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Spin-Transfer Driven Magnetization Dynamics in Spin Valves and Magnetic Tunnel Junctions

Spin-Transfer Driven Magnetization Dynamics in Spin Valves and Magnetic Tunnel Junctions. Huanlong Liu Thesis adviser: Prof. Andrew D. Kent Department of Physics, New York University 4 Washington Place, New York, New York 10003, USA. Introduction. Charge current. Spin current.

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Spin-Transfer Driven Magnetization Dynamics in Spin Valves and Magnetic Tunnel Junctions

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  1. Spin-Transfer Driven Magnetization Dynamics in Spin Valves and Magnetic Tunnel Junctions Huanlong Liu Thesis adviser: Prof. Andrew D. Kent Department of Physics, New York University 4 Washington Place, New York, New York 10003, USA

  2. Introduction Charge current Spin current Spintronics: utilize the spin and its associated magnetic moment of an electron. Physics inside: the interaction between the spin of itinerant electronsand the magnetizationof ferromagnetic materials.

  3. GMR effects • Giant magnetoresistance (GMR): • Discovered (1988) • Albert Fert, the University of Paris-Sud, France, • Peter Grünberg, Forschungszentrum Jülich, Germany • Nobel Prize in Physics (2007) ferromagnet non-magnetic metal ferromagnet Resistance depends on the relative orientation of the two ferromagnetic layers R

  4. Explanation – GMR Magnetization influences the spin of electrons Spin polarized Magnetoresistance ratio: typically a few percent or less

  5. Spin Transfer Torque • J. C. Slonczewski (1996) Spins of the electrons can also influence the magnetization Spin transfer torque (STT) This thesis: Spin-transfer driven magnetization dynamics in magnetic nanopillars Angular momentum conservation spin-polarized current • Dimensions: tens/hundreds of nanometers in x and y, several nm in z (height) • Timescales: tens/hundreds of picoseconds (intrinsic timescale) to DC magnetization change with time

  6. Magnetic Energy • Exchange energy • Dipole energy Coulomb interaction + Pauli exclusion principle 1 2 for ferromagnetic materials 2 1

  7. Magnetic Energy • Zeeman energy • Uniaxial anisotropy energy • Total energy for one spin is the sum of all the four contributions: Spin – orbit coupling

  8. Domains • For a ferromagnetic system with many spins: • Exchange energy uniformly distributed spins • Dipole energy multi-domain structure Exchange energy dominates Simplify

  9. Single Domain – MacrospinModel • is a constant everywhere. • Sum of dipole energy demagnetization energy. • Zeeman energy and uniaxial anisotropy energy take a similar form after summation. is the demagnetization factor depending on the shape of the FM material

  10. Applications in Spintronics – two out of many • Hard disks: • Magnetic Random Access Memory (MRAM): • non-volatile • low power consumption • high density • fast read/write time “A universal memory” in development

  11. Outline – projects and collaborators Spin transfer switching and relaxation in all-perpendicular spin valves 1. Eric Fullerton Jordan Katine StéphaneMangin Jonathan Sun Huanlong Liu Daniel Bedau Andrew D. Kent Switching and precession in magnetic tunnel junction devices 2. Juergen Langer Jordan Katine Huanlong Liu Daniel Bedau Dirk Backes Andrew D. Kent

  12. Spin transfer switching and relaxation in all-perpendicular spin valves D. Bedau, H. Liu, J. Z. Sun, J. A. Katine, E. E. Fullerton, S. Mangin, and A. D. Kent Appl. Phys. Lett.97, 262502 (2010) D. Bedau, H. Liu, J. J. Bouzaglou, A. D. Kent, J. Z. Sun, J. A. Katine, E. E. Fullerton, and S. ManginAppl. Phys. Lett. 96, 022514 (2010) H. Liu, D. Bedau, J. Z. Sun, S. Mangin, E. E. Fullerton, J. A. Katine, and A. D. Kent Phys. Rev. B85, 220405(R) (2012)

  13. Introduction – spin transfer switchingand relaxation in all-perpendicular spin valves damping magnetizationrotation spin transfer torque Spin transfer torque (STT): Project 2: MTJs Project 1: all-perp. spin valves • J. C. Slonczewski (1996) Landau-Lifshitz-Gilbert (LLG) equation + STT: Intrinsic timescales: tens/hundreds of picoseconds

  14. Introduction – spin transfer switching and relaxation in all-perpendicular spin valves • Two ferromagnetic layers separated by a non-magnetic metal layer • Free layer (FL): • Design to be switched • Two preferred directions • Reference layer (RL): • Magnetization remain fixed during FL switching • Generate spin-polarized current to switch the FL • Detect the FL direction through GMR • Non-magnetic metal layer: • Long spin diffusion length (SDL) • Cu: SLD ~ hundreds of nanometers at room temperature Project 2: MTJs Project 1: all-perp. spin valves

  15. Introduction – spin transfer switching and relaxation in all-perpendicularspin valves Project 2: MTJs Project 1: all-perp. spin valves • Magnetization in thin films tends to stay in-plane due to demagnetization energy. • Perpendicular anisotropy found in multilayer structures such as: Co/Pt, Co/Pd and Co/Ni. • Magnetocrystalline anisotropy energy > demagnetization energy • First spin-transfer experiments in all-perpendicular device: Mangin et. al., Nat. Mater. 5, 210 (2006) • Only quasi-static measurements. Need faster experiments to probe the magnetization dynamics.

  16. In-plane versus perpendicular Project 2: MTJs Project 1: all-perp. spin valves • Sun, Phys. Rev. B (2000) • Mangin et al., Nat. Mater. (2006) • Mangin et al., Appl. Phys. Lett. (2009) • Bedau et al., Appl. Phys. Lett. (2010) • Bedau et al., Appl. Phys. Lett. (2010) needs to overcome the demag field, which doesn’t contribute to the stability. switching current is proportional to the stability.

  17. All-perpendicular spin valves • High energy barrier • Low critical current • High density • High symmetry Project 2: MTJs Project 1: all-perp. spin valves

  18. Sample structure • [Co/Ni] free layer (FL), 1.6 nm thick • [Co/Ni]|[Co/Pt] reference layer (RL) • high coercive field (> 0.5 T) • Measured > 20 samples • Present results on: • 100 nm x 100 nm • 50 nm x 50 nm samples Project 2: MTJs Project 1: all-perp. spin valves

  19. Modeling Is there an analytic prediction for experiments?

  20. A macrospin model minus damping Project 2: MTJs Project 1: all-perp. spin valves Current Pulse: In general, both STTand thermal fluctuations influence the switching process. • θ0: Initial magnetization angle when current pulse is applied, a distributed quantity whose probability is determined by the Boltzmann distribution. • θτ: Final magnetization angle when current pulse stops, determines whether or not a switching event would result.

  21. STT Thermal fluctuations Initial state Final state Large current – short time limit: STT > Thermal fluctuations Small current – long time limit: STT < Thermal fluctuations Project 2: MTJs Project 1: all-perp. spin valves Pulse simplify simplify • Thermally distributed initial states and deterministic switching process (only STT). • Thermal activation over an energy barrier which is modified by STT. deterministic

  22. Analytic solutions • Short time: • Linear boundary: • Long time: • Exponential boundary: Project 2: MTJs Project 1: all-perp. spin valves STT Current Pulse: damping Switching Probability:

  23. Experiments on Switching How does the switching probability P depend on the pulse amplitude I and duration τ?

  24. Measurement circuit Bias-tee: τ< 10 ns Switch: τ > 5 ns Project 2: MTJs Project 1: all-perp. spin valves μ0Happ top bottom top e- bottom sample

  25. Experimental setup Project 2: MTJs Project 1: all-perp. spin valves

  26. Switching at DC Project 2: MTJs Project 1: all-perp. spin valves Room temperature coercive field: 100 mT Hysteresis loop shift: 25 mT Switching currents: -7 mA, 4 mA P AP

  27. Switching at DC Project 2: MTJs Project 1: all-perp. spin valves Room temperature coercive field: 90 mT Hysteresis loop shift: -40 mT Switching currents: 0.4 mA, -1 mA P AP

  28. Switching at DC Project 2: MTJs Project 1: all-perp. spin valves • Ratio of size: 4 • Ratio of resistance: ~ 1 / 3 • Ratio of MR ~ 1 • Ratio of coercive field: ~ 1 • Ratio of critical current: ~ 8

  29. Pulse measurements μ0Happ = 0.2 T 3 1 2 4 μ0Happ = 0 T Project 2: MTJs Project 1: all-perp. spin valves Apply measurement field and current Saturate Check if switched Apply pulse If switched go here If NOT switched go here Apply the same pulse 100 – 10,000 times

