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Magnetic Properties of C 60 Polymers Antonis N. Andriotis

Magnetic Properties of C 60 Polymers Antonis N. Andriotis Institute of Electronic Structure and Laser, (IESL), Foundation for Research and Technology – Hellas, (FORTH), P.O.Box 1527, 71110 Heraklio, Crete, Greece andriot@iesl.forth.gr Lexington, KY, 07 April 2004

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Magnetic Properties of C 60 Polymers Antonis N. Andriotis

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  1. Magnetic Properties of C60 Polymers Antonis N. Andriotis Institute of Electronic Structure and Laser, (IESL), Foundation for Research and Technology – Hellas, (FORTH), P.O.Box 1527, 71110 Heraklio, Crete, Greece andriot@iesl.forth.gr Lexington, KY, 07 April 2004 Work supported by the EU-GROWTH research project AMMARE (G5RD-CT-2001-00478) “New Nanoscale Materials for Advanced Magnetic Storage Devices”

  2. Collaborators Prof. Madhu Menon (Center for Computational Sciences and Dpt. of Physics and Astronomy, Univ. of Kentucky, Lexington, KY) Dr. R. Michael Sheetz (Center for Computational Sciences, Univ. of Kentucky, Lexington, KY) Prof. Leonid Chernozatonskii (Institute of Biochemical Physics, Russian Academy of Sciences, Moscow)

  3. Outline • Computational methods used • Magnetism in C-based materials - Some (representative) experimental results - Proposed theoretical models • Ferromagnetism of Rh-C60 : Present work • Features of C-based FMs • Conclusions

  4. Computational methods used • Tight Binding Molecular Dynamics (TBMD) Orthogonal Non-orthogonal [Menon-Subbaswamy, PR B50, 11577 (1994)] Real space and k-space calculations • Ab initio methods (at B3LYP level of approximation) (Gaussian 98)

  5. Magnetism in C-based materials • Some (Representative) Experimental results

  6. Experimental resultsMagnetism in carbon-based materials Rh-C60 • Pressure polymerized fullerenes ; Rh-C60 at 1,020-1,050 K [T.L.Makarova et al (Nature, 413, 716 (2001)] • Activated Carbon Fibers (ACFs) [Shibayama et al, PRL 84, 1744 (2000)] • Fluorinated graphite [Panich et al JPCS 62, 959 (2001)] • Carbon foam [Umemoto et al PRB 64, 193409 (2001)] • TDAE-C60B.Narymbetov et al, Nature, 407, 883 (2000); T.Sato et al, PRB 55, 11052 (1997) ] • p-nitrophenyl-nitronyl-nitroxide P-nnn

  7. Experimental resultsMagnetism in carbon-based materials Rh-C60 • Pressure polymerized fullerines ; Rh-C60 at 1,020-1,050 K [T.L.Makarova et al (Nature, 413, 716 (2001)] • Activated Carbon Fibers (ACFs) [Shibayama et al, PRL 84, 1744 (2000)] (Mean size 30 Å and one spin per ACF leads to inter-spin distance of 30Å.)Exchange interaction between localized non-bonding -electrons mediated by conducting -electrons similar to the s-d interaction.Charge transfer interaction between edge states and the -bands favors the development of the conduction-electron-mediated interaction network. • Fluorinated graphite [Panich et al JPCS 62, 959 (2001)] Paramagnetism is caused by local moments of dangling bonds the latter resulting from the reaction of a F and a C atom which converts an sp2 to an sp3 bond. Strong exchange between these moments may be mediated by a C-C bond. • Carbon foam [Umemoto et al PRB 64, 193409 (2001)]

  8. Experimental resultsMagnetism in TDAE- C60 • TDAE-C60 [Tc = 16 K ] [ B.Narymbetov et al, Nature, 407, 883 (2000); T.Sato et al, PRB 55, 11052 (1997) ] (donor-acceptor type material) • Key feature for FM-ism to appear : Mutual orientation of adjacent fullerene molecules • Existence of two phases(FM, PM) associated withtwopossible bonding configurations (6-6 , 5-6)  FMism appears when Magn. Energy > Config. Energy. - Resonance structure effect ?

  9. TDAE-C60 : Properties • It is a donor-acceptor type magnetic material • Monoclinic structure • Unusually short distances between neighbouring C60 molecules • -form Ferromagnetic ; ’-form : Paramagnetic ; ’-form turns to -form by annealing • T(Curie)=16 K • No band-FM-ism; no SPM-ism; it is a nearly isotropic Heisenberg ferromagnet.

  10. Experimental resultsMagnetism in p-nnn • p-nitrophenyl-nitronyl-nitroxide • p-nitrophenyl-nitronyl-nitroxide : 1st made purely organic FM

  11. Experimental resultsMagnetism in p-nnnK.Awaga and Y.Maruyama, CPL 158, 556 (1989) • p-nitrophenyl-nitronyl-nitroxide • It exhibits a quinoid resonance structure • Dipole-dipole interact. • Spin polarization effect is probably enhanced by n- exchange interaction (n=el-ns in nitro group)

  12. Experimental results (1)Magnetic polymerized fullerenes • In pressure polymerized fullerenes the magnetic phase appears when fullerene cages are about to break down (formation of graphitized fullerenes) • From a set of samples prepared at nominally identical conditions only part of samples show magnetism ; the determination of the structural difference between magnetic and non-magnetic sampleshas not been achieved by conventional characterization methods.

  13. Experimental results (2)Magnetic polymerized fullerenes • Samples are polymeric and crystalline • Samples contain impurities. However, magnetism is not influenced by them • Samples gave no indication of superparamagnetism

  14. Experimental results (3)Magnetic polymerized fullerenes • The magnetic phase appears as islands in a non magnetic matrix forming stripe domains as well as corrugated domain patterns • Sample-magnetism is determined by preparation conditions

  15. Magnetism in C-based materials • Some (Representative) Experimental results • Theory : Proposed models for : - Mechanisms leading to unpaired electrons - FM coupling among unpaired electrons

  16. THEORY Mechanisms leading to unpaired electrons Mechanisms leading to FM coupling of unpaired electrons

  17. Theory : Mechanisms leading to unpaired electrons (1a) [M.Hjort and S.Stafstrom, PR B61, 14089 (2000)] • Vacancies in graphite create new states below EF . These states contribute an extra -electron localized at the vacancy. • For non-interacting vacancies this extra electron gives rise to an unpaired spin

  18. Theory : Mechanisms leading to unpaired electrons (1b) [A.A.El-Barbary et al, PR B68, 144107 (2003)] • Formation of pentagon-one dangling bond (5-1db)

  19. Theory : Mechanisms leading to unpaired electrons (2) • Edge carbon atoms[K.Harigaya, CPL 340, 123 (2001)] • Shift of one layer relative to the neighbouring ones necessary for bulk magnetic appearance • Defect sites (or active side atoms A,B,A’,B’) and interlayer coupling affect magnetic properties

  20. Theory : Mechanisms leading to unpaired electrons (3) Stone-Wales defects [Kim et al, PR B68, 125420 (2003)] Tetrapod (Negative gaussian curvature) [Park et al PRL, 91, 237204 (2003)]

  21. Stone-Wales defect • A 90 degrees local bond rotation in a graphitic network leads to the formation of two heptagons and two pentagons • Static (dynamic) activation barrier for formation 8-12 (3.6) eV in SWCNs

  22. Magnetism in C-based MaterialsSynopsis (1a) • Theory : Origin of unpaired spins - Disorder C-atoms(vacancies) Localized spins in (disordered) C-materials are most probably due to - electrons localized at the vacancy. - Edge states (on zig-zag edge-carbon atoms) [Yoshiwaza et al, Carbon 32, 1517 (1994); Fujita et al JPSJ 65, 1920 (1996)] The localized spins are considered to originate from the nonbonding edge states of the -electron.

  23. Magnetism in C-based MaterialsSynopsis (1b) • Theory : Origin of FM coupling • Exchange interaction between localized non-bonding -electrons mediated by conducting -electrons similar to the s-d interaction.Charge transfer interaction between edge states and the -bands favors the development of the conduction-electron-mediated interaction network (case of activated carbon fibers). • Strong exchange between magnetic moments may be mediated by a C-C bond (case of fluorinated graphite).

  24. Geometric frustration upon polymerization Avoiding frustration • Avoid geometrical frustration by stress-driven bond selection • Applied anisotropic stress selects the directions of bonding [L.Marques et al, PR B68, 193408 (2003)] Frustrated C60 polymer

  25. Geometric frustration and FM-ism M.J.Harris et al, PRL 79, 2554 (1997) H.Tsunetsugu and Y. Motome, PR B68, 060405 (2003) The presence of local Ising anisotropy leads to a geometrically frustrated g.s. In the presence of a magnetic field, magnetic order develops Pyrochlore lattice

  26. Geometric frustration and FM-ism[O.Tchernyshyov et al PRL, 88, 067203 (2002)] • The geometrically frustrated system is revealed by the vast degeneracy of its g.s. • It undergoes a magnetic Jahn-Teller (“spin-Teller”) distortion • The lifting of frustration may be achieved through a coupling between spin and lattice degrees of freedom (elastic versus magnetic energy)

  27. Magnetism in C-based materials • Some (Representative) Experimental results • Theory : Proposed models leading to : - Mechanisms leading to unpaired electrons - FM coupling among unpaired electrons • Our results

  28. Polymeric fullerenes Orthorombic Tetragonal Rombohedral T<650 K , P~1-9GPa T>650 K ; P~2GPa T~1000-1100 K ; P=6GPa • Tetragonal and Rombohedral polymeres are 2D (along <110> and <111> directions respectively) ; interlayer coupling of van der Waals type as in graphite. The orthorombic phase is 3D.

  29. Methods for synthesizing C60-polymers • Photochemical methods They lead to a distorted fcc structure with isotropic polymerization along all nn directions • High Pressure – High Temperature (HP-HT) They lead to ordered structures • All polymers exhibit the same polymeric bond : 2+2 cycloaddition

  30. 2+2 66/66 cycloaddition 1 2 3 4 • In the 1-4 atoms (all with sp3 bonds) of the cycloaddition bond there is accumulation of negative charge leading to a higher occupancy of the pz orbital (z-axis perpendicular to plane of 4-atoms). • Defects in C60 molecules do not change this feature • Defects in C60 molecules accumulate positive charge

  31. 2+2 cycloadditionS.Okada and A.Oshiyama, PR B68, 235402 (2003) • In C60(65)-polymer : a=9.19 A ; c=24.5 A ; r(C-C)=1.56 A metallic, non-magnetic ; E(ABC)  E(ECB) E(per atom) = 0.702-0.719 eV • In C60(66)-polymer : r(C-C)=1.64 A semiconductor ; indirect gap 0.5 E(ABC)=E(ACB) ; E(per atom)= 0.428 eV

  32. C60 versus Rh-C60 • In C60-polymers the distance between the C60 molecules is ~9.1-9.2 A. In non polymerized systems the distance is ~10 A. • Polymerized C60 is a geometrically frustrated system.

  33. C60 - Band Gap : 2.3-2.5eV (1.6 eV Xu-Scuseria PRL 74, 274 (1995) - Diameter : 7.1 Å Rh-C60 [ “66/66” 2+2 cycloaddition bonds 1.64 Å] [Xu-Scuseria PRL 74, 274 (1995)] - Band Gap 1.0 eV - Diameter of C60 7.1 Å d(C60 -C60 )=9.17 (9.2exp ) Å (in plane) d(C60 -C60 ) = 9.8 Å (interplane) Inclusion of “56” bonding makes material less stable but with vanishing gap C60 versus Rh-C60

  34. Various 2D and 1D polymeric C60-based structures[ A.N.Andriotis et al, PRL 90, 026801 (2003) ] • (a), (b), (c ) contain sp3and sp2 bonded C-atoms • (d) contains only sp2bonded C-atoms

  35. 2D rhombohedralC60 (Rh-C60) with vacancies • Vacancies appear among carbon atoms colored in red in the above picture; sp3 bonded C-atoms (resulting from the 2+2-cycloaddition mechanism at the C60-interfaces) are shown in green.

  36. Turning on e-e correlationsValues of soth(in eV) for different structures considered in this work (TBMD calculation). • Structure No vacancy • (a)Rd-C600.85 • (b)Tetragonal1.00 • (c)Linear A0.70 • (d)Linear B0.80

  37. Turning on e-e correlationsValues of soth(in eV) for different structures considered in this work. • Structure No With vacancy vacancy • (a)Rd-C600.850.03 • (b)Tetragonal1.000.20 • (c)Linear A0.700.10 • (d)Linear B0.800.70

  38. Magnetic Moment of Rd-C60 • SQUID magnetometry on Rh-C60 : • Sample-mass  3.2 mgr • Msat 0.2 G 1.29 B / 2C60 • (in high quality samples it reaches 1B / C60 ) • <  >  0.01 B per atom • U  10 eV (exp) • so= U < >/2 0.05 eV

  39. Band Structure Results(TBMD calculation) • Energies along the -M (-X) direction for the hexagonal (square) structures. In particular, • For Rh-C60the band energies (in eV) along the -M directionhave the following dispersion (setting EF =0.00 and with degeneracies in parenthesis): -0.20(1), 0.00(2), 0.20(1), 1.26(1), 1.35(1). • For the square-C60the corresponding dispersion structure in the -X direction is : -0.08(1), 0.02(1),0.12(1), 1.30(1), 2.19(1); No degeneracy

  40. Band Structure of Rh-C60 • Band energies along the -M direction • Band at EF is doubly degenerate

  41. Band Structure of defect free C60 • (Top) : S.Okada and S.Saito PR B57, 4039 (1997). (Energies measured with respect to top of valence band). • (Bottom) : A.V.Okotrub et al JCP, 115, 5637 (2001)

  42. Band Structure of defect free C60S.Okada and A.Oshiyama, PR B68, 235402 (2003) • The C60(65)-polymer is : metallic, non-magnetic ; E(per atom) = 0.702-0.719 eV • The C60(66)-polymer is: semiconductor ; indirect gap 0.5 E(per atom)= 0.428 eV

  43. C60- C60 dimer (Ab initio calculations) • atoms participating in the C60- C60 coupling : - are all sp3 - accumulate0.5 |e| (in pz) - not affected by vacancy • atoms surrounding each vacancy (3 per vacancy) : - loose 0.5 |e| - Electric dipole moment 2.264 Debye per C60 - are related with the appearance of non-zero m.m.

  44. C60- C60 dimer (Ab initio calculations) Atoms participating in the C60- C60 coupling accumulate0.5 |e| mainly in the pz orbital Thus, in Rh-C60 moments favor FM alignment while in tetragonal C60 this is more difficult to be achieved

  45. Atomic charges from Natural population analysis • Atoms in red box (40, 44, 60, 62) participate in 2+2 cycloaddition • Atoms in blue boxes surround vacancies

  46. Charge-wave along C60-dimer ?

  47. Synopsis (2) Characteristic features ofRh-C60 • It has high symmetry • It has a degenerate ground state • It exhibits defects • It develops intra-molecular charge transfer and large electric dipole moment • It has flat bands at EF

  48. Synopsis (2) Characteristic features ofRh-C60 • It has high symmetry • It has a degenerate ground state • It exhibits defects • It develops intra-molecular charge transfer and large electric dipole moment • It has flat bands at EF • These appear in one way or the other as basic properties of non-metallic FM-nets

  49. Rh-C60 : I-V characteristics Symmetric bias Asymmetric bias

  50. Electron DOS of Rh-C60

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