Nanomagnetism Part III Atomic-scale properties

Transcription

1 Nanomagnetism Part III Atomic-scale properties Olivier Fruchart Institut Néel (CNRS-UJF-INPG) Grenoble - France

2 SKETCH OF THE LECTURES Part I Magnetization reversal Part II Techniques Part III Atomic-scale properties Olivier Fruchart IWOS MASENA Hanoi, Vietnam, Nov.2010 p.2

3 MOTIVATING THE LECTURE The need for nanomagnetism (reminder) Fundamental issues for nanomagnetism Magnetic grain media of current hard disks Is a small grain (ferro)magnetic? Count number of surface atoms 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 Decades-old (yet still modern) topic Olivier Fruchart IWOS MASENA Hanoi, Vietnam, Nov.2010 p.3

4 TABLE OF CONTENTS 1. Ferromagnetic order in low dimensions Structure and magnetic order Magnetic moments (surfaces etc.) Magnetic ordering (thermal effects) 2. Magnetic energy anisotropy 3. Interfacial effects Olivier Fruchart IWOS MASENA Hanoi, Vietnam, Nov.2010 p.4

5 1. FERROMAGNETIC ORDER Metastable phases (fcc Fe) Robustness of ferromagnetic orders Properties of bulk Fe Theory: phase diagram of fcc iron (Fe) (P,T) ambiant conditions Body-Centered Cubic (bcc) Ferromagnetic 2.2 B atom 1 Low Spin T C =1043 K T>1185 K Face-Centered Cubic (fcc, -Fe) Non-Magn. No magnetic order & Low Spin Anti-Ferro High Spin V. L. Moruzzi et al., PRB39, 6957 (1989) See also: O.K. Andersen, Physica B 86, 249 (1977) Olivier Fruchart IWOS MASENA Hanoi, Vietnam, Nov.2010 p.5

6 1. FERROMAGNETIC ORDER Metastable phases (fcc Fe) Effect of strain on the crystalline structure Magnetism of fcc Fe Fe/Cu(001) 300K growth with MBE: fcc>bcc 300K growth with PLD: fcc High-spin and low-spin fcc phases? P. Ohresser et al., PRB59, 3696 (1999) Olivier Fruchart IWOS MASENA Hanoi, Vietnam, Nov.2010 p.6

7 1. FERROMAGNETIC ORDER Metastable phases (fcc Fe) Spin-density wave antiferromagnetism Fe/Cu(001) Ferro. SDW - AF See also: H. L. Meyerheim et al., Phys. Rev. Lett. 103, (2009) D. Qian et al., PRL87, (2001) Olivier Fruchart IWOS MASENA Hanoi, Vietnam, Nov.2010 p.7

8 1. FERROMAGNETIC ORDER Surface magnetism Naive views 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 IWOS MASENA Hanoi, Vietnam, Nov.2010 p.8

9 1. FERROMAGNETIC ORDER Surface magnetism Towards single atoms 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 IWOS MASENA Hanoi, Vietnam, Nov.2010 p.9

10 1. FERROMAGNETIC ORDER Surface magnetism Polarizability and Stoner criterium Exchange polarization at interfaces Pd(D)/Ni(111)/Re(0001) Spontaneous polarization Stoner criterieum Small Rh(4d) clusters studied in flight (Stern-Gerlach experiment) TOM U. Gradmann, Handbook Fe/Pd multilayers XMCD A. J. Cox et al., PRL71, 923 (1993) A. J. Cox et al., PRB49, (1994) J. Vogel et al., PRB55, 3663 (1997) Conclusion: Pd sigifnicantly polarized over several layers Handwavy explanation based on Stoner criterium I, F 1 Conclusion: recuced bandwidth may even drive ferromagnetism Olivier Fruchart IWOS MASENA Hanoi, Vietnam, Nov.2010 p.10

11 1. FERROMAGNETIC ORDER Magnetic ordering 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 IWOS MASENA Hanoi, Vietnam, Nov.2010 p.11

12 1. FERROMAGNETIC ORDER Magnetic ordering 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-dependant 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 IWOS MASENA Hanoi, Vietnam, Nov.2010 p.12

13 1. FERROMAGNETIC ORDER Magnetic ordering Effect of lateral size H.J.Elmers et al., Phys.Rev.Lett.73, 898(94) U. Gradmann, Handbook of Magn. Mater. 7 (1993) Conclusion Tc also depends on size of islands (lateral dimensions) Olivier Fruchart IWOS MASENA Hanoi, Vietnam, Nov.2010 p.13

