Introduction to magnetism Part II – Magnetization reversal 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/
Sep.2011: next European School on Magnetism (ESM). Romania. http://esm.neel.cnrs.fr Olivier Fruchart – School of GdR nanoalloys – Fréjus, June 2010 – p.2 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/
→ Introduction to magnetism – Magnetization reversal ToC 1. Energies and length scales in magnetism 2. Single-domain magnetization reversal 3. Magnetostatics 4. Magnetization reversal in materials 5. Recent ways for reversing magnetization Olivier Fruchart – School of GdR nanoalloys – Fréjus, June 2010 – p.3 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/
1. ENERGIES AND LENGTH SCALES – Hysteresis and magnetic materials Manipulation of magnetic materials: Application of a magnetic field S pontaneous ≠ S aturation = − µ E H.M Zeeman energy: Z 0 s Spontaneous magnetization M s Remanent magnetization M r Another notation M M J s = 0 M s Coercive field H c Hext Hext Losses ∫ = µ E H d M 0 ext Olivier Fruchart – School of GdR nanoalloys – Fréjus, June 2010 – p.4 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/
1. ENERGIES AND LENGTH SCALES – Soft and hard magnetic materials Soft materials Hard materials M M Hext Hext Transformers Flux guides, sensors Permanent magnets, motors Magnetic shielding Magnetic recording Olivier Fruchart – School of GdR nanoalloys – Fréjus, June 2010 – p.5 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/
1. ENERGIES AND LENGTH SCALES – 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 – School of GdR nanoalloys – Fréjus, June 2010 – p.6 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/
1. ENERGIES AND LENGTH SCALES – 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 – School of GdR nanoalloys – Fréjus, June 2010 – p.7 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/
1. ENERGIES AND LENGTH SCALES – 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 – School of GdR nanoalloys – Fréjus, June 2010 – p.8 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/
→ Introduction to magnetism – Magnetization reversal ToC 1. Energies and length scales in magnetism 2. Single-domain magnetization reversal 3. Magnetostatics 4. Magnetization reversal in materials 5. Recent ways for reversing magnetization Olivier Fruchart – School of GdR nanoalloys – Fréjus, June 2010 – p.9 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/
2. SINGLE-DOMAIN REVERSAL – Coherent rotation (1/4) Framework = M = m ) ( r Cte Approximation : (strong!) H [ ] θ H 2 = θ − µ θ − θ E V K sin M H cos( ) tot ext eff 0 S H = + K K K mc d eff θ M Dimensionless units: sin 2 = θ − θ − θ = e ( ) 2 h cos( ) e E / VK H = h H / H a = µ H 2 K / M a 0 S L. Néel, Compte rendu Acad. Sciences 224, 1550 (1947) E. C. Stoner and E. P. Wohlfarth, Phil. Trans. Royal. Soc. London A240, 599 (1948) IEEE Trans. Magn. 27(4), 3469 (1991) : reprint Names used Uniform rotation / magnetization reversal Coherent rotation / magnetization reversal Macrospin etc. Olivier Fruchart – School of GdR nanoalloys – Fréjus, June 2010 – p.10 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/
