118
4 Tunnelling Magnetoresistance (TMR)
of ferromagnetic electrodes. In this context, we must mention that spin polarizations
of ferromagnetic electrodes can be obtained from the experiments on superconductors. Jullière formula is the most suitable for comparing TMR values for MTJs,
consisting of different ferromagnetic electrodes but the same spacer layers because
TMR in this case is evaluated in terms of the spin polarization. To summarize,
in the light of Jullière’s model, (a) spin orientations remain conserved, i.e., spin
reorientation/flipping does not take place during electron tunnelling. As a result,
tunnelling phenomenon of ↑and ↓ spin electrons can be supposed to take place independently with respect to each other; (b) process of tunnelling is spin independent.
Hence, conductance process corresponding to a particular spin species (↑/↓) is only
decided by the appropriate density of states of the two ferromagnetic electrodes. In
order to obtain a more credible theoretical formulation, two additional effects should
be included: (1) At the Fermi level, DOS is not necessarily proportional to the total
polarization; (2) At the vicinity of the barrier, the wavefunctions of the majority
and minority electrons need not be the same. In that case, transmission coefficient is
supposed to acquire a spin dependence which in turn influences MR.
4.4 Effect of Various Parameters on Tunnel
Magnetoresistance
Here we will discuss, (i) the changes in the basic elastic processes induced by the
interface, (ii) inelastic tunnelling phenomenon produced by magnetic excitations both
at the ferromagnetic electrodes or at the interfaces, (iii) the changes in the magnetic
structure of the surface, and (iv) charging effects.
4.4.1 Effect of Paramagnetic Impurities at the Interface
on Magnetoresistance
According to our earlier discussion, magnetization of the ferromagnetic electrodes
is aligned when the external magnetic field is applied. However, because of the existence of isolated paramagnetic impurities at the interface, a much higher external
magnetic field is required to attain such parallel alignment of magnetization of
the ferromagnetic electrodes. Presence of such misaligned impurities can lead to
diversified transport processes.
Let us suppose resonant tunnelling through a single paramagnetic impurity found
at the barrier between two ferromagnetic electrodes, as shown in the illustration
(Fig. 4.8). In this case, electrons are supposed to transit elastically from one ferromagnetic electrode to the impurity at the interface and then to the second ferromagnetic electrode. Obviously, such transit of electrons would take place without losing
any coherence.
4 Tunnelling Magnetoresistance (TMR)
of ferromagnetic electrodes. In this context, we must mention that spin polarizations
of ferromagnetic electrodes can be obtained from the experiments on superconductors. Jullière formula is the most suitable for comparing TMR values for MTJs,
consisting of different ferromagnetic electrodes but the same spacer layers because
TMR in this case is evaluated in terms of the spin polarization. To summarize,
in the light of Jullière’s model, (a) spin orientations remain conserved, i.e., spin
reorientation/flipping does not take place during electron tunnelling. As a result,
tunnelling phenomenon of ↑and ↓ spin electrons can be supposed to take place independently with respect to each other; (b) process of tunnelling is spin independent.
Hence, conductance process corresponding to a particular spin species (↑/↓) is only
decided by the appropriate density of states of the two ferromagnetic electrodes. In
order to obtain a more credible theoretical formulation, two additional effects should
be included: (1) At the Fermi level, DOS is not necessarily proportional to the total
polarization; (2) At the vicinity of the barrier, the wavefunctions of the majority
and minority electrons need not be the same. In that case, transmission coefficient is
supposed to acquire a spin dependence which in turn influences MR.
4.4 Effect of Various Parameters on Tunnel
Magnetoresistance
Here we will discuss, (i) the changes in the basic elastic processes induced by the
interface, (ii) inelastic tunnelling phenomenon produced by magnetic excitations both
at the ferromagnetic electrodes or at the interfaces, (iii) the changes in the magnetic
structure of the surface, and (iv) charging effects.
4.4.1 Effect of Paramagnetic Impurities at the Interface
on Magnetoresistance
According to our earlier discussion, magnetization of the ferromagnetic electrodes
is aligned when the external magnetic field is applied. However, because of the existence of isolated paramagnetic impurities at the interface, a much higher external
magnetic field is required to attain such parallel alignment of magnetization of
the ferromagnetic electrodes. Presence of such misaligned impurities can lead to
diversified transport processes.
Let us suppose resonant tunnelling through a single paramagnetic impurity found
at the barrier between two ferromagnetic electrodes, as shown in the illustration
(Fig. 4.8). In this case, electrons are supposed to transit elastically from one ferromagnetic electrode to the impurity at the interface and then to the second ferromagnetic electrode. Obviously, such transit of electrons would take place without losing
any coherence.