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How do spins interact with their surroundings?

How do spins interact with their surroundings?. Zeeman effect: Flip spins along magnetic field (Origin of Stern-Gerlach). B. H = - m .B = -g m B BS z. m B =qħ/2m = 9.27 x 10 -24 J/T ≈ 60 m eV/T. ‘g’ factor ~ 2 for electrons. Magnetic field splits the energy levels.

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How do spins interact with their surroundings?

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  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 10-24 J/T ≈ 60 meV/T ‘g’ factor ~ 2 for electrons

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

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

  5. Can we transition between the spins? H = -gmBBSz = -gmBBħ/2 1 0 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 0 -1

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

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

  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 http://thefutureofthings.com/upload/image/articles/2006/mram/mram-write.jpg Write: STTRAMs Rotate with current Also  Rotate with strain (multiferroics)

  17. Computing: Datta-Das “FET” Use Rashba field to rotate spins in a modulator with a gate (sxky-sykx)Ez H = aR http://www.material.tohoku.ac.jp/~kotaib/jpg/spinFET.jpg

  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

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