2. SINGLE-DOMAIN REVERSAL – Coherent rotation (2/4) ( ) sin 2 = θ + θ θ = 180 ° H>0 e ( ) 2 h cos( ) H Equilibrium states ∂ ∂ e e ( ) = ⇒ θ = = θ θ − 0 cos( ) h 2 sin cos h m ∂ θ ∂ θ -90° 0° 90° 180° 270° [ ] θ ≡ π 0 Stability 2 ∂ e 2 ∂ e = − ( 0 ) 2 ( 1 h ) = θ − θ 2 cos 2 2 h cos 2 ∂ θ 2 ∂ θ 2 ∂ e 2 = θ − − θ 4 cos 2 2 h cos 2 θ = − ( ) 2 ( h 1 ) m 2 ∂ θ 2 ∂ e π = + ( ) 2 ( 1 h ) 2 ∂ θ Energy barrier Switching ∆ = θ − e e ( ) e ( 0 ) max 2 2 = − + − 1 h 2 h 2 h = h 1 ( ) 2 = = µ = − H H 2 K / M 1 h a 0 s with exponent 1.5 in general 1 − h Olivier Fruchart – School of GdR nanoalloys – Fréjus, June 2010 – p.11 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/
2. SINGLE-DOMAIN REVERSAL – Coherent rotation (3/4) EASY ~ HARD ‘Astroid’ curve H H 90 θ H ( ) 120 60 Sw H Hard axis H = 0 -90° 0° 90° 180° 270° -90° 0° 90° 180° 270° 150 30 1 H = 0.2 Ha = H ( ) 180 0 Sw 3 / 2 Easy axis Easy axis 2 / 3 2 / 3 θ + θ sin cos H H 210 330 H = 0.7 Ha Hard axis 240 300 270 H = Ha 1 H Sw (θ) is a signature of = H ( ) Sw 3 / 2 reversal modes 2 / 3 2 / 3 θ + θ sin cos H H J. C. Slonczewski, Research Memo RM 003.111.224, IBM Research Center (1956) Olivier Fruchart – School of GdR nanoalloys – Fréjus, June 2010 – p.12 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/
2. SINGLE-DOMAIN REVERSAL – Coherent rotation (4/4) Switching field = Reversal field 1 M A value of field at which an irreversible (abrupt) jump of magnetization angle occurs. 0 Can be measured only in single particles. 90° 70° 0° Coercive field 10° 45° 30° -1 The value of field at which M.H = 0 ( H ± ) -1.5 -1 -0.5 0 0.5 1 1.5 h A quantity that can be measured in real 1 = h materials (large number of ‘particles’). ( ) Sw 3 / 2 2 / 3 2 / 3 θ + θ sin cos H H May be or may not be a measure of the mean 1.0 switching field at the microscopic level Normalized field 0.8 Reversal field Reversal field 90 Hard 0.6 135 45 Coerciv Coercive 0.4 Coercive Easy e field field 180 0 0.2 field 1 = θ h Abs (sin 2 ) Easy c H 2 0.0 0 45 90 135 180 225 315 Angle Hard 270 Olivier Fruchart – School of GdR nanoalloys – Fréjus, June 2010 – p.13 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/
2. SINGLE-DOMAIN REVERSAL – Coherent rotation, experimental relevance (1/2) Experimental evidence First evidence: W. Wernsdorfer et al., 0.3 Phys. Rev. Lett. 78, 1791 (1997) 0.04K 0.2 0.1 µ 0 H z (T) 0 -0.1 -0.2 -0.3 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 M. Jamet et al., Phys. Rev. Lett., 86, 4676 (2001) µ 0 H y (T) Extensions: 3D, arbitrary anisotropy etc. M. Jamet et al., PRB69, 024401 (2004) A. Thiaville et al., PRB61, 12221 (2000) Olivier Fruchart – School of GdR nanoalloys – Fréjus, June 2010 – p.14 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/
2. SINGLE-DOMAIN REVERSAL – Experimental relevance (2/2) Size-dependent magnetization reversal Size in micrometers Astroids of flat magnetic elements with increasing size Conclusion over coherent rotation The simplest model Fails for most systems because 0.2x0.5 0.37x0.75 they are too large: apply model with great care!.. Hc<<Ha for most large systems (thin films, bulk): do not use Hc to estimate K! Early known as Brown’s paradox 0.2x0.75 0.27x1.37 J. Z. Sun et al., Appl. Phys. Lett. 78 (25), 4004 (2001) Olivier Fruchart – School of GdR nanoalloys – Fréjus, June 2010 – p.15 Institut Néel, Grenoble, France http://perso.neel.cnrs.fr/olivier.fruchart/slides/ http://perso.neel.cnrs.fr/olivier.fruchart/slides/
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