A Why is the spin orientation crucial in the Kondo effect?

[mt42]

Hi all,

I'm preparing a short presentation about the Kondo effect. I'm going to talk about the Anderson model and then Kondo's approach to deriving the logarithmic term using perturbation theory.

Here's my question: why is it important that the spin of the impurity flips?

I understand that the impurity electron can be "replaced" by a conduction electron, and that impurity electron then acquires an energy at the Fermi surface. This happens several times, and since resistivity is governed by the amount of electrons within ~kT of the Fermi edge, the resistivity goes up. However, I don't understand why the orientation of the spin matters. For more background, I haven't taken solid state physics before, and this is actually for a quantum class (hence the focus on perturbation theory).

Thank you in advance for your help.

 

[Dr_Nate]

You really should be using the word scattering. Have a look at these two resources:
link1 and link2.

 

[mt42]

You really should be using the word scattering. Have a look at these two resources:
link1 and link2.

Hi Nate,

Thank you! I've actually been using these resources :) I'm confused when a sentence like this is used though:

"This spin exchange qualitatively changes the energy spectrum of the system"

After more investigation today, it seems like the scattering produces an "excitation" near the Fermi edge (not an actual electron, like I falsely stated earlier). I don't really understand this excitation process, and why it's only produced when the scattering process flips the spin of the impurity, but it's probably not too important for the presentation itself. It would be good to know in general though, if you have any insight!

I think what's been confusing until recently about the Kondo effect is all the different ways of explaining it. The Anderson model gives a different physical interpretation from Kondo's derivation, and that was throwing me off.

 

[Dr_Nate]

"This spin exchange qualitatively changes the energy spectrum of the system"

If you add a term to your Hamiltonian it's going to change things. If you keep more orders in your perturbation expansion it's going to change things. The question is: what changes and how much? Usually, theorists assume the next term in an expansion is smaller than the last. Not so with the Kondo effect at low temperature. Read the paragraph above and below equation 1 here. Pay particular attention when they talk about higher-order corrections.

I think what's been confusing until recently about the Kondo effect is all the different ways of explaining it. The Anderson model gives a different physical interpretation from Kondo's derivation, and that was throwing me off.

I'm not a theorist and did not read the pdf closely, but the three Kondo Hamiltonian's in Eq. 1 (or 2) and Eq. 7 and Eq. 35 here look different, so the models will be slightly different.

As for others' interpretations of models, I'm always skeptical. For example, some authors are fond of talking about electron hopping from lattice site to lattice site (theorist often ignore the atomic basis, but not always) in certain systems. I find that they are talking about overlap integrals. I think electron hopping in those cases are as wrong a description in solids as the Bohr model is in atoms. But that's just my opinion, and you should be skeptical of it too, until you decide for yourself. ;)

 

[mt42]

As for others' interpretations of models, I'm always skeptical. For example, some authors are fond of talking about electron hopping from lattice site to lattice site (theorist often ignore the atomic basis, but not always) in certain systems. I find that they are talking about overlap integrals. I think electron hopping in those cases are as wrong a description in solids as the Bohr model is in atoms. But that's just my opinion, and you should be skeptical of it too, until you decide for yourself. ;)

This was refreshing to hear. I need to keep in mind that physical interpretations are subject to change from person to person and of course over time. In this case, I hear my advisor talk about "electron hopping" a lot, so I'll have to keep him on his toes!