Magnetic Force Microscopy

Transcription

1 Magnetic Force Microscopy Olivier Fruchart Institut Néel (CNRS-UJF-INPG) Grenoble - France /

2 WHY DO WE NEED MAGNETIC MICROSCOPY? Origins of magnetic energy Echange energy Magnetocrystalline anisotropy energy EEch = J1, 2 S1.S 2 = A( θ ) 2 M 2 E = K sin (θ ) mc Hext Zeeman energy (enthalpy) Dipolar energy 2 1 EZ = µ 0 M S.H 1 Ed = µ 0 M S.H d 2 Olivier Fruchart Solemio School Synchrotron Soleil p.2

3 WHY DO WE NEED MAGNETIC MICROSCOPY? Magnetic characteristic length scales Typical length scale: Bloch wall width B Numerical values λb = π A / K λ B = 2 3 nm Hard λ B 100 nm Soft e = A( dθ / dx ) + K sin 2 θ 2 Exchange J/m Anisotropy J/m 3 Olivier Fruchart Solemio School Synchrotron Soleil p.3

4 WHY DO WE NEED MAGNETIC MICROSCOPY? Magnetic domains Bulk material Mesoscopic scale Nanometric scale Numerous and complex magnetic domains Small number of domains, simple shape Magnetic single-domain Co(1000) crystal SEMPA A. Hubert, Magnetic domains Microfabricated dots Kerr magnetic imaging A. Hubert, Magnetic domains Nanomagnetism ~ mesoscopic magnetism R.P. Cowburn, J.Phys.D:Appl.Phys.33, R1 (2000) Olivier Fruchart Solemio School Synchrotron Soleil p.4

5 Why do we need microcopy? What information may be sought Conditions and environment Distribution of magnetization in Temperature Magnetic field Electrical current, light etc. Additional microscopies sample Direction & magnitude Depth resolution Elemental resolution Lateral resolution Time resolution Olivier Fruchart Solemio School Synchrotron Soleil p.5

6 Atomic Force Microscopy Working principle Key elements of an Atomic Force Microscope (AFM) Measures forces (vertical and lateral) between sample and tip Olivier Fruchart Solemio School Synchrotron Soleil p.6

7 Atomic Force Microscopy Cantilevers and tips Chip Batch fabrication Cantilever Millimeters Full tip + apex 100μm Price /tip Radius of curvature 5nm Images : Olympus catalog ( Olivier Fruchart Solemio School Synchrotron Soleil p.7

8 AFM Many uses Measures Modes of operation Topography Mechanical properties Electric properties Piezoelectric properties Long-range forces (electrostatic, magnetic) Static (deflection) When contact is needed : electric, friction etc. Dynamic (cantilever oscillation) Less damage to sample and tip More sensitive Micromanipulation & fabrication Olivier Fruchart Solemio School Synchrotron Soleil p.8

9 Mechanical oscillator Equations Mechanical excitation of cantilevers m z + Γ z + k z=f (z,t ) m Inertia Γ Damping k Spring F (z,t) External force Notations Seek solutions for F =0 z (t )=z 0 e j ωt Reference angular velocity ω0 = Quality factor Q= k m k m Γ Transfert function H= z 1 = F k 1 2 ( ) ( ) ω j ω + +1 ω0 Q ω0 Olivier Fruchart Solemio School Synchrotron Soleil p.9

10 Mechanical oscillator Solutions Gain 7 G= H = Q=10 / k 5 kg [ ( )] ( ) ω 1 ω0 2 Peak at : 1 Q=1/ ω r =ω0 3 1 ω + 2 Q ω0 kg (0)= Q kg (ω r )=Q ω /ω0 kg ( )=0 Dephasing Q>> cos φ = -1.0 φ Q=1/ Q=10 / ( ) [ ( ) ] ( ) ω 1 ω0 ω 1 ω ω + 2 Q ω0 2 ω r ω0 φ (ωr ) π /2 Δ ωr 3 ω0 Q φ (0)=0 2 3 ω /ω0 φ ( )= π Olivier Fruchart Solemio School Synchrotron Soleil p.10

11 Mechanical oscillator Tip-sample interaction treated as perturbation m z + Γ z + k z=f (z ) with F (z)=f (z 0 )+ (z z 0 ) z F Mere renormalization : ( ω0,eff =ω0 1 1 F 2k z ) Phase shift Attractive force δ φ = Q F k z Red shift Repulsive force Blue shift Forces monitored through phase shift ω exc =ω0 Olivier Fruchart Solemio School Synchrotron Soleil p.11

12 AFM Tapping mode (topography) Resonance spectrum Full resonance spectrum Amplitude 280 khz Amplitude 288 khz 0 khz 500 khz Resonance in tapping mode Phase φ=0 Amplitude φ= - π 79 khz Peak is cut 82 khz Olivier Fruchart Solemio School Synchrotron Soleil p.12