  30. Pulse measurements Switching diagram Project 2: MTJs Project 1: all-perp. spin valves Duration scan Amplitude scan

  31. 50% switching boundary A: dynamic parameter, the slope. – Efficiency Ic: zero temperature critical current, the intercept at x-axis. – Threshold Project 2: MTJs Project 1: all-perp. spin valves Intrinsic damping Icτ Net charge (I – Ic)τ

  32. 50% switching boundary Project 2: MTJs Project 1: all-perp. spin valves

  33. 50% switching boundary Project 2: MTJs Project 1: all-perp. spin valves

  34. Field dependence of A andIc Initial state Final state Project 2: MTJs Project 1: all-perp. spin valves Pulse • Possible reasons causing the discrepancy: • Switching process is not uniform • Thermal fluctuations influence the switching process as well

  35. 50% switching boundary Short time regime Project 2: MTJs Project 1: all-perp. spin valves Long time regime Cross over regime • Measure with pulse durations over 10 order of magnitude in time. • Model yields correct forms at both short and long time limits. • Three regimes can be distinguished.

  36. Probability ~ pulse duration Project 2: MTJs Project 1: all-perp. spin valves short time regime: long time regime:

  37. Probability ~ pulse amplitude Project 2: MTJs Project 1: all-perp. spin valves short time regime: long time regime:

  38. Probability ~ angular momentum • Probability only depends on the net charge in short time regime • Angular momentum conservation • Refine short time regime net charge: Project 2: MTJs Project 1: all-perp. spin valves

  39. Double Pulse Experiments How to resolve the magnetization relaxation? • Liu et. al., Phys. Rev. B 85, 220405(R) (2012)

  40. Motivation • Always exists after each switching attempt. • Important information for application. • Not fully explored by experiments. Project 2: MTJs Project 1: all-perp. spin valves Difficulty: no electrical signal during relaxation

  41. Basic idea Use the second pulse to probe the magnetization dynamics excited by the first pulse tdelay I1 I2 I1 I2 t1 t2 • Apply double pulses • Measure switching probability (SP) • Compare with single pulses SP t1 t2 Project 2: MTJs Project 1: all-perp. spin valves

  42. Double pulses SP (switching probability) tdelay tdelay I1 I1 I2 t1 • If tdelayis long enough: • Otherwise, tdelay is within the relaxation time of the first pulse. t1 t2 t2 Project 2: MTJs Project 1: all-perp. spin valves I2

  43. Experiment – Relaxation to the initial state long delay: short delay: Project 2: MTJs Project 1: all-perp. spin valves AP AP 1 2 t1 = 1 ns I1 = 8.5 mA First pulse Second pulse AP AP or P t2 = 0~5 ns I2 = 8.5 mA

  44. “Similar” distributions tdelay tdelay I I I I I t2 t1 t1 Project 2: MTJs Project 1: all-perp. spin valves True for all t2 δt δt + t2

  45. δt ~tdelay tdelay I I • Thermal effects need to be considered! t1 Project 2: MTJs Project 1: all-perp. spin valves LLG: Time scale of the relaxation dynamics δt

  46. Fokker – Planck calculation • For uniaxial symmetry: Project 2: MTJs Project 1: all-perp. spin valves • Stationary state: • Effective “energy” barrier for I < Ic0: • For dynamics: no analytical solutions. Solved numerically by two methods: • finite difference method – easier method • eigenvalue method – first non-trivial eigenvalue gives the switching rate for high probability tails : probability to find the magnetization at angle θ at time τ

  47. High probability tail Eigenvalue method: Project 2: MTJs Project 1: all-perp. spin valves First non-trivial eigenvalue: determine the slope 6σ 3σ

  48. Tracking the probabilities 1 ns I1 I2 >5 ns 0.9 ns Double pulse: End of the 1st pulse End of the delay Project 2: MTJs Project 1: all-perp. spin valves

  49. Simulation results Project 2: MTJs Project 1: all-perp. spin valves

  50. Summary: all-perp. spin valves Switching Relaxation Project 2: MTJs Project 1: all-perp. spin valves • Experiments with pulse durations from 50 ps to 1 s s. • Short time regime: switching probability mainly depends on the net charge, a result of angular momentum conservation. • Long time regime: thermal activation over an energy barrier. • Analytic results agrees with experiments at both limits. • Resolve relaxation down to 50 ps with MR ~ 0.3%. • A single pulse + delay gives a state with the same average ensemble as a single pulse with a modified duration δt. • δt exponentially decays with the delay and the lifetime of the decay is 0.28 ns. • Thermal noise needs to be considered for relaxation.

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