Tunnel Magneto Resistance

In 1975, JULLIERE [73] was the first one who measured TMR in MTJs. He already gave a simple explanation for the TMR effect and defined $a$ and $a'$ as the fractions of tunneling electrons in the two ferromagnetic materials that are parallel to the magnetisation. With the spin polarisations of the two ferromagnets defined as $P = 2a-1$ and $P' = 2a'-1$, the relative conductance variation is defined as:

$${\rm TMR} = \frac{2PP'}{1-PP'}$$ (1.15)

JULLIERES explanation is just a very simple model for the TMR and does not include temperature or voltage dependencies. For two different ferromagnetic electrodes in a MTJ, the model also gives a wrong positive sign for the polarisation of the 3d-ferromagnets. There are more open questions, e.g. the connection between the spin-polarisation of the different electron bands to the measured TMR ratio, and until today, there is no comprehensive theory about it. The interested reader is encouraged to read the article from STEARNS [120] and the PhD thesis of LECLAIR [84], where some more elaborate approaches are summarised.