13 AFM Close-loop versus open-loop operation Close-loop operation Feedback signal and setpoint: amplitude Map at constant force Ex : map = topography with setpoint on the amplitude Open-loop operation Map The force along a predefined trajectory (plane, lift-height etc.) Ex : map = magnetic stray field above sample Olivier Fruchart Solemio School Synchrotron Soleil p.13

14 AFM Tapping mode (topography) Images Phase image Increasing pressure Height image (topography) To notice Non-contact part (bottom of image) Phase does not reflect topography Noise and phase depend on set point Sample : self-organized Anodized Alumina (synthesis L. Cagnon, Institut Néel) Olivier Fruchart Solemio School Synchrotron Soleil p.14

15 AFM Tip shadowing effects Schematics Examples Tip 1.8 x 2 microns Sample : M. Miron (Spintec) Lithography : S. Pizzini (Néel) Sample S. Y. Suck et al., APL95, (2009) Notice Lateral (base) size is over-estimated with AFM Shading, not convolution (no true retrieval possible) Tips are less sharp for MFM due to magnetic coating Olivier Fruchart Solemio School Synchrotron Soleil p.15

16 AFM Tip effects ZIP disk, 400x400 nm Usual tip SWCNT tip Tip : A. M. Bonnot (Institut Néel) Olivier Fruchart Solemio School Synchrotron Soleil p.16

17 MFM Two-pass technique Second pass Monitor long-range forces (magnetic, electrostatic) First-pass Feedback ON Monitor topography (height) and any other signal (phase etc.) Olivier Fruchart Solemio School Synchrotron Soleil p.17

18 Reminder about magnetostatics Calculate energy with magnetic dipoles Magnetic field arising from a magnetic dipole H d (r)= μ0 4πr 3 [ 3(μ 1. r)r r 2 μ 1 μ2 ] μ1 F 2 (r)= E 1,2=μ0 (Hd.μ 2) F 2 (r)= E 1,2 with E 1,2 = μ0 μ 2. Hd Calculate energy with magnetic dipoles Analogy with electrostatics thanks to div(hd ) = div(m) div[m(r ' )].(r ' r ) 3 [m(r ' ).n(r ' )].(r ' r ) 2 Hd (r ) = Ms d r' + d r' 3 3 space sample 4 π r r ' 4 π r r ' ρ (r ) = -M sdiv[m(r )] Volume charges σ (r ) = M sm(r ).n(r ) Surface charges E 1,2 =μ0 σ. ϕ with Hd = ϕ Olivier Fruchart Solemio School Synchrotron Soleil p.18

19 MFM tip/sample interaction Tip is a dipole Tip is a monopole E 1,2 = μ0 μ 2. Hd E 1,2 =μ0 σ. ϕ E 1,2 = μ0 (μ x. H d, x + μ y. H d, y + μ z. H d, z ) δφ= Q μ0 μ i 2z H d, i k F z= μ 0 σ Hd, z δφ= Q μ σ H k 0 z d,z In practice, a combination of both models is best suited (dipole is more important) MFM is sensitive to some derivative(s) of the stray field from the sample MFM may be sensitive to in-plane field, depending on the tip moment. Olivier Fruchart Solemio School Synchrotron Soleil p.19

20 MFM Single-domain nanostructures (planar) Topography MFM, saturated MFM, partly reversed S. Y. Suck et al., APL95, (2009) Single-domain in-plane magnetized dots appear as dipoles Olivier Fruchart Solemio School Synchrotron Soleil p.20

21 MFM Single-domain nanostructures (perpendicular) Structure (SEM) MFM, partly reversed T. Wang et al., APL 92, (2008) Single-domain out-of-plane magnetized dots appear as monopoles Olivier Fruchart Solemio School Synchrotron Soleil p.21

22 MFM Single-domain nanostructures (mutual interaction) Permalloy (15nm), 3x8 microns Principle : 1. Stray field magnetizes sample 2. Sample is non -uniform stray field 3. Tip measures sample's stray field Contrast : -0.1, LM tip Lithography : S. Pizzini (Institut Néel) Imaging : Z. Ishaque (Institut Néel) It is a DOMAIN contrast Interaction is ALWAYS attractive : red shift Contrast is proportionnal to the square of the tip moment Olivier Fruchart Solemio School Synchrotron Soleil p.22

23 MFM Domains in films with perpendicular anisotropy FePt (4nm), 5x5 microns It is a DOMAIN contrast The direction of magnetization is deduced Sample : A. Marty (CEA-Grenoble) Imaging : M. Darques (Institut Néel) Contrast : ±0.4, LM tip Quantitative analysis : L. Belliard et al., J. Appl. Phys. 81, 3849 (1997) Olivier Fruchart Solemio School Synchrotron Soleil p.23

