112
4 Tunnelling Magnetoresistance (TMR)
repeating the same procedure. Finally, we may calculate the magnetoresistance ratio
by using G P and G AP .
4.3.4 The Jullière Formula
The TMR effect was first explained by Jullière in his famous 1975 paper (Julliere
1975). In fact, a systematic study of spin-valve magnetoresistance was carried out by
Jullière in his innovative effort made in the early years. In the context of TMR, we
may discuss one of his pioneering work where Jullière proposed a formula for the
junction magnetoresistance (JMR) ratio. Such derivation of JMR ratio takes place
from the transfer matrix model as discussed above. The intriguing point is that Jullière
formula establishes a relation between JMR and spin polarizations of charge carriers
at the Fermi level of the ferromagnetic electrodes. The paramount importance of this
formula lies on the fact that this is widely employed to analyse data obtained from
spin valve experiments. Moreover, such formula can also efficiently take account
of spin relaxation in the intermediate paramagnetic spacer layer. Considering its
historical significance, we present here the derivation of Jullière formula.
Before going into the details of Jullière formula, let us mention different kinds
of spin valve effect investigated for a wide variety of ferromagnetic electrodes
with various types of intermediate paramagnetic layers. Corresponding magnetoresistances have been defined in terms conductances of the device in parallel and
antiparallel configuration of magnetizations of its ferromagnetic electrodes. Three
commonly used magnetoresistance ratios are as follows:
(a) Tunnelling magnetoresistance (TMR) ratio,
TMR =
G P − G AP
G AP
(b) Junction magnetoresistance (JMR) ratio,
JMR =
G P − G AP
G P
(c) The spin conductance ratio,
Spin Conductance Ratio =
G P − G AP
G P + G AP
These three magnetoresistance ratios are related to each other.
4 Tunnelling Magnetoresistance (TMR)
repeating the same procedure. Finally, we may calculate the magnetoresistance ratio
by using G P and G AP .
4.3.4 The Jullière Formula
The TMR effect was first explained by Jullière in his famous 1975 paper (Julliere
1975). In fact, a systematic study of spin-valve magnetoresistance was carried out by
Jullière in his innovative effort made in the early years. In the context of TMR, we
may discuss one of his pioneering work where Jullière proposed a formula for the
junction magnetoresistance (JMR) ratio. Such derivation of JMR ratio takes place
from the transfer matrix model as discussed above. The intriguing point is that Jullière
formula establishes a relation between JMR and spin polarizations of charge carriers
at the Fermi level of the ferromagnetic electrodes. The paramount importance of this
formula lies on the fact that this is widely employed to analyse data obtained from
spin valve experiments. Moreover, such formula can also efficiently take account
of spin relaxation in the intermediate paramagnetic spacer layer. Considering its
historical significance, we present here the derivation of Jullière formula.
Before going into the details of Jullière formula, let us mention different kinds
of spin valve effect investigated for a wide variety of ferromagnetic electrodes
with various types of intermediate paramagnetic layers. Corresponding magnetoresistances have been defined in terms conductances of the device in parallel and
antiparallel configuration of magnetizations of its ferromagnetic electrodes. Three
commonly used magnetoresistance ratios are as follows:
(a) Tunnelling magnetoresistance (TMR) ratio,
TMR =
G P − G AP
G AP
(b) Junction magnetoresistance (JMR) ratio,
JMR =
G P − G AP
G P
(c) The spin conductance ratio,
Spin Conductance Ratio =
G P − G AP
G P + G AP
These three magnetoresistance ratios are related to each other.