# Spin FET Transistor

Spin FET Transistor. When a gate voltage is applied to a current of spin polarized electrons, a spin precession will occur. If this spin precession is enough to make the bulk electron spin polarization anti-parallel to a ferromagnet, why is it that the electrons will not flow through the ferromagnet? Basically my question is: Why won't electrons spin polarized in a direction anti-parallel to a ferromagnet's spin polarization flow through this material?

Assuming everything is ideal...

## 1 Answer

Generally in a ferromagnet each atom has $Z-1$ paired electrons, with zero net spin, and one unpaired electron. The unpaired electron spins on neighboring atoms like to be parallel, which is why the material has a bulk magnetization.

If you try to inject another electron into the ferromagnetic material, that other electron has to go somewhere — into an orbital around some atom. If it wants to go into the lowest-energy orbital, its spin has to be antiparallel to the spin of the unpaired electron that's already there. If the spins of the injected are fixed to be parallel to the unpaired electron spins in the material, then all of the lowest-energy orbitals appear "full," and the injection requires more energy. Effectively the ferromagnet has a different work function for different electron spins.

Complicating any handwavy discussion of this is the fact that the electron magnetic moment is negative.

I'm not a solid-state guy, so I invite others to correct me …

The review paper you linked in the comments calls the source and drain materials "half-metallic ferromagnets." I think this means that the electrons in the conduction band all have one polarization, and electrons with the other polarization have Fermi energies in the band gap. In that case all of the conduction would have to take place via electrons with the correct polarization.

I don't know whether all ferromagnets are "half-metallic" like this, or whether those materials must be engineered. If they're engineered, I don't know whether it's possible to tune which spin state conducts. Very interesting!

Here is a page about half-metallic ferrormagnets with figures and references. In particular the first figure shows the differing densities of states for majority- and minority-spin electrons in one material:

I think that producing these sorts of diagrams for a real material involves lots of solid-state black magic, but the fact that a gap appears at the Fermi energy for minority-spin electrons does mean that all the conduction electrons will be polarized.

• From what I have seen in some papers, it seems like the current will not flow when the electrons are anti-parallel to the ferromagnet's polarization. From your description it seems to be the opposite. Am I thinking about this correctly? May 4, 2014 at 4:55
• I think that may be where it matters that the electron's magnetic moment is negative. Link to a useful paper?
– rob
May 4, 2014 at 5:06
• arxiv.org/abs/0909.3823 Pages 12-14 essentially. There they are describing it as transmission amplitude. May 4, 2014 at 5:06
• Hmmm. Figure 1 (p113) shows the source and drain polarized the same way, and transmission proportional to $\cos \phi/2$, for precession angle $\phi$. So you're correct that the drain wants to accept correctly-polarized electrons.
– rob
May 4, 2014 at 5:33
• The paper says that source and drain materials are "half-metallic." Does that mean that electrons with one polarization have Fermi energies in the conduction band, but electrons with the other polarization have Fermi energies in the band gap?
– rob
May 4, 2014 at 5:39