24 MFM Imaging domain walls (Bloch) Fe dot (25nm), 2.5x1 microns Contrast is MONOPOLAR Informs about the polarity of the wall core Down core Up core Olivier Fruchart Solemio School Synchrotron Soleil p.24

25 MFM Imaging domain walls (Néel) Permalloy dot (16nm) 2x2 microns Permalloy film (20nm) 10x10 microns J. M. Garcia et al., APL 79, 656 (2001) Néel wall give rise to DIPOLAR contrast Informs about the chirality of the wall core Olivier Fruchart Solemio School Synchrotron Soleil p.25

26 MFM Imaging domain walls (head-to-head) Permalloy stripes (15nm), 250nm wide Contrast : ±0.3, tip 5nm CoCr Known as vortex domain-wall R. McMichael and M. Donahue, IEEE Trans. Magn. 33, 4167 (1997) Walls in in-plane magnetized stripes MONOPOLAR Contrast informs about head-to-head ot tail-to-tail Olivier Fruchart Solemio School Synchrotron Soleil p.26

27 Tips influencing samples Moderate Moderate Repulsion Attraction Attraction Scanning Repulsion 2. Permalloy (15nm) 500nm wide FePt (4nm) Image 5 microns Permalloy (15nm) 500nm stripes Sample : S. Pizzini Imaging : Z. Ishaque Sample : A. Marty Imaging : M. Darques Sample : S. Pizzini Imaging : Z. Ishaque 1. Co (0.6nm)/ graphene (20 mic) C. Dieudonné Repeat measurement and/or change scanning direction Low-coercive samples require low-moment tips Commercial 'low-moment' may not be low enough Olivier Fruchart Solemio School Synchrotron Soleil p.27

28 Sample influencing tip Forward scan FePt thick film Backward scan G. Ciuta (Institut néel) Moment of tip reverses during scan Permanent magnet Choose high-coercivity tips (eg Asylum) Olivier Fruchart Solemio School Synchrotron Soleil p.28

29 Sample influencing cantilever Soft cantilever (70kHz) Stiff cantilever (300kHz) NdFeB thick film Cantilever repeled for tip and sample opposite 'Attractive' domains are over-dominant in the image 'Repulsive' domains lack of resolution Use stiff cantilever for permanent magnets Contrast : ±20 Contrast : ±0.5 Sample : G. Ciuta (Institut néel) Olivier Fruchart Solemio School Synchrotron Soleil p.29

30 MFM under magnetic field Co(5)\Cu(5)\Py(15nm) 5 microns image Agglomerated Fe3O4 superparamagnetic particles In-plane field (30mT) Out-of-plane field (400mT) Sample : A. Masseboeuf (CEA-Grenoble) Sample : K. Aissou (LCPO, Bordeaux) Coercive field of usual tips of the order of 50mT Olivier Fruchart Solemio School Synchrotron Soleil p.30

31 Tips and cantilevers Summary of choices Moment Cantilever Normal moment for most samples (30-50nm CoCr) Normal stifness ('force modulation') resonance at 70kHz Low moment, or even : Superparamagnetic or ultra-low moment Low-coercivity samples Increased resolution At the expense of sensitivity Tip sharpness Large stifness High stray-field samples (typically permanent magnets) At the expense of sensitivity Coercivity Normal resolution (50nm) Normal (30-70mT) Sharp tips (resolution 25nm), expense : High coercivity (eg Asylum) Commercial and/or spacial High stray-field samples Loss of sensitivity At the expense of cost fabrication (FIB etc.) (typically permanent magnets) Olivier Fruchart Solemio School Synchrotron Soleil p.31

32 Calibration of tips and cantilevers 25nm 40nm 80nm 120nm 55nm Compare tips! Use identical sample and imaging parameters Sample : MnAs(001) R. Belkhou (Soleil) Olivier Fruchart Solemio School Synchrotron Soleil p.32

33 Comparing MFM with other microscopies Game of the seven differences... XMCD-PEEM MFM Olivier Fruchart Solemio School Synchrotron Soleil p.33

34 Comparing MFM with other microscopies XMCD-PEEM MFM Lorentz Olivier Fruchart Solemio School Synchrotron Soleil p.34

35 References Some references Y. Zhu Ed., Modern techniques for characterizing magnetic materials, Springer (2005) A. Schwartz et al., Scanning probe techniques: MFM and SP-STM, in : series Handbook of magnetism and advanced magnetic materials, Novel techniques for characterizing and preparing samples (vol.3), H. Kronmüller, S. Parkin Ed. (2007) Why we DO need 'SOLEIL' A. Hubert, R. Schäfer, Magnetic domains, Springer (1999) Repository of the European School on Magnetism : See 2005 School : «New experimental approaches to Magnetism» Olivier Fruchart Solemio School Synchrotron Soleil p.35

36 The European School on Magnetism 2011 Request participation before May 15th Olivier Fruchart Solemio School Synchrotron Soleil p.36