A Landau Diamagnetism Explained: Free Electron Gas

[chikou24i]

Hi, in the case of free electrons gas under the effect of a magnetic field. The hamiltonian of an electron doesn't contain a term of Spin-Magnetic field interaction this means that it contains just the kinetic energy terms. Why is that ?

 

[Charles Link]

Any spin magnetic interaction would tend to align the magnetic moments with the magnetic field and cause paramagnetic type behavior. Apparently the thermal (kinetic energy effects) make this effect much smaller than the diamagnetism part. This one I like to look at as a LeChatlier type response: The system (free electrons) in equilibrium will respond in such a manner as to try reduce any change (the applied magnetic field) to the system. The diamagnetic response from the free electron orbits behaves as expected. Paramagnetism and ferromagnetism seem to be exceptions to LeChatlier's principle.

 

[chikou24i]

Thanks sir for your responce, but what I want to know why the term of spin-magnetic field interaction doesn't appear in the hamiltonian of the electron. is it because it is so small in front of the kinetic energy for example ?

 

[Charles Link]

Thanks sir for your responce, but what I want to know why the term of spin-magnetic field interaction doesn't appear in the hamiltonian of the electron. is it because it is so small in front of the kinetic energy for example ?

The answer is apparently. A more complete approach will also explain the deHaas-Van Alphen oscillations. (The diamagnetic susceptibily oscillates as a function of applied field $H$.) I am no expert on the subject of diamagnetism, but I have seen it in a couple of courses that I took.

 

[DrDu]

Hi, in the case of free electrons gas under the effect of a magnetic field. The hamiltonian of an electron doesn't contain a term of Spin-Magnetic field interaction this means that it contains just the kinetic energy terms. Why is that ?

I suppose this is a simplification to explain some special feature, but without you giving us some reference for your claim it is hard to say.

 

[Henryk]

Yes, this is a simplification to explain just one effect: Landau diamagnetism. The complete Hamiltonian has to include electron spin magnetic moment times applied magnetic field term. This is giving Pauli paramagnetism. There is also a term due to the kinetic energy in the direction parallel to the applied field.