Please guide how can we define overall band gap in the figure attached (regardless of spin up and spin down band gaps)?
Secondly, what will be the transition of electrons from valence to conduction band in the case of ferromagnetic semiconductor because both spin channels have different band gaps? So electron transition from which band to which band with respect to its spin (either up spin or down spin transition between two bands)?
Hi there!
Dipole selection rules forbid a transition where mS is not 0, so transitions from the majority to the minority band and vice versa are very unlikely, although I would say that they might be possible if it is a many body process. For example if you have a simultaneous excitation of two electrons, one from spin-up to spin-down and the other from spin-down to spin-up. Such a process would of course be extremely unlikely.
Thus I would answer your question as follows: In ferromagnetic semiconductors you have the possibility of two different gaps, one each for the two spin channels. In practice the smaller one of the two will be the more important one (in your example the minority state), as this lower energy will be sufficient to excite carriers into the conduction band. The lower number of total charge carriers should not play a role since you excite very few electrons (and holes) anyhow. Once you provide enough energy to bridge the larger of the two gaps you should, in my opinion, see a jump in conduction however.
Also there is the possibility to only excite one spin channel in experiments I think (spin-resoved ARPES), but I do not really know anything about that.
To conclude: The total gap should be the smallest one, but gaps from both spin channels should be reported. Excitations from one spin channel to another are forbidden.
My question is in general terms, not for some specific material, just wanna to understand the correct calculation of band gap in ferromagnetic semiconductors and the Physics behind such band gaps. I have attached a figure as a reference.
Hi there!
Dipole selection rules forbid a transition where mS is not 0, so transitions from the majority to the minority band and vice versa are very unlikely, although I would say that they might be possible if it is a many body process. For example if you have a simultaneous excitation of two electrons, one from spin-up to spin-down and the other from spin-down to spin-up. Such a process would of course be extremely unlikely.
Thus I would answer your question as follows: In ferromagnetic semiconductors you have the possibility of two different gaps, one each for the two spin channels. In practice the smaller one of the two will be the more important one (in your example the minority state), as this lower energy will be sufficient to excite carriers into the conduction band. The lower number of total charge carriers should not play a role since you excite very few electrons (and holes) anyhow. Once you provide enough energy to bridge the larger of the two gaps you should, in my opinion, see a jump in conduction however.
Also there is the possibility to only excite one spin channel in experiments I think (spin-resoved ARPES), but I do not really know anything about that.
To conclude: The total gap should be the smallest one, but gaps from both spin channels should be reported. Excitations from one spin channel to another are forbidden.
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