Stochastic Behavior of Magnetic Processes on a Nanoscale

1. Stochastic Behavior of Magnetic Processeson a Nanoscale Mi-Young ImCenter for X-ray Optics, LBNL Berkeley, CA, USA mim@lbl.gov

2. Challenge in Nano-magnetism Nano-Magnetism Ultra-fast Ultra-small 1 ms 1 ns 1 ps 1 fs 1 cm 1 mm 1 µm 1 nm Ultrathin Films Nanowire Nanoparticles Thermal activation Damping Precession Thermalization Novel Manuplating Technique Controllability Vortex switching B-field Spin current Thermal Domain wall motion

3. Contents • Background • Statistical Behavior of Magnetic Processes • --- Domain Nucleation Process in Ultra Thin Magnetic Film (2D) • --- Domain Wall Depinning Process in Notch Patterned Nanowires (1D) --- Vortex- State (chirality) Creation Process in Circular Nanodot Arrays (0D) • Summary

4. Statistical Behavior Whether the magnetic process is deterministic or stochastic Scientific Point of View : century old long-standing question - Is there any unifying physical mechanism?- Is there any specific law, which governs the complicate magnetic phenomena?- Which is dominant factor for determination of statistical nature? Technological Point of View: substantial issue for application - Is the spin reversal phenomena repeatable?- Is the domain wall motion controllable? - What is the way to acheive the tunable and repeatable spin reversal and dynamics?

5. Review J. M. Deutsche et al., Phys. Rev. Lett.(2004) • Macroscopic or k-space • Contradictory Reproducible Hysteresis loop Irreversible Reversal M. S. Pierce et al., Phys. Rev. Lett. (2003) • Direct observation in real space • Statistical measurement Simulation for DW Process DWM at Single Time A. J .Zambano et al., Appl. Phys.Lett. (2004) E. Martinez et al., Phys. Rev. Lett. (2007) • Theoretical approach • Single measurement Switching Field Distribution Reversal Process in Nanodot Justin M. Shaw et al., J. Appl. Phys. (2007) V. Novosad, et al., Phys. Rev. B, (2002)

6. Our Goal G. Meier et al. PRL (2007) Nanowires Ultrathin Films Nanodot Ultra Thin Film (2D) Nanowire (1D) Nanodot (0D) solution for unsolved-question possibility for controllable spin process S. Parkin US Patent 309, 6,834,005 (2004). S. Parkin US Patent 309, 6,834,005 (2004). Observation Understanding Controlling

7. Magnetic soft X-ray microscopy at XM-1 XMCD contrast polarization element specificity E = 250 eV - 1.8 keV l= 0.7 nm - 5 nm E/E=500  t<70 ps Hmax= 5 kOe (perp.) = 2 kOe (long.) lateral resolution 3rd generation synchrotron source r< 25 nm CCD 2048x2048 px2 Mag ~ 2000 FOV ~ 10-15 mm time resolution

8. Domain Nucleation Process in Ultra Thin Magnetic Film

9. Magnetic Domain Evolution Patterns +400 Oe +600 Oe +200 Oe 2m -H -H -H 0 Oe +H -200 Oe Sample: 50–nm (Co 82Cr18)87 Pt13 / 40-nm Ti / 200-nm Si3N4 • Nucelation-mediatedmagnetization reversal behavior that originated from individual switching of grain M.-Y. Im et al., APL 83, 4589 (2003)

10. Stochastic Nature 1st cycle 2nd cycle 1st cycle (left branch) 2nd cycle (right branch) Both cycles (branches) Magnetic domain configurations in repeated hysteretic cycles and different branches • Stochastic and asymmetric nature ofmagnetic domain nucleation process

11. Degree of Stochastic Nature Average correlation coefficient among domain configurations X and Y : same size matrices 1 : existence 0 : nonexistence of domain nucleation in each pixel r=0 : totally differentr=1: completely identical M.-Y. Im et al., Adv. Mater 20, 1750 (2008) • Correlation coefficient in both casesincreases as magnetization reversal is progressed

12. Thermal Fluctuation Effect Micromagnetic simulation of magnetization reversal patterns in repeated hysteretic cycles at 300 K LLG equation incl. thermal term • gyromagnetic ratio • dimensionless damping coefficient parameter hfluc fluctuating magnetic field • Thermal flucutation effect play a role onstochastic nature in domain nucleation process

13. Domain Wall Depinning Process in Notch Patterned Nanowires

14. Notch Patterned Permalloy Nanowire -H -H -H +H Permalloy (Ni80Fe20) SEM images MTXM image Wire width (w): 150, 250, 450 nm Notch depth (Nd): 30, 50 % Film thickness (t): 50, 70 nm

15. Domain Wall Evolution Patterns w= 150 nm w= 450 nm w= 250 nm -47 Oe -141 Oe -24 Oe -383 Oe -189 Oe -106 Oe -413 Oe -236 Oe -430 Oe -124 Oe -259 Oe -489 Oe -371 Oe -129 Oe -319 Oe • Domain walls are stopped at precise position

16. Stochastic Nature Depinning field of domain wall in repeated hysteretic cycles -100 Oe H -530 Oe • DW depinning process is not completely governed byDW pinning mechanism • DW depinning process shows stochastic behavior in repeated measurements

17. Multiplicity of Domain-wall Types courtesy S. Parkin Transverse wall -440 Oe -450 Oe Vortex wall -485 Oe -490 Oe • Themultiplicity of domain-wall typegenerated in the vicinity of a notch is responsible for the observed stochastic nature

18. Degree of Stochastic Nature Standard deviationof DW depinning field M.-Y. Im et al, Phys. Rev. Lett. 102, 147204 (2009) • The DW depinning process can be controllable in properly designed nanowire • Standard deviation of the depinning field is minimized tobelow 7 Oe

19. Vortex State (chirality) Creation Process in Nanodot Arrays

20. Permalloy Nanodot Arrays Normalized Images In-plane Out-of-plane Vortex State 1000 nm 800 nm • Chiralityin-plane circular domain structure • Polarityout-of-plane component of magnetization 600 nm 400 nm 200 nm MTXM Image Ni80Fe20 :t=100 nm, r=800 nm 800 nm Dot Size (r): 200, 400, 600, 800, 1000 nmFilm Thickness (t): 40, 70, 100 nm

21. Statistical Behavior of Vortex State (chirality) Creation Process Overlapped images Switched Dots Overlapped images Switched Dots In-plane domain state in repeated measurements and changing the field direction Ni80Fe20 (t=40 nm, r=1000 nm, d=200 nm) 1st 2nd +x H +x saturation -x saturation • Stochastic nature of creation process of chirality in repeated (different saturation field direction) measurements M.-Y. Im, Peter Fischer, et al., in preparation

22. Summary Statistical Behavior of Magnetic Processes on a Nanoscale • Direct observation of stochastic behavior - Domain nucleation process in ultra thin ferromagnetic system - Domain wall depinning process in nanowire system - Vortex state creation process in nanodot system • Investigation of the origin (thermal fluctuation, multiplicity, aspect ratio, etc.) of stochastic behavior • Answering for long-standing fundamental question on nanomagnetism • Providing of controllable magnetic process

23. Thanks to… Thank you for attention! • Peter Fischer, B. Mesler, A.E. Sakdinawat, W. Chao, R. Oort, B. Gunion, S.B. Rekawa, P. Denham, E.H. Anderson, D.T. Attwood (CXRO Berkeley USA) • S.-C. Shin (KAIST, Taejeon), S.-K. Kim (SNU, Seoul), S.B. Choe (SNU, Seoul), D.-H. Kim (Chungbuk U) • L. Bocklage, Judith Moser, A. Vogel, R. Eiselt, M. Bolte, G. Meier, B. Krüger (U Hamburg, Germany) • S. Kasai (NIMS in Jap.), K. Yamada, K. Kobayashi, T. Ono (U Kyoto), A. Thiaville (U Paris-Sud) • ALS and CXRO staff