Magnetic properties of self-organized systems [ Individual and - PowerPoint PPT Presentation

Magnetic properties of self-organized systems [ Individual and collective aspects ] O.Fruchart Laboratoire Louis Néel (CNRS-UJF-INPG) Grenoble Laboratoire Louis N Louis Né éel, Grenoble el, Grenoble, France , France. . Laboratoire Laboratoire Louis Néel, Grenoble, France. http:/ / lab http:/ / lab- - neel.grenoble.cnrs.fr neel.grenoble.cnrs.fr / / them es them es/ couches/ / couches/ ext ext / / slides slides/ / http:/ / lab-neel.grenoble.cnrs.fr/ them es/ couches/ ext/ slides/

TABLE OF CONTENTS Magnetic properties of self-organized systems : TOC 1 . I ntroduction to m agnetism 2 . I ndividual properties 3 . Collective properties 4 . Tow ards m aterials? Laboratoire Louis N Laboratoire Louis Né éel, Grenoble el, Grenoble, France , France. . Olivier Fruchart – SON School (Cargèse) – July 17-23, 2005 – p.2 Laboratoire Louis Néel, Grenoble, France. http:/ / lab http:/ / lab- - neel.grenoble.cnrs.fr neel.grenoble.cnrs.fr / / them es them es/ couches/ / couches/ ext ext / / slides slides/ / http:/ / lab-neel.grenoble.cnrs.fr/ them es/ couches/ ext/ slides/

INTRODUCTION TO MAGNETISM – Currents, magnetic fields and magnetization Oersted field Magnetic moment Magnetic material µ µ = 0 B π µ 3 4 r I = 0 B ⎡ ⎤ π 3 2 r × − ( µ.r ) r µ ⎢ ⎥ Magnetization: A.m -1 ⎣ ⎦ 2 r Magnetic moment: A.m 2 Laboratoire Louis N Laboratoire Louis Né éel, Grenoble el, Grenoble, France , France. . Olivier Fruchart – SON School (Cargèse) – July 17-23, 2005 – p.3 Laboratoire Louis Néel, Grenoble, France. http:/ / lab http:/ / lab- - neel.grenoble.cnrs.fr neel.grenoble.cnrs.fr / / them es them es/ couches/ / couches/ ext ext / / slides slides/ / http:/ / lab-neel.grenoble.cnrs.fr/ them es/ couches/ ext/ slides/

INTRODUCTION TO MAGNETISM – Hysteresis loops Manipulation of magnetic materials: � Application of a magnetic field = − µ E H.M Zeeman energy: Z 0 Spontaneous magnetization M s Remanent magnetization M r M M Coercive field H c Hext Hext Losses ∫ = µ E H d M 0 ext Laboratoire Louis N Laboratoire Louis Né éel, Grenoble el, Grenoble, France , France. . Olivier Fruchart – SON School (Cargèse) – July 17-23, 2005 – p.4 Laboratoire Louis Néel, Grenoble, France. http:/ / http:/ / lab lab- - neel.grenoble.cnrs.fr neel.grenoble.cnrs.fr / / them es them es/ couches/ / couches/ ext ext / / slides slides/ / http:/ / lab-neel.grenoble.cnrs.fr/ them es/ couches/ ext/ slides/

INTRODUCTION TO MAGNETISM – Magnetically soft and hard magnetic materials Soft materials Hard materials M M Hext Hext Transformers Flux guides Permanent magnets, motors Magnetic shielding Magnetic recording Laboratoire Louis N Laboratoire Louis Né éel, Grenoble el, Grenoble, France , France. . Olivier Fruchart – SON School (Cargèse) – July 17-23, 2005 – p.5 Laboratoire Louis Néel, Grenoble, France. http:/ / lab http:/ / lab- - neel.grenoble.cnrs.fr neel.grenoble.cnrs.fr / / them es them es/ couches/ / couches/ ext ext / / slides slides/ / http:/ / lab-neel.grenoble.cnrs.fr/ them es/ couches/ ext/ slides/

INTRODUCTION TO MAGNETISM – Sources of magnetic energy Echange energy Magnetocrystalline anisotropy energy = − S S E J . 1 2 M Ech 1 , 2 = ∇ θ 2 = θ A ( ) 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 Laboratoire Louis N Laboratoire Louis Né éel, Grenoble el, Grenoble, France , France. . Olivier Fruchart – SON School (Cargèse) – July 17-23, 2005 – p.6 Laboratoire Louis Néel, Grenoble, France. http:/ / http:/ / lab lab- - neel.grenoble.cnrs.fr neel.grenoble.cnrs.fr / / them es them es/ couches/ / couches/ ext ext / / slides slides/ / http:/ / lab-neel.grenoble.cnrs.fr/ them es/ couches/ ext/ slides/

INTRODUCTION TO MAGNETISM – Magnetic characteristic length scales Typical length scale: Bloch wall width λ B Numerical values λ = π A / K B λ = − λ B ≥ 2 3 nm 100 nm B Hard Soft ( ) = θ + θ 2 2 e A d / dx K sin Exchange Anisotropy 3 J/m J/m Laboratoire Louis N Laboratoire Louis Né éel, Grenoble el, Grenoble, France , France. . Olivier Fruchart – SON School (Cargèse) – July 17-23, 2005 – p.7 Laboratoire Louis Néel, Grenoble, France. http:/ / lab http:/ / lab- - neel.grenoble.cnrs.fr neel.grenoble.cnrs.fr / / them es them es/ couches/ / couches/ ext ext / / slides slides/ / http:/ / lab-neel.grenoble.cnrs.fr/ them es/ couches/ ext/ slides/