14 3. Magnetic anisotropy 1. Ferromagnetic order in low dimensions 2. Magnetic energy anisotropy Microscopic origins of Magnetic Anisotropy Energy (MAE) Surface versus magneto-elastic anisotropy From surfaces (2D) to atoms (0D) 3. Interfacial effects Olivier Fruchart IWOS MASENA Hanoi, Vietnam, Nov.2010 p.14

15 2. Magnetic anisotropy Basics Dipolar energy Mutual energy of two magnetic dipoles : E1,2 = µ0 3 μ. μ ( μ. r ).( μ. r ) π r 3 r2 2 Let us assume two magnetic dipoles with vertical direction, either up or down : E1,2 (θ ) = µ0 4π r 3 [ 2 µ 1µ cos θ ] cos 2 (θ C ) = 1/ 3 Parallel alignment is favored for θ < θ C Antiparallel alignment is favored for θ > θ C θ 1 Cone of alignment Conclusions Nanostructures: long axis favored Films: in-plane favored edz = 1 µ 0M Z2 2 Olivier Fruchart IWOS MASENA Hanoi, Vietnam, Nov.2010 p.15

16 2. Magnetic anisotropy Basics 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 IWOS MASENA Hanoi, Vietnam, Nov.2010 p.16

17 2. Magnetic anisotropy Basics Magneto-elastic anisotropy + => + Result Origin Distortion of orbitals & crystal field Correction to the magneto-crystalline energy Emel = K mel,1 cos 2 (θ ) +... K mel,i ~ Bi ε Olivier Fruchart IWOS MASENA Hanoi, Vietnam, Nov.2010 p.17

18 2. Magnetic anisotropy Basics 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 IWOS MASENA Hanoi, Vietnam, Nov.2010 p.18

19 2. Magnetic anisotropy Surface anisotropy Magnetic Anisotropy Energy (MAE): Link with anisotropy of orbital moment Theory Ab initio calculations Perturbation theory for 3d metals: MAE = α µ L ξ 4µ µ B L High precision needed: 1 µ ev < < 10 ev P. Bruno, PRB39, 865 (1989) does not rotate in 3d metals -> MAE reflects cost in ξ Covers magnetocrystalline, magnetoelastic and surface anisotropy Experiments Bulk (Fe, Ni, ) µ L 10 4 µ B / atom MAE 1µ ev O. Hjortstam et al., PRB55, (1997) Conclusions Origin of MAE = anisotropy of orbital moment No strict linearity depend on thickness in thin films (band structure) may alsodirect measurement of MAE preferable Olivier Fruchart IWOS MASENA Hanoi, Vietnam, Nov.2010 p.19

20 2. Magnetic anisotropy Surface anisotropy 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 IWOS MASENA Hanoi, Vietnam, Nov.2010 p.20

21 2. Magnetic anisotropy Surface anisotropy Structural relaxation Effect on anisotropy Pseudomorphic range Magneto-elastic anisotropy: Relaxation range (introduction of dislocation) k mel ~ Bmelε Strain relaxation regime: k (t ) = k bulk + α Bmel / t Conclusion: tc ε (t ) ~ (asubstrate abulk ) tc t W. A. Jesser et al., Phys. Stat. Sol. 19, 95 (1967) Mixing of surface and magneto-elastic contributions 2k S e(t ) = k V + t C. Chappert and P. Bruno., JAP64, 5736 (1988) Co/Cu(111) U. Gradmann, Appl. Phys.3, 161 (1974) Olivier Fruchart IWOS MASENA Hanoi, Vietnam, Nov.2010 p.21

22 2. Magnetic anisotropy Interface anisotropy What use? Main use in applications : perpendicular magnetic anisotropy 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 IWOS MASENA Hanoi, Vietnam, Nov.2010 p.22

23 2. Magnetic anisotropy Interface anisotropy What use? Main use in applications : perpendicular magnetic anisotropy Decreased dipolar coupling in HDD media Longitudinal recording ( ) Enhanced anisotropy for solid-state memories Concerns MRAM: Magnetic Random Access Memories C. Chappert et al., The emergence of spin electronics in data storage, Nat. Mater. 6, 813 (2007) Perpendicular recording (2005 -) Reminder for the thermal stability fo small flat elements: H c= S. N. Piramanayagam, J. Appl. Phys. 102, (2007) High anisotropy with low spread angle Reduced intra- and inter-grain dipolar coupling See lecture: Laurent RANNO 25k B T 2K 1 0 M S KV In-plane magnetization 1 K = N 0 M 2S 2 Issue: N is small with flat elements Perpendicular magnetization 1 2 K 0 M S 2 Olivier Fruchart IWOS MASENA Hanoi, Vietnam, Nov.2010 p.23

24 2. Magnetic anisotropy Interface anisotropy from 2D to atoms From surfaces (2D) to wires (1D) and atoms (0D) Views of the model systems Method XMCD STM, 8.5nm, 5.5K Fit magnetization curves Magnetic Anisotropy Energy Bulk Co: 40 ev/atom Co ML: 140 ev/atom Co bi-wire: 0.34meV/atom Co wire: 2meV/atom Co bi-atom: 3.4meV/atom Co atom: 9.2meV/atom Conclusions: Model systems to highlight trends in applied materials Anisotropy per atom increases in low dimensions P. Gambardella et al., Nature 416, 301 (2002) P. Gambardella et al., Science 300, 1130 (2003) The TOTAL anisotropy decreases Not thermally stable Olivier Fruchart IWOS MASENA Hanoi, Vietnam, Nov.2010 p.24

25 TABLE OF CONTENTS 1. Ferromagnetic order in low dimensions 2. Magnetic energy anisotropy 3. Interfacial effects Exchange bias RKKY coupling Dipolar effects Olivier Fruchart IWOS MASENA Hanoi, Vietnam, Nov.2010 p.25

26 3. INTERFACIAL EFFECTS Exchange-bias 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 IWOS MASENA Hanoi, Vietnam, Nov.2010 p.26

27 3. INTERFACIAL EFFECTS Exchange-bias: what use? Increase coercivity of layers Application Concept of spin-valve in magnetoresistive 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 IWOS MASENA Hanoi, Vietnam, Nov.2010 p.27

28 3. INTERFACIAL EFFECTS RKKY interlayer coupling 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 IWOS MASENA Hanoi, Vietnam, Nov.2010 p.28

29 3. INTERFACIAL EFFECTS RKKY interlayer coupling 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 IWOS MASENA Hanoi, Vietnam, Nov.2010 p.29

30 3. INTERFACIAL EFFECTS RKKY interlayer coupling What use? What constraints? Synthetic Ferrimagnets (SyF) Crude description What use? Increase coercivity of pinned layers Decrease intra- and inter- dot F2 F1 dipolar coupling Hypothesis: Two layers rigidly coupled Reversal modes unchanged Neglect dipolar coupling e1 M 1 e2 M 2 M= e1 e2 e K e K K= e 1 e2 AF F21 Reference layer F22 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 IWOS MASENA Hanoi, Vietnam, Nov.2010 p.30

31 3. INTERFACIAL EFFECTS Collective effects: bilayers Stacked dots : dipolar In-plane magnetization Out-of-plane magnetization Stacked dots : orange-peel coupling In-plane magnetization Always parallel coupling L. Néel, C. R. Acad. Sci. 255, 1676 (1962) (valid only for thick films) Hint: An upper bound for the dipolar coupling is the self demagnetizing field Notice: similar situation as for RKKY coupling J. C. S. Kools et al., J. Appl. Phys. 85, 4466 (1999) (valid for any films) Out-of-plane magnetization May be parallel or antiparallel J. Moritz et al., Europhys. Lett. 65, 123 (2004) Olivier Fruchart IWOS MASENA Hanoi, Vietnam, Nov.2010 p.31

32 3. INTERFACIAL EFFECTS Collective effects: range of interaction Upper bound for dipolar fields in 2D Estimation of an upper range of dipolar field in a 2D system Hd (R ) 2π rdr Non-homogeneity of dipolar fields in 2D Example: flat stripe with thickness/height = Integration r3 Local dipole: 1/r3 R Hd (R ) Cte + 1/ R Convergence with finite radius (typically thickness) Real Average Position (a.u.) Dipolar fields are weak and short-ranged in 2D or even lower-dimensionality systems Dipolar fields can be highly non-homogeneous in anisotropic systems like 2D Consequences on dot s non-homogenous state, magnetization reversal, collective effects etc. Olivier Fruchart IWOS MASENA Hanoi, Vietnam, Nov.2010 p.32

33 Some literature 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 IWOS MASENA Hanoi, Vietnam, Nov.2010 p.33

34 Online literature: Olivier Fruchart IWOS MASENA Hanoi, Vietnam, Nov.2010 p.34

35 Charte graphique ToC I. Overview of self-organization processes 1. Introduction 2. Self-assembled epitaxial growth 3. Self-organized epitaxial growth 4. Engineered and 3D self-organization 5. Perspectives of self-organization 6. X-ray investigation of SO systems Olivier Fruchart IWOS MASENA Hanoi, Vietnam, Nov.2010 p.35