Magnetic Force Microscopy Olivier Fruchart Institut Néel (CNRS-UJF-INPG) Grenoble - France http://neel.cnrs.fr Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/
WHY DO WE NEED MAGNETIC MICROSCOPY ? – Origins of magnetic energy Echange energy Magnetocrystalline anisotropy energy = − E J S . S 1 2 Ech 1 , 2 M = ∇ θ 2 A ( ) = θ sin 2 E K ( ) mc Hext Zeeman energy (enthalpy) Dipolar energy 2 1 1 = − µ E M . H S d = − µ d 0 E M . H 2 S Z 0 Olivier Fruchart – Solemio School – Synchrotron Soleil – 2011-05-05 – p.2 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides
WHY DO WE NEED MAGNETIC MICROSCOPY ? – – Magnetic characteristic length scales Typical length scale: Numerical values Bloch wall width B λ = π A / K B λ = − λ B ≥ 2 3 nm 100 nm B Hard Soft ( ) 2 = θ + θ 2 e A d / dx K sin Exchange Anisotropy J/m 3 J/m Olivier Fruchart – Solemio School – Synchrotron Soleil – 2011-05-05 – p.3 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides
WHY DO WE NEED MAGNETIC MICROSCOPY ? – Magnetic domains Bulk material Mesoscopic scale Nanometric scale Numerous and complex Small number of domains, Magnetic magnetic domains simple shape single-domain Microfabricated dots Kerr magnetic imaging Co(1000) crystal – SEMPA A. Hubert, Magnetic domains A. Hubert, Magnetic domains R.P. Cowburn, Nanomagnetism ~ mesoscopic magnetism J.Phys.D:Appl.Phys.33, R1 (2000) Olivier Fruchart – Solemio School – Synchrotron Soleil – 2011-05-05 – p.4 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides
Why do we need microcopy ? What information may be sought Conditions and environment Distribution of magnetization in Temperature sample Magnetic field Direction & magnitude Electrical current, light etc. Depth resolution Additional microscopies Elemental resolution Lateral resolution Time resolution Olivier Fruchart – Solemio School – Synchrotron Soleil – 2011-05-05 – p.5 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides
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 – 2011-05-05 – p.6 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides
Atomic Force Microscopy – Cantilevers and tips Chip – Batch fabrication Cantilever Millimeters Full tip + apex 100μm Price 10-200€/tip Radius of curvature ≈ 5nm Images : Olympus catalog (http://www.olympus.co.jp/probe) Olivier Fruchart – Solemio School – Synchrotron Soleil – 2011-05-05 – p.7 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides
AFM – Many uses Measures Modes of operation Topography Static (deflection) Mechanical properties • When contact is needed : electric, friction etc. Electric properties Dynamic (cantilever oscillation) Piezoelectric properties • Less damage to sample and tip Long-range forces (electrostatic, magnetic) • More sensitive Micromanipulation & fabrication Olivier Fruchart – Solemio School – Synchrotron Soleil – 2011-05-05 – p.8 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides
Mechanical oscillator – Equations Mechanical excitation of cantilevers m ¨ z + Γ ˙ z + k z = F ( z ,t ) m Inertia Γ Damping Spring k F ( z ,t ) External force Notations j ω t F = 0 z ( t )= z 0 e Seek solutions for Transfert function ω 0 = √ k H = z F = 1 1 Reference angular velocity m − ( ω 0 ) Q ( ω 0 ) + 1 k 2 ω + j ω Q = √ k m Quality factor Γ Olivier Fruchart – Solemio School – Synchrotron Soleil – 2011-05-05 – p.9 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides
Mechanical oscillator – Solutions Gain G =∣ H ∣= 1 1 7 Q = 10 / √ 2 √ [ 1 − ( 6 k ] 2 ω 0 ) 2 ( ω 0 ) 2 2 ω + 1 ω 5 Q 4 kG 3 ω r =ω 0 √ kG ( 0 )= 1 2 1 − 1 Peak at : 1 Q = 1 / √ 2 2 2Q kG (ω r )= Q 0 1 2 3 ω/ω 0 kG (∞)= 0 Dephasing Q>>1 1 − ( ω 0 ) 2 ω r ≈ω 0 ω 0.0 -0.5 cos φ= φ(ω r )≈−π/ 2 √ [ 1 − ( -1.0 ] 2 ω 0 ) 2 ( ω 0 ) 2 2 ω + 1 ω φ -1.5 ≈ √ 3 Δ ω r Q Q = 1 / √ 2 -2.0 ω 0 Q -2.5 Q = 10 / √ 2 φ( 0 )= 0 -3.0 0 1 2 3 φ(∞)=−π ω/ω 0 Olivier Fruchart – Solemio School – Synchrotron Soleil – 2011-05-05 – p.10 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides
Mechanical oscillator Tip-sample interaction treated as perturbation m ¨ z + Γ ˙ z + k z = F ( z ) F ( z )= F ( z 0 )+ ( z − z 0 )∂ z F with ω 0,eff =ω 0 ( 1 − 1 2k ∂ z F ) Mere renormalization : Phase shift Attractive force Red shift δφ=− Q k ∂ z F Repulsive force Blue shift Forces monitored through phase shift ω exc =ω 0 Olivier Fruchart – Solemio School – Synchrotron Soleil – 2011-05-05 – p.11 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides
AFM – Tapping mode (topography) Resonance spectrum Full resonance spectrum Amplitude Amplitude 288 kHz 280 kHz 500 kHz 0 kHz Phase Resonance in tapping mode φ=0 ← Peak is cut Amplitude φ= - π 79 kHz 82 kHz Olivier Fruchart – Solemio School – Synchrotron Soleil – 2011-05-05 – p.12 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides
AFM – Close-loop versus open-loop operation Close-loop operation Feedback signal and setpoint: amplitude Ex : map = topography with Map at constant force setpoint on the amplitude Open-loop operation Map The force along a predefined Ex : map = magnetic stray field trajectory (plane, lift-height etc.) above sample Olivier Fruchart – Solemio School – Synchrotron Soleil – 2011-05-05 – p.13 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides
AFM – Tapping mode (topography) Images Height image (topography) Phase image Increasing pressure 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 – 2011-05-05 – p.14 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides
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, 162503 (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 – 2011-05-05 – p.15 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides
AFM – Tip effects ZIP disk, 400x400 nm SWCNT tip Usual tip Tip : A. M. Bonnot (Institut Néel) Olivier Fruchart – Solemio School – Synchrotron Soleil – 2011-05-05 – p.16 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides
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 – 2011-05-05 – p.17 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides
Reminder about magnetostatics Calculate energy with magnetic dipoles Magnetic field arising from a magnetic dipole 3 [ − μ 1 ] μ 2 H d ( r )= μ 0 3 ( μ 1 .r ) r 2 4 π r r μ 1 F 2 ( r )=− ∇ E 1,2 =μ 0 ∇ ( H d . μ 2 ) F 2 ( r )=− ∇ E 1,2 =μ 0 ∇ ( H d . μ 2 ) F 2 ( r )=− ∇ E 1,2 E 1,2 =−μ 0 μ 2 .H d with Calculate energy with magnetic dipoles = − div ( H ) div ( M ) Analogy with electrostatics thanks to d − − div [ m ( r ' )].( r ' r ) [ m ( r ' ). n ( r ' )].( r ' r ) ∫∫∫ 3 ∫∫ 2 = − + H ( r ) M d r ' d r ' d s 3 3 space sample π − π − 4 r r ' 4 r r ' ρ = ( r ) - M div[ m ( r ) ] Volume charges s E 1,2 =μ 0 σ . ϕ H d =− ∇ ϕ with σ = ( r ) M m ( r ) . n ( r ) Surface charges s Olivier Fruchart – Solemio School – Synchrotron Soleil – 2011-05-05 – p.18 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides
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