1. How do spins interact with
their surroundings?

2. Zeeman effect: Flip spins along magnetic field
(Origin of Stern-Gerlach) B
H = - m.B = -gmBBSz
mB =qħ/2m = 9.27 x J/T ≈ 60 meV/T
‘g’ factor ~ 2 for electrons

3. 1 0 0 -1 Magnetic field splits the energy levels B = 0 B ≠ 0
H = -gmBBSz = -gmBBħ/2
B = 0
B ≠ 0

4. D Ferromagnet: Internal B field can split levels E EF H = - JS1.S2k
H = - JS1.S2
J is the exchange
parameter EF E k
Internal field
B ~ J<S> D

5. 1 0 0 -1 Can we transition between the spins? H = -gmBBSz = -gmBBħ/2
Need (i) an off-diagonal term coupling the states for transitions  E.g., a field along the x-axis
(ii) a resonant AC field to provide the transition energy

6. 1 0 0 -1 0 1 1 0 Electron Spin Resonance (ESR) B B1coswt
H = -gmBBSz = -gmBBħ/2
H1 = -gmBB1(t)Sx = -(gmBB1ħcoswt)/2

7. Electron Spin Resonance (ESR)B
B1coswt
iħ/t = [H + H1(t)] y y
Solve analytically using some approximations
or numerically

8. Electron Spin Resonance (ESR)B
B1coswt
P(t)
So we can transition between spins with a suitable field

9. What about internal fields?
Exchange fields in metallic magnets
Spin-orbit fields in semiconductors

10. Spin-Orbit coupling +
Electron orbiting in electric field of nucleus

11. + What the electron sees B ~ v x E
Nucleus orbiting, creating a net current
and thus  DRUMROLL…. a magnetic field !!

12. + What the electron sees The Zeeman coupling of the electron spin to
this motional field is the Spin-Orbit effect
(within a factor of 2)
H ~ -S.B ~ S.(p x E) ~ S.(p x r)dU/dr
H ~ -S.L(dU/dr)

13. S-O coupling: Various manifestations
Atom: Gives rise to Hund’s Rule
Solid: Split-off states in valence band
Gated transistor: Rashba coupling
H ~ S.(p x r)E
~ r.(S x p)E
~ (sxky-sykx)Ez

14. Spintronic Devices

15. Read: GMR, TMR, spin valves
(Memory, Sensors)

16. Write: MRAMs Rotate with field Write: STTRAMs Rotate with current
Write: STTRAMs
Rotate with current
Also  Rotate with strain (multiferroics)

17. Computing: Datta-Das “FET”
H = aR
(sxky-sykx)Ez
Use Rashba field to
rotate spins in a
modulator with a
gate

18. Computing with 104 spins NkTln(pon/poff) for N charges
~kTln(pon/poff) for N spins !!

19. Using spin for computing
All spin Logic
Memristors
MQCA

20. Summary: Spin is a new
variable. It can be used
for energy-efficient
Computing
Q Transport to calculate
Spin current