INTRODUCTION TO MAGNETISM – What is nanomagnetism? One possible definition: mesoscopic magnetism Bulk material Mesoscopic scale Nanometric scale Numerous and complex Small number of domains, Magnetic magnetic domains simple shape single-domain Microfabricated dots Co(1000) crystal – SEMPA Kerr magnetic imaging A. Hubert, Magnetic domains A. Hubert, Magnetic domains R.P. Cowburn, Magnetic recording essentially makes use of J.Phys.D:Appl.Phys.33, single-domain particles R1 (2000) Laboratoire Louis N Laboratoire Louis Né éel, Grenoble el, Grenoble, France , France. . Olivier Fruchart – SON School (Cargèse) – July 17-23, 2005 – p.8 Laboratoire Louis Néel, Grenoble, France. http:/ / lab http:/ / lab- - neel.grenoble.cnrs.fr neel.grenoble.cnrs.fr / / them es them es/ couches/ / couches/ ext ext / / slides slides/ / http:/ / lab-neel.grenoble.cnrs.fr/ them es/ couches/ ext/ slides/

TABLE OF CONTENTS Magnetic properties of self-organized systems : TOC 1 . I ntroduction to m agnetism 2 . I ndividual properties 3 . Collective properties 4 . Tow ards m aterials? Laboratoire Louis N Laboratoire Louis Né éel, Grenoble el, Grenoble, France , France. . Olivier Fruchart – SON School (Cargèse) – July 17-23, 2005 – p.9 Laboratoire Louis Néel, Grenoble, France. http:/ / lab http:/ / lab- - neel.grenoble.cnrs.fr neel.grenoble.cnrs.fr / / them es them es/ couches/ / couches/ ext ext / / slides slides/ / http:/ / lab-neel.grenoble.cnrs.fr/ them es/ couches/ ext/ slides/

INDIVIDUAL PROPERTIES – Ferromagnetic order Naïve m odel Molecular field + m Nw M J 1 = µ 0 0 0 N s N b T . . c 0 3 J k B N neighbors − 2 ( N N ) = − ∆ -1 b s N N T ( t ) ~ t b c t Less naïve… Experim ents Thickness-dependant molecular field λ - ∆ T ( t ) ~ t c λ = 1 G.A.T. Allan, PRB1 , 3 5 2 ( 1 9 7 0 ) Conclusion : U. Gradm ann, Naïve views are roughly correct Handbook of Magn. Mater. Vol.7 , ch.1 ( 1 9 9 3) Laboratoire Louis N Laboratoire Louis Né éel, Grenoble el, Grenoble, France , France. . Olivier Fruchart – SON School (Cargèse) – July 17-23, 2005 – p.10 Laboratoire Louis Néel, Grenoble, France. http:/ / lab http:/ / lab- - neel.grenoble.cnrs.fr neel.grenoble.cnrs.fr / / them es them es/ couches/ / couches/ ext ext / / slides slides/ / http:/ / lab-neel.grenoble.cnrs.fr/ them es/ couches/ ext/ slides/

INDIVIDUAL PROPERTIES – Ferromagnetic order Stripes on vicinal surfaces Magnetic order in 2D: finite-size scaling Curie tem perature as a function of stripe w idth Fe( 0 .5 ML) / W ( 1 1 0 ) 250 x 250 nm J.Hauschild et al. , λ = Phys.Rev.B57, R677(1998) 1 . 03 in agreement with Ising model (=1) H. J. Elmers et al., PRL73, 898 (1994) λ = ± 1 . 2 0 . 3 for Fe stripes / Pd(110) D. Li et al., PRB64, 144410 (2001) Laboratoire Louis N Laboratoire Louis Né éel, Grenoble el, Grenoble, France , France. . Olivier Fruchart – SON School (Cargèse) – July 17-23, 2005 – p.11 Laboratoire Louis Néel, Grenoble, France. http:/ / lab http:/ / lab- - neel.grenoble.cnrs.fr neel.grenoble.cnrs.fr / / them es them es/ couches/ / couches/ ext ext / / slides slides/ / http:/ / lab-neel.grenoble.cnrs.fr/ them es/ couches/ ext/ slides/

INDIVIDUAL PROPERTIES – Magnetic anisotropy Magnetocrystalline anisotropy energy Electronic cloud Atom nucleus (crystal structure) Spin-orbit coupling � the energy of both spin and orbital m om ent depends on orientation Series development on an angular basis: Anisotropy energy Norm alized m agnetization com ponents 2 4 = + + E K m K m ... Uniaxial mc z z 1 2 Alignem ent of m agnetization is favored along 2 2 2 2 2 2 = + + + E K ( m m m m m m ) ... given axes of the crystal mc x y y z z x 4 Cubic … (Derived from slide of A. Thiaville – CNRS/Orsay) Laboratoire Louis N Laboratoire Louis Né éel, Grenoble el, Grenoble, France , France. . Olivier Fruchart – SON School (Cargèse) – July 17-23, 2005 – p.12 Laboratoire Louis Néel, Grenoble, France. http:/ / http:/ / lab lab- - neel.grenoble.cnrs.fr neel.grenoble.cnrs.fr / / them es them es/ couches/ / couches/ ext ext / / slides slides/ / http:/ / lab-neel.grenoble.cnrs.fr/ them es/ couches/ ext/ slides/