A flavor of Nanomagnetism and Spintronics

Transcription

1 A flavor of Nanomagnetism and Spintronics Olivier Fruchart Institut Néel (CNRS-UJF-INPG) Grenoble - France /

2 Short presentation Local environment Grenoble : inhabitants with surroundings Universities : Université Joseph Fourier (UJF) / Grenoble Institute of Technology (INP) National Institutes : CNRS (broad topic), CEA (energy), INSERM (health) etc. Large scale facilities : ILL (neutrons) and ESRF (synchrotron) Fundamental research and technology (ex : Minatec, LETI, STMicroelectronics etc.) Institut Néel Staff : 170 scientists ; 125 technical staff ; 140 students & post-docs 3 departments : Nanosciences, low temperatures, materials & functions Nanosciences : 7 research teams Micro- and NanoMagnetism team : 35 staff, including 15 full-staff scientists. Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.2

3 MOTIVATING THE LECTURE Miniaturization is a key for technology Telegraphone (1898, W. Poulsen) Same concept over 100 years Technological innovation? New science? RAMAC (IBM, 1956) 2 kbit/in2 50 disks Ø 60 cm Total 5Mbytes Modern hard disk drive (>1 To) Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.3

4 MOTIVATING THE LECTURE The principle of magnetic recording (hard disk drives) Principle of hard-disks Magnetic bits CoPtCrTaB Hard disk (old ) Coils MR Shielding ~100nm Shielding ~7-8nm Substrate Read/Write head Disk (rotation rpm) S. Takenoiri, J. Magn. Magn. Mater. 321, 562 (2009) Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.4

5 Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.5

6 MOTIVATING THE LECTURE The need for nanomagnetism Fundamental issues for nanomagnetism Magnetic grain media of current hard disks Is a small grain stable against thermal fluctuations? 21 k B T 300 K 4 10 J 25 mev 100 k B T 300 K 2.5 ev Derive from macroscopic arguments Is a small grain (ferro)magnetic? Count number of surface atoms S. Takenoiri, J. Magn. Magn. Mater. 321, 562 (2009) Decades-old (yet still modern) topic Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.6

7 MOTIVATING THE LECTURE The need for spin electronics The technological need for spin electronics Requires nanometer length scales Coils ~7-8nm Magneto-transport. Shielding Field of spin electronics MR Convert magnetic information to electric signal Substrate How to read information? Shielding ~100nm Official birth: discovery of magneto-resistance N. M. Baibich, Phys. Rev. Lett. 61, 2472 (1988) G. Binach, Phys. Rev. B 39, 4828 (1989) Novel prize 2007: A. Fert & P. Grünberg Disk (rotation rpm) Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.7

8 NANOMAGNETISM ToC 0. Motivation 1. Introduction on magnetism 2. Energies and length scales in magnetism 3. Single-domain magnetization reversal 4. Magnetostatics 5. Surfaces and interfaces Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.8

9 INTRODUCTION TO MAGNETISM Currents, magnetic fields and magnetization Oersted field Magnetic dipole Magnetic material μ µ 0I B= 2π r µ0 B= 4π r (μ.r)r r μ Magnetic dipole: A.m2 Magnetization: A.m-1 Magnetic moment: A.m2 Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.9

10 INTRODUCTION TO MAGNETISM Hysteresis and magnetic materials Manipulation of magnetic materials: Spontaneous Saturation Application of a magnetic field Zeeman energy: E Z = µ 0H.Ms Remanent magnetization Mr Spontaneous magnetization Ms Another notation M J s= 0 M s Coercive field Hc Hext Losses E= µ 0 H ext dm Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.10

11 INTRODUCTION TO MAGNETISM 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 Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.11

12 NANOMAGNETISM ToC 0. Motivation 1. Introduction on magnetism 2. Energies and length scales in magnetism 3. Single-domain magnetization reversal 4. Magnetostatics 5. Surfaces and interfaces Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.12

13 ENERGIES AND LENGTH SCALES Sources of magnetic energy Echange energy EEch = J1, 2 S1.S 2 = A( θ ) 2 Magnetocrystalline anisotropy energy M Hext Zeeman energy (enthalpy) Emc = K sin 2 (θ ) Dipolar energy 2 1 EZ = µ 0 M S.H 1 Ed = µ 0 M S.H d 2 Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.13

