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Outline ( Mid 90’s to now)

Initial goal: 70’s: Search for « macroscopic » quantum tunneling in magnetism Measurements on « narrow domain walls », ensemble of nanoparticles…. Nanomagnetism: From Classical to Quantum Nano-particles, atomic clusters, molecules, ions . _________. Outline ( Mid 90’s to now)

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Outline ( Mid 90’s to now)

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  1. Initial goal:70’s: Search for « macroscopic » quantum tunneling in magnetismMeasurements on « narrow domain walls », ensemble of nanoparticles… Nanomagnetism: From Classical to Quantum Nano-particles, atomic clusters, molecules, ions. _________ Outline (Mid 90’s to now) Single-particles measurements Classical dynamics, phonons bath… quantum effects ?...Tunneling of ensembles of large spins molecules (Mn12-ac).Slow quantum dynamics and transition to classical dynamicsSome effects of the spin bath (tunneling and decoherence).Case of a large molecule withspins ½ (V15) A gapped spin 1/2 molecule, phonons bathExtension to Rare-Earth ionsRole of strong hyperfine coupling, electro-nuclear entanglement,From slow to fast quantum dynamics: towards a new type of spins qubits

  2. Collaborations (Louis Néel lab) S. Bertaina (Post-doc, LLN) R. Giraud (LPN), I. Chiorescu (FSU), E. Bonet (LLN), W. Wernsdorfer (LLN), L. Thomas (IBM) Other Collaborations D. Mailly (LPN), A. Benoit (CRTBT) S. Gambarelli (DRF-Grenoble), A. Stepanov (Marseille) B. Malkin, M. Vanyunin (Kazan) H. Pascard (Palaiseau), A.M. Tkachuk (St Petersbourg), H. Suzuki (Tsukuba), D. Gatteschi (Florence), G. Cristou (FSU) , A. Müller (Bielefeld) Tupitsyn, Stamp and Prokof’ev

  3. stray field particle ≈ 1 µm Josephson junctions • Fabricated by electron beam lithography (D. Mailly, LPM, Paris) • Sensivity ~ 10-4 f0, 10-18 emu, 102mB Micro-SQUID magnetometry I ~ Ic DM Large dB/dt H ~ Hsw M - M Superconducting Normal W. Wernsdorfer, K. Hasselbach, D. Mailly, B. Barbara, A. Benoit, L.Thomas, JMMM, 145, 33 (1995).

  4. Particles from micrometers to 100 nanometers Obtained by: Lithography, Electro-depositionMeasurements: Micro-Squids 100 nm 50 nm x 1mm 1mm x 2 mm Small ellipse Nanowire Large ellipse SINGLE - DOMAIN Single Nucleation Curling MULTI – DOMAIN: nucleation, pinning, propagation and annihilation of domain walls

  5. Evidence of the « curling mode » (nanowires) Frei, Shtrikman, D. Treves et A. Aharoni, 1957 Fig. 25

  6. Evidence of the 2-D Stoner-Wohlfarth astroid Phil. Trans. R. Soc.,240, 599 (1948) FeS, filled nanotuble N. Demoncy, H. Pascard, A. Loiseau 5 nm W. Wernsforfer, E. Bonet, B. Barbara, N. Demoncy, H. Pascard, A. Loiseau, JAP, 81, 5543 (1997).

  7. Observation of 3D Stoner-Wohlfarth astroid and origin of the magnetic anisotropy Josephson junctions Co (20 nm) and BaFeO (10 nm)Shape anistropy + Surface anisotropyE. Bonet, W. Wernsdorfer, B. Barbara, A. Benoit, D. Mailly, A. Thiaville, PRL, 83, 20, 4188 (1999). Co clusters (3 nm) Interface anisotropy M. Jamet et al, J. Magn.Magn.Mat. 237, 293-301 (2001); PRL, 86, 10 (2001) 281. clusters

  8. ∆t ≈ 1 s Temperature dependence of the switching fields of a 3nm Co cluster

  9. Effect of a transverse field close to the anisotropy field: Telegraph noise 106 spins Single phonons shots Reversal up, down, up… - W. Wernsdorfer, E. Bonet, K. Hasselbach, A. Benoit, B. Barbara, N. Demoncy, A. Loiseau, H. Pascard, D. Mailly, Phys. R.ev. Lett., 78, 1791 (1997) - B. Barbara et al, Proc. Mat. Res. Symp. 475, 265 (1997); Lecture Notes in Physics (2001) http://www.springer.de

  10. Néel-Brown model • M ~ (Min- Meq)e-t/t + Meq • t • 1/t = 1/t0e-E0(1-H/H0)3/2/kT • HMP ~ H0 [1 – (kT/E0)2/3.(ln(s0/ t0vH))2/3] • H(t) • sT~ (2H0/3)(kT/E0)2/3.(ln(s0T/ vH))-1/3 • - J. Kurkijärvi, PRB 6, 832 (1972) • - L. Gunther and B. Barbara, PRB 49, 3926 (1994) M H Hsw Two types of measurements

  11. Switching field Measurements of the 20 nm Co particle One switch

  12. 20nm Co particle embeeded in Carbone • W. Wernsdorfer, E. Bonet, K. Hasselbach, A. Benoit, B. Barbara, • N. Demoncy, A. Loiseau, H. Pascard, D. Mailly, Phys. Rev. Lett., 78, 1791 (1997). • - B. Barbara, W. Wernsdorfer, E. Bonet, K. Hasselbach, D. Mailly, A. Benoit, M.P. Pileni, • Proc. Mat. Res. Symp. 475, 265 (1997). N. Demoncy, A. Loiseau, H. Pascard D. Mailly E0 ≈ 2.2 10 5 K ≈ (20 nm)3 t0 ~ 4 10-9 s Exponential relaxation and Arrhenius law Most probable switching field

  13. Hysteresis measurements of ferromagnetic nanoparticles made by the micro-Squid technique (last decade)Obtained by: Lithography, Electro-deposition, Arc discharge, LECBD 1mm x 2 mm 50 nm x 1mm 100 nm 20 nm

  14. Waiting time measurements Non-exponential single particle relaxation: Low T: b < 1 Nucleation-creep Propagation (surface) High T: b > 1 Nucleation-coalescence

  15. Macroscopic Quantum Tunneling of 105mB ? Easy axis 3D - astroid Barium ferrite Insulating ferri. nanoparticle (10 nm) W. Wernsdorfer, E. Bonet, K. Hasselbach, A. Benoit, D. Mailly, O. Kubo, H. Nakano, and B. Barbara, PRL, 79, 4014, (1997)

  16. Quantum description E. Chudnovsky, PRB 54, 389 (1996) Hy=250 mT Hy=180 mT Hy= 0 mT Bigger particle Teff Tc=0.31 K T W. Wernsdorfer, E. Bonet, K. Hasselbach, A. Benoit, D. Mailly, O. Kubo, H. Nakano, and B. Barbara, PRL, 79, 4014, (1997)

  17. Nanometer scale S = 10 50 103 106 Single Molecule Magnetic Protein Cluster Nanoparticle 1 nm 2 nm 3 nm 20 nm

  18. Single Molecule Magnets The molecules are regularly arranged in the crystal

  19. Tunneling of Magnetization in Mn12-ac, S=10 Resonances at Hn= nD/gmB= 450.n mT Magnetic relaxation Thomas et al Nature (1996); Friedman et al, PRL (1996). Barbara et al (ICM’94) NATO ASI workshop QTM’94 Chichilianne and Grenoble (B.Barbara, L.Gunther, N.Garcia, A. Leggett). ……. …. Slow quantum dynamics of molecule magnets spins ….

  20. Mn12acetate Mn(III) S=2 Mn(IV) S=3/2 Total Spin =10

  21. Magnetization of a single crystal of Mn12-ac DH= 108 21 fig2 Tupitsyn and Barbara, review, Wiley-VCH (2001)

  22. Coexistence of tunneling and hysteresis Barrier in zero field (symmetrical)H= - DSz2 - BSz4 - E(S+2 + S-2) - C(S+4 + S-4) Landau-Zenertransition at avoided level crossing (single molecule) Thermally activated tunneling D H // -M New resonances at gmBHn= nD (B=0) Tunneling probability: P=1 – exp[-p(D/ħ)2/gc] c = dH/dt

  23. From a single molecule to an ensemble of molecules at T ~0 : Both tunneling rate and decoherence increase H= - DSz2 - BSz4 - E(S+2 + S-2) - C(S+4 + S-4) - gmBSzHz LZ probability: PLