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4 Tunnelling Magnetoresistance (TMR)
tunnel magnetoresistance has also been discussed. Measurement of spin relaxation
length and time in the spacer layer is also explained in the chapter.
4.7 Exercises
1. What is magnetic tunnel junction (MTJ)?
2. What is tunnelling magnetoresistance (TMR)?
3. What are contact and tunnel-type junction?
4. What do you mean by spin-dependent conductance of charge carriers?
5. Discuss transfer matrix model for both cases when (i) no spin-scattering at
the interface and (ii) spin scattering takes place at the interface.
6. Formulate Jullière model. Hence write the expression for tunnelling magnetoresistance (TMR) ratio, junction magnetoresistance (JMR) ratio and spin
conductance ratio.
7. Explain the conditions required for the formulation of the Jullière model.
8. What is two-current model?
9. Give simple description of tunnelling phenomenon and hence derive the
equation related to tunnelling magnetoresistance.
10. Show how with the following Jullière model, one can estimate the magnitude
of TMR from the known values of the spin polarization of the ferromagnetic
electrodes.
11. What are the main factors that determine the TMR in multilayer films?
12. How does the TMR get affected by the presence of magnetic impurities at the
interface?
13. What is the effect of external magnetic field in TMR of the granular system?
14. What is tunnelling magnetoresistance (TMR)? Derive the equation tunnelling
magnetoresistance (TMR) =
2P L P R
1−P L P R
, where P L and P R are the polarization of
the left and right electrodes, respectively.
15. How the spin relaxation length and time in the spacer layer could be estimated
from spin valve experiments?
16. What are the basic differences between GMR and TMR effect?
17. What are the two basic assumptions, based on which Jullière explained TMR
effect?
18. Derive modified Jullière formula. State its significance.
19. Suppose a magnetic tunnel junction with thicker paramagnetic spacer layer
of thickness 2 nm, spin polarizations of the DOS at the Fermi level of both
the ferromagnetic electrodes are 0.4, tunnelling magnetoresistance obtained at
room temperature is 0.2. What is the spin relaxation length in the paramagnetic
spacer layer?
20. What do you mean by incoherent tunnelling and resonant tunnelling?
4 Tunnelling Magnetoresistance (TMR)
tunnel magnetoresistance has also been discussed. Measurement of spin relaxation
length and time in the spacer layer is also explained in the chapter.
4.7 Exercises
1. What is magnetic tunnel junction (MTJ)?
2. What is tunnelling magnetoresistance (TMR)?
3. What are contact and tunnel-type junction?
4. What do you mean by spin-dependent conductance of charge carriers?
5. Discuss transfer matrix model for both cases when (i) no spin-scattering at
the interface and (ii) spin scattering takes place at the interface.
6. Formulate Jullière model. Hence write the expression for tunnelling magnetoresistance (TMR) ratio, junction magnetoresistance (JMR) ratio and spin
conductance ratio.
7. Explain the conditions required for the formulation of the Jullière model.
8. What is two-current model?
9. Give simple description of tunnelling phenomenon and hence derive the
equation related to tunnelling magnetoresistance.
10. Show how with the following Jullière model, one can estimate the magnitude
of TMR from the known values of the spin polarization of the ferromagnetic
electrodes.
11. What are the main factors that determine the TMR in multilayer films?
12. How does the TMR get affected by the presence of magnetic impurities at the
interface?
13. What is the effect of external magnetic field in TMR of the granular system?
14. What is tunnelling magnetoresistance (TMR)? Derive the equation tunnelling
magnetoresistance (TMR) =
2P L P R
1−P L P R
, where P L and P R are the polarization of
the left and right electrodes, respectively.
15. How the spin relaxation length and time in the spacer layer could be estimated
from spin valve experiments?
16. What are the basic differences between GMR and TMR effect?
17. What are the two basic assumptions, based on which Jullière explained TMR
effect?
18. Derive modified Jullière formula. State its significance.
19. Suppose a magnetic tunnel junction with thicker paramagnetic spacer layer
of thickness 2 nm, spin polarizations of the DOS at the Fermi level of both
the ferromagnetic electrodes are 0.4, tunnelling magnetoresistance obtained at
room temperature is 0.2. What is the spin relaxation length in the paramagnetic
spacer layer?
20. What do you mean by incoherent tunnelling and resonant tunnelling?