14 ENERGIES AND LENGTH SCALES Magnetic characteristic length scales Bloch parameter Exchange length 2 2 E= A ( x θ ) +K d sin θ Exchange J/m Dipolar energy J/m3 Λ= A/ K d = 2A /μ 0 M 2s Λ 3 10 nm 2 E= A ( x θ ) +K sin2 θ Exchange J/m Anisotropy J/m 3 Bloch parameter: = A / K 1 nm 100 nm Hard Soft Single-domain critical size relevant for nanoparticules made of soft magnetic material Notice: Other length scales: with field etc. Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.14

15 ENERGIES AND LENGTH SCALES 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 Microfabricated dots Kerr magnetic imaging A. Hubert, Magnetic domains A. Hubert, Magnetic domains Nanomagnetism ~ mesoscopic magnetism R.P. Cowburn, J.Phys.D:Appl.Phys.33, R1 (2000) Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.15

16 NANOMAGNETISM ToC 0. Motivation 1. Introduction on magnetism 2. Energies and length scales in magnetism 3. Single-domain magnetization reversal 4. Magnetostatics 5. Surfaces and interfaces Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.16

17 SINGLE-DOMAIN REVERSAL Coherent rotation (1/2) Framework Approximation: r m=0 (uniform magnetization) (strong!) E =EV =V [ K eff sin2 0 M S H cos H ] θh H K eff =K mc K d Dimensionless units: 2 e=sin 2 hcos H e = E / KV h =H /Ha H a =2K / 0 M S θ M 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 Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.17

18 SINGLE-DOMAIN REVERSAL Coherent rotation (2/2) 2 e=sin 2 h cos Example for H =180 H>0 Equilibrium states e=2sin cos h cos m =h e= [ ] Stability e =2cos 2 2 h cos e 0 2 = 4cos 2 2 h cos Energy barrier e =e max e 0 =1 h 2 2h 2 2h 2 = 1 h =2 1 h 2 e m =2 h 1 e =2 1 h Switching h =1 H = H a =2K / 0 M S 1 h with exponent 1.5 in general Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.18

19 SINGLE-DOMAIN REVERSAL What is the use of easy and hard axes? Easy axis Hard axis High +/- remanence Coercivity Reversibility Linearity Memory, permanent magnet etc. Sensor, shielding etc. Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.19

20 Think one step ahead You see things and say «Why?», but I dream things that never were and I say «Why not» G. B. Shaw Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.20

21 SINGLE-DOMAIN REVERSAL Thermal energy Barrier height Thermal activation Brown, Phys.Rev.130, 1677 (1963) 2 e=e max e 0 = 1 h h= 0 M S H /2 K h=0.2 E kbt s = 0 exp E =k B T ln / 0 Lab measurement : 1 s H c= Hc E 25 k B T 25k B T 2K 1 0 MS KV Blocking temperature T T b KV /25k B E. F. Kneller, J. Wijn (ed.), Handbuch der Physik XIII/2: Ferromagnetismus, Springer, 438 (1966) M. P. Sharrock, J. Appl. Phys. 76, (1994) 9 Notice, for magnetic recording : 10 s KV b 40 60k B T Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.21

22 SINGLE-DOMAIN REVERSAL What use for nanoparticles? (1/2) Ferrofluids Principle Example of use Surfactant-coated nanoparticles, preferably superparamagnetic Avoid agglomeration of the particles Fluid and polarizable Seals for rotating parts R. E. Rosensweig, Magnetic fluid seals, US patent 3,260,584 (1971) Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.22

23 SINGLE-DOMAIN REVERSAL What use for nanoparticles? (2/2) Health and biology RAM (radar absorbing materials) Beads = coated nanoparticles, preferably superparamagnetic Avoid agglomeration of the particles Cell sorting F=. B M Hyperthermia Hext Principle Absorbs energy at a well-defined frequency (ferromagnetic resonance) dl =Γ= 0 H= 0 l H dt d = 0 H dt Use ac magnetic field H c =H c,0 1 ln / 0 k B T KV Contrast agent in Magnetic Resonance Imaging (MRI) = g J e 0 2 me s /2 28 GHz/T Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.23

24 NANOMAGNETISM ToC 0. Motivation 1. Introduction on magnetism 2. Energies and length scales in magnetism 3. Single-domain magnetization reversal 4. Magnetostatics 5. Surfaces and interfaces Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.24

25 MAGNETOSTATICS Treatment of dipolar energy (1/2) Density of dipolar energy E d (r ) = 1 µ M(r ).H (r ) d 2 0 By definition div(hd ) = div(m). As curl(hd ) = 0 we have (analogy with electrostatics): Notation Hd (r ) = Ms div[m(r ' )].(r ' r ) space 4π r r ' 3 M(r)= M s m i (r)u i d3 r ' ρ (r ) = -M sdiv[m(r )] volume density of magnetic charges To lift the divergence arising at sample boundaries: Hd (r ) = Ms space div[m(r ' )].(r ' r ) 4π r r ' 3 3 d r' + sample [m(r ' ).n(r ' )].(r ' r ) 4π r r ' 3 d r ' 2 σ (r ) = M sm(r ).n(r ) surface density of magnetic charges, where n(r) is the outgoing unit vector at boundaries Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.25

26 MAGNETOSTATICS Treatment of dipolar energy (2/2) E= 1µ 2 0 sample M.Hd.dV = 1µ 2 0 space H2d.dV E is always positive Examples of magnetic charges + Notice: no charges + + and E=0 for infinite + cylinder Charges on surfaces Surface and volume charges x Magnetization will tend to align parallel to long axis of samples Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.26

27 MAGNETOSTATICS Demagnetizing coefficients (1/2) Hypothesis Uniform magnetization (strong assumption!) M(r)= M s m i u i Demagnetizing coefficients < Hd (r ) > = M s N.m N is a positive second-order tensor Ed = K dnij mi m j = K d t m.n.m Nx N= Ny Nz and can be defined and diagonalized for any sample shape Ed = K d (N x mx2 + N y my2 + Nz mz2 ) < H d,i (r ) > = M sni Valid along main axes only! N x + N y + Nz = 1 What with ellipsoids??? Requires Hd(r) is uniform. Satisfied only in volumes limited by polynomial surfaces of order 2 or less:slabs, cylinders, ellisoids etc. J. C. Maxwell, Clarendon 2, (1872) Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.27

28 MAGNETOSTATICS Demagnetizing coefficients (2/2) Ellipsoids Nx = Nx = 1 abc 2 0 α 2 1 α α 1 Nx = 2 α 1 α 1 (a 2 + η ) (a 2 + η )(b 2 + η )(c 2 + η ) dη 2 2 For prolate revolution ellipsoid: 1 (a,c,c) with =c/a<1 N y = Nz = 21 (1 N x ) α 2 1 For oblate revolution ellipsoid: (a,c,c) with =c/a>1 α 1 α Asinh α Asin α General ellipsoid: main axes (a,c,c) 2 Cylinders N x = 0; N y = c /( b + c ); N z = b /( b + c ) For a cylinder along x J. A. Osborn, Phys. Rev. 67, 351 (1945). For prisms, see: A. Aharoni, J. Appl. Phys. 83, 3432 (1998) More general forms, FFT approach: M. Beleggia et al., J. Magn. Magn. Mater. 263, L1-9 (2003) Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.28

29 MICROMAGNETISM Beyond single-domain state C state S state At least 8 nearly-equivalent ground-states for a rectangular dot Numerical simulation becomes important Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.29

30 MICROMAGNETISM Magnetic domain walls and vortices Magnetic vortex Magnetic domain wall Thick and large stripes P.-O. Jubert & R. Allenspach, PRB 70, /1-5 (2004) UP UP DOWN DOWN DOWN UP UP DOWN UP T. Shinjo et al., Science 289, 930 (2000) 500-nm wide, 15nm FeNi thick stripes T. Okuno et al., JMMM240, 1 (2002) Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.30

31 SINGLE-DOMAIN REVERSAL Precessional dynamics Basics of precessional switching Démonstration: 1999 Magnetization dynamics: Landau-Lifshitz-Gilbert equation: dm α dm = γ 0 M H eff + M dt M s dt [ γ0 ] Gyromagnetic factor γ = γ 0 = µ 0γ gq 2m γ / 2π = 28 GHz/T H e ff Effective field (including applied) µ 0H eff = α Emag M Damping coefficient (10-3 > 10-1) C. Back et al., Science 285, 864 (1999) Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.31

32 SINGLE-DOMAIN REVERSAL Precessional dynamics Precessional trajectories using energy conservation (1) E = (2) 1 µ M 2N m s z z Kmx2 µ 0 M s Hmy In-plane uniaxial anisotropy mx2 + my2 + mz2 = 1 Starting condition: mx = 1 (1) e= 1 N m2 2 z z hk mx2 hmy Using (2) Can be rewritten: Using (2) Can be rewritten: m x2 = 1 mx2 ( my + h / N z ) 2 = hk / N z mz2 = ( 2h Nz my my2 N z + hk N z + hk h2 N z (N z + hk ) 2h hk my my2 N z + hk N z + hk 2 mz2 hk Nz + hk ) h h = + my hk hk 2 Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.32

33 SINGLE-DOMAIN REVERSAL Precessional dynamics my mz Magnetization trajectories h>hk hk>h>0.5hk h<0.5hk h=0.5hk mx mx -h -1 mx ( my + h / N z ) 2 = ω 0.847γ 0 M s (H HK ) / 2 h2 N z (N z + hk ) 1 + hk / N z 0 Field at 135 mz h=0.01 h>0.5hk h=0.5hk h<0.5hk my 0 ( mz2 hk Nz + hk 0.5 ) 2 h h = + my h h K K 21 M. Bauer et al., PRB61, 3410 (2000) Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.33

34 NANOMAGNETISM ToC 0. Motivation 1. Introduction on magnetism 2. Energies and length scales in magnetism 3. Single-domain magnetization reversal 4. Magnetostatics 5. Surfaces and interfaces Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.34

35 SURFACE MAGNETISM Ordering and magnetic moments (1/4) Probing surface magnetization Some results Surface techniques at OK Fe/W(110) : 0.14ML(+0.35µ ) UHV/Fe(110); Ag/Fe(110): 0.26ML(+0.65µ ) Cu/Ni(111): -0.5ML Overlayers: Pd/Ni(111)/Re(0001) B Mossbauer with probe layers B Plot m(t) at 0K: Magnetometry XMCD (Too) simple picture: band narrowing at surfaces E Bulk picture s-p Enhanced moment at surfaces E d Surface picture k s-p d k Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.35

36 SURFACE MAGNETISM Ordering and magnetic moments (2/4) Co/Pt(997) Co/Pt(111) A. Dallmeyer et al., Phys.Rev.B 61(8), R5153 (2000) Conclusions Bulk: m =0.14µ /at. P. Gambardella et al., Science 300, 1130 (2003) Surface: m =0.31µ /at. Conclusions Bi-atomic wire: m =0.37µ /at. From bulk to atoms: considerable increase of orbital moment Mono-atomic wire: m =0.68µ /at. 2 atoms closer to wire than 1 atom bi-atom: m =0.78µ /at. bi-atomic wire closer to surface than wire atom: m =1.13 µ /at. P. Gambardella et al., Nature 416, 301 (2002) L B L B L L L L B B B B Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.36

37 SURFACE MAGNETISM Ordering and magnetic moments (3/4) Elements of theory Ising (1925). No magnetic order at T>0K in 1D Ising chain. (1930). No magnetic order at T>OK in 2D Heisenberg. Bloch (spin-waves; isotropic Heisenberg) N. D. Mermin, H. Wagner, PRL17, 1133 (1966) (1944) + Yang (1951). Onsager 2D Ising model: Tc>0K Experiments Ni(111)/Re(0001) Magnetic anisotropy stabilizes ordering R. Bergholz and U. Gradmann, JMMM45, 389 (1984) Tc interpreted with molecular field Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.37

38 SURFACE MAGNETISM Ordering and magnetic moments (4/4) Naïve model Molecular field 0 z n W,1 n g2j 2B J J 1 T C= 3 kb z neighbors zb N atomic layers Less naïve z =z b 2 z b z s N zs Tc (t ) ~ t -1 Experiments Thickness-dependent molecular field Tc (t ) ~ t - λ λ = 1 G.A.T. Allan, PRB1, 352 (1970) Conclusion: Naïve views are roughly correct U. Gradmann, Handbook of Magn. Mater. Vol.7, ch.1 (1993) Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.38

39 SURFACE MAGNETISM Magnetic anisotropy (1/3) Magnetocrystalline anisotropy energy Electronic cloud Atom nucleus (crystal structure) Spin-orbit coupling the energy of both spin and orbital moment depends on orientation Series development on an angular basis: Anisotropy energy Normalized magnetization components Emc = K1 mz2 + K 2mz Uniaxial Emc = K 4 (m x2m y2 + m y2mz2 + mz2m x2 ) +... Alignement of magnetization is favored along given axes of the crystal Cubic (Derived from slide of A. Thiaville CNRS/Orsay) Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.39

40 SURFACE MAGNETISM Magnetic anisotropy (2/3) Surface anisotropy L. Néel, J. Phys. Radium 15, 15 (1954) «Superficial magnetic anisotropy and orientational superstructures» Overview Breaking of symmetry for surface/interface atoms Correction to the magneto-crystalline energy Es = K S,1 cos 2 (θ ) + K S,2 cos 4 (θ ) +... «This surface energy, of the order of 0.1 to 1 erg/cm2, is liable to play a significant role in the properties of ferromagnetic materials spread in elements of dimensions smaller than 100Å» Pair model of Néel: Ks estimated from magneto-elastic constants Does not depend on interface material Yields order of magnitude only: correct value from experiments or calculations (precision!) Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.40

41 SURFACE MAGNETISM Magnetic anisotropy (3/3) History of surface anisotropy : STEP 1 (1/t plot) First example of perpendicular anisotropy E tot (t ) = k V t + 2k S e(t ) = k V + 2k S t Bulk e(t) Bulk ce urfa S --> e p o Sl s t=2al 1/t U. Gradmann and J. Müller, Phys. Status Solidi 27, 313 (1968) Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.41

42 SURFACE MAGNETISM Magnetic anisotropy, implementation Main use in applications : perpendicular magnetic anisotropy in thin films Magneto-optical recording Materials and geometry Interfacial elements with large spin-orbit: Pt, Au, Pd Why: large magneto-optical response Material: 3D-Rare-Earth based Often: multilayers T. Johnson et al., Co/Au film M. Rep. Prog. Phys. 59, 1409 (1996) A. Fert et al., J. Magn. Magn. Mater. 200, 338 (1999) S. Tsunashima, J. Phys. D 34, R87 (2001) Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.42

43 SURFACE MAGNETISM Magnetic anisotropy, implementation Main use in applications : perpendicular magnetic anisotropy Decreased dipolar coupling in HDD media Enhanced anisotropy for solid-state memories Longitudinal recording ( ) Concerns MRAM: Magnetic Random Access Memories C. Chappert et al., The emergence of spin electronics in data storage, Nat. Mater. 6, 813 (2007) Reminder for the thermal stability fo small flat elements: Perpendicular recording (2005 -) H c= S. N. Piramanayagam, J. Appl. Phys. 102, (2007) In-plane magnetization High anisotropy with low spread angle Reduced intra- and inter-grain dipolar coupling 25k B T 2K 1 0 MS KV 1 K = N 0 M 2S 2 Issue: N is small with flat elements Perpendicular magnetization 1 2 K 0 MS 2 Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.43

44 SURFACE MAGNETISM Exchange bias (1/2) Seminal studies FM Oxidized Co nanoparticles AFM ZFC FC Field-cooled hysteresis loops: Increased coercivity µ0he 0.2 T Shifted in field Exchange bias J. Nogués and Ivan K. Schuller J. Magn. Magn. Mater. 192 (1999) 203 Meiklejohn and Bean, Phys. Rev. 102, 1413 (1956), Phys. Rev. 105, 904, (1957) Exchange anisotropy a review A E Berkowitz and K Takano J. Magn. Magn. Mater. 200 (1999) Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.44

45 SURFACE MAGNETISM Exchange bias (2/2) Increase coercivity of layers Application Concept of spin-valve in magneto-resistive elements AF F2 Crude approximation for thin layers: K AF t AF H F AF H F 1 K FtF B. Diény et al., Phys. Rev. B 43, 1297 (1991) Sensors Memory cells Etc. Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.45

46 SURFACE MAGNETISM Interlayer exchange coupling (1/2) The physics Figures Spin-dependent quantum confinement in the spacer layer Constructive and destructive interferences Maxima and minima of n r B, B Forth & back phase shift =q t A B r A, A Coupling strength: E S =J t cos in J /m2 = m1, m2 A with: J t = 2 sin q t t Spin-independent + q=k k - Spin-dependent r A, A,r B, B P. Bruno, J. Phys. Condens. Matter 11, 9403 (1999) Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.46

47 SURFACE MAGNETISM Interlayer exchange coupling (2/2) Illustration of coupling strength J t = A 2 t sin P t2 Note: J(t) extrapolated for t=3å S. S. P. Parkin, Phys. Rev. Lett. 67, 3598 (1991) Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.47

48 SURFACE MAGNETISM Synthetic antiferromagnets Synthetic Ferrimagnets (SyF) Crude description What use? Increase coercivity of pinned layers Decrease intra- and inter- dot F2 F1 dipolar coupling Hypothesis: AF Two layers rigidly coupled Reversal modes unchanged Neglect dipolar coupling e1 M 1 e2 M 2 M= e1 e2 F21 Reference layer F22 e K e K K= e 1 e2 F1 Free layer Practical aspects H c= e 1 M 1 H c, 1 e 2 M 2 H c, 2 e1 M 1 e2 M 2 Ru spacer layer (largest effect) Control thickness within a few Angströms! Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.48

49 Some reading (single-domain, domains and domain walls) [1] Magnetic domains, A. Hubert, R. Schäfer, Springer (1999, reed. 2001) [2] R. Skomski, Simple models of Magnetism, Oxford (2008). [3] R. Skomski, Nanomagnetics, J. Phys.: Cond. Mat. 15, R (2003). [4] O. Fruchart, A. Thiaville, Magnetism in reduced dimensions, C. R. Physique 6, 921 (2005) [Topical issue, Spintronics]. [5] O. Fruchart, Couches minces et nanostructures magnétiques, Techniques de l Ingénieur, E (2007) [FRENCH] [6] Lecture notes from undergraduate lectures, plus various slides: / [7] G. Chaboussant, Nanostructures magnétiques, Techniques de l Ingénieur, revue 10-9 (RE51) (2005) [8] D. Givord, Q. Lu, M. F. Rossignol, P. Tenaud, T. Viadieu, Experimental approach to coercivity analysis in hard magnetic materials, J. Magn. Magn. Mater. 83, (1990). [9] D. Givord, M. Rossignol, V. M. T. S. Barthem, The physics of coercivity, J. Magn. Magn. Mater. 258, 1 (2003). [10] J.I. Martin et coll., Ordered magnetic nanostructures: fabrication and properties, J. Magn. Magn. Mater. 256, (2003) [11] Lecture notes in magnetism: Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.49

50 Some literature (surfaces / interfaces) Moment and anisotropy of ultrathin films Magneto-elasticity in thin films U. Gradmann, Handbook of magnetic materials vol. 7, K. H.K. Buschow Ed., Elsevier, Magnetism of transition metal films, 1 (1993) D. Sander, The correlation between mechanical stress and magnetic anisotropy in ultrathin films, Rep. Prog. Phys. 62, 809 (1999) M. Farle, Ferromagnetic resonance of ultrathin metallic layers, Rep. Prog. Phys. 61, 755 (1998) P. Poulopoulos et al., K. Baberschke, Magnetism in thin films, J. Phys.: Condens. Matter 11, 9495 (1999) H. J. Elmers, Ferromagnetic Monolayers, Int. J. Mod. Phys. B 9 (24), 3115 (1995) O. Fruchart, Epitaxial self-organization: from surfaces to magnetic materials, C. R. Phys. 6, 61 (2005) Theory (misc) T. Asada et al., G. Bihlmayer, S. Handschuh, S. Heinze, P. Kurz, S. Blügel, First-principles theory of ultrathin magnetic films, J. Phys.: Condens. Matter 11, 9347 (1999) F. J. Himpsel et al., Magnetic Nanostructures, Adv. Phys. 47 (4), 511 (1998) O. Fruchart et al., Magnetism in reduced dimensions, C. R. Phys. 6, 921 (2005) P. Bruno, Theory of interlayer exchange interactions in magnetic multilayers, J. Phys.: Condens. Matter 11, 9403 (1999) Perpendicular anisotropy F. E. Gabaly et al., Noble metal capping effects on the spin-reorientation transitions of Co/Ru(0001), N. J. Phys. 10, (2008) M. T. Johnson et al., Magnetic anisotropy in metallic multilayers, Rep. Prog. Phys. 59, 1409 (1996) Exchange-bias J. Nogues et al., I. K. Schuller, Exchange bias, J. Magn. Magn. Mater 192 (2), 203 (1999). Olivier Fruchart Physics at nanoscale Devět Skal, May 30 June 3, 2011 p.50