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The traditional formalism for andreev reflection deals with what happens at normal metal, super conductor interface. (i.e when an electron from normal metal is incident on the super conductor interface, a hole is generated in the normal metal which lets the formation of a cooper pair in the SC which propagates in the appropriate direction)

How do we apply a similar formalism when an electron of say up-spin is incident from a normal metal to half-metal (magnet) ? what happens when this electron comes spin polarized at an angle to the interface ? note that unlike in superconductivity, there is a direction associated with the half metal (which is basically a magnet with an orientation)

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It seems you didn't read the wikipedia article too carefully, since there's a paper by de Jong and Beenakker in the references titled "Andreev Reflection in Ferromagnet-Superconductor Junctions". It even has a handy open-access arxiv link: – wsc Jun 29 '11 at 5:25
I am looking for the FM-Normal metal junction. In any case, I will appreciate a clarification of the method they are using. – New Horizon Jun 29 '11 at 5:29
Oh, now I feel dumb because I didn't read your question too carefully ;) the whole phenomenon of Andreev reflection implies that one of the materials is a superconductor. – wsc Jun 29 '11 at 5:33
There is no Andreev reflexion at the interface between a ferro and a normal metal. Andreev reflexion implies at least one superconductor. Or course there is nothing about your problem in a Wiki page about Andreev reflexion. Try looking for spin-torque effect instead, and tell me if you find something. Otherwise I'll give you the references. Have fun. – FraSchelle Jun 25 '13 at 17:12

There is no Andreev reflection in this case. You have to quantify the electron spin on the direction of the half-metal. The quantization direction is up to you, the electron does not decide.

If the electron is up, it will be transmitted with some probability depending on the precise band-structure matching. If it is down, it will be 100% reflected (assuming an ideal half-metal). If it happens to be at an angle, then you will just describe it as a quantum combination of up and down states, and you will get an angle-dependent transmission probability.

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I have the same question several years ago, because the particle-hole space in the BdG equation is just like the spin space for the spin relevant problem. So that the particle-hole components can be considered as a psudo-spin. The current in the NS junction corresponds to the spin current in the NF junction. If we write down the Hamiltonian of a magnet with the spin splitting along the x-axis, then the off-diagonal elements are just like the pair potential in the superconductor. However, the spin-down component of the diagonal elements is different from the hole part in the BdG Hamiltonian, because there is no "particle-hole" symmetry in the magnet Hamiltonian(I think this is not very important, the key point is the pair potential). Now the question is if it is possible to use the formalism from the NS junction to the NF junction?(more specifically, from psudo-spin to real spin?) The answer is yes, given that there is actually no difference between the maths for the psudo-spin and real spin, so the scattering problem is almost the same. The only difference is the statistics of the electron-hole and the spin-up,spin-down electrons, so maybe the current in the NS junction and the spin current in the NF junction have different formulas. Interestingly, when I want to study the problem in about 2011, I find a PRL paper on the similar problem:

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