Stochastic behavior of magnetic processes on a nanoscale
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Stochastic Behavior of Magnetic Processes on a Nanoscale. Mi-Young Im Center for X-ray Optics, LBNL Berkeley, CA, USA Challenge in Nano-magnetism. Nano-Magnetism. Ultra-fast. Ultra-small. 1 ms 1 ns 1 ps 1 fs.

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Stochastic Behavior of Magnetic Processes on a Nanoscale

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Stochastic behavior of magnetic processes on a nanoscale

Stochastic Behavior of Magnetic Processeson a Nanoscale

Mi-Young ImCenter for X-ray Optics, LBNL Berkeley, CA, USA

Challenge in nano magnetism

Challenge in Nano-magnetism




1 ms 1 ns 1 ps 1 fs

1 cm 1 mm 1 µm 1 nm

Ultrathin Films



Thermal activation




Novel Manuplating Technique


Vortex switching


Spin current


Domain wall motion



  • 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

Statistical behavior

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?



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)

Our goal

Our Goal

G. Meier et al. PRL (2007)


Ultrathin Films


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).




Magnetic soft x ray microscopy at xm 1

Magnetic soft X-ray microscopy at XM-1

XMCD contrast


element specificity

E = 250 eV - 1.8 keV

l= 0.7 nm - 5 nm


 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

Stochastic behavior of magnetic processes on a nanoscale

Domain Nucleation Process in Ultra Thin Magnetic Film

Magnetic domain evolution patterns

Magnetic Domain Evolution Patterns

+400 Oe

+600 Oe

+200 Oe





0 Oe


-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)

Stochastic nature

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

Degree of stochastic nature

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

Thermal fluctuation effect

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

    hflucfluctuating magnetic field

  • Thermal flucutation effect play a role onstochastic nature in domain nucleation process

Stochastic behavior of magnetic processes on a nanoscale

Domain Wall Depinning Process in Notch Patterned Nanowires

Notch patterned permalloy nanowire

Notch Patterned Permalloy Nanowire





Permalloy (Ni80Fe20)

SEM images

MTXM image

Wire width (w): 150, 250, 450 nm Notch depth (Nd): 30, 50 % Film thickness (t): 50, 70 nm

Domain wall evolution patterns

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

Stochastic nature1

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

Multiplicity of domain wall types

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

Degree of stochastic nature1

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

Stochastic behavior of magnetic processes on a nanoscale

Vortex State (chirality) Creation Process in Nanodot Arrays

Permalloy nanodot arrays

Permalloy Nanodot Arrays

Normalized Images



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

Statistical behavior of vortex state chirality creation process

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)





+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



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

Stochastic behavior of magnetic processes on a nanoscale

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

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