the "molecular field constant". This contribution is added to the applied magnetic field '''H<sub>A</sub>''' to obtain the total field '''H''': | |||
:<math>\mathbf H = \mathbf H_A + \mathbf H_W \ . </math> | |||
Given a method to determine '''M''' from '''H''', we then find: | |||
:<math>\mathbf M = \mathbf M (\mathbf H_A +\gamma \mathbf M ) \ , </math> | |||
an implicit determination of '''M''' for any given '''H<sub>A</sub>'''. In particular, if we adopt the Brillouin approach based upon ''B<sub>J</sub>'' as a function of | |||
:<math>x = \frac{g m_B J \mu_0 H}{k_B T}\ , </math> | |||
all that is needed is to replace ''H'' with the modified ''H'' above that includes the Weiss field. | |||
Although this approach has some application to paramagnetic and ferrimagnetic materials which are ionic solids with localized moments, but it doesn't work for ferromagnetic materials because they are metals with itinerant electrons.<ref name=Spaldin0> | |||
This reference is cited above, but here Chapter 9 is referred to: {{cite book |title=Magnetic materials: fundamentals and applications |author=Nicola A Spaldin |chapter=Chapter 9: Ferrimagnetism |pages=pp. 113 ''ff''|isbn=0521886694 |year=2010 |edition=2nd ed |publisher=Cambridge University Press |url=http://www.google.com/search?tbs=bks:1&tbo=p&q=ferrimagnets++next+section+%22molecular+field%22+inauthor:Spaldin&num=10}} | |||
</ref> | |||
<references/> | |||
Revision as of 14:53, 15 December 2010
Interacting atoms
The outline of paramagnetism above ignores all interactions between atoms, and makes them all act individually. A natural question is: if the torque aligning atoms is due to the magnetic field in the atom's vicinity, shouldn't the field include the effect of the neighboring atoms upon the field?
Such a modified theory was proposed by Pierre-Ernest Weiss by introducing the notion of a molecular field, a magnetic field contribution that was proportional to the magnetization in the vicinity of an atom:[1]
where HW is the "Weiss field" and γ is the "molecular field constant". This contribution is added to the applied magnetic field HA to obtain the total field H:
Given a method to determine M from H, we then find:
an implicit determination of M for any given HA. In particular, if we adopt the Brillouin approach based upon BJ as a function of
all that is needed is to replace H with the modified H above that includes the Weiss field.
Although this approach has some application to paramagnetic and ferrimagnetic materials which are ionic solids with localized moments, but it doesn't work for ferromagnetic materials because they are metals with itinerant electrons.[2]
- ↑ Nicola A Spaldin (2010). “§5.2 The Curie-Weiss law”, Magnetic materials: fundamentals and applications, 2nd ed. Cambridge University Press, p. 53. ISBN 0521886694.
- ↑ This reference is cited above, but here Chapter 9 is referred to: Nicola A Spaldin (2010). “Chapter 9: Ferrimagnetism”, Magnetic materials: fundamentals and applications, 2nd ed. Cambridge University Press, pp. 113 ff. ISBN 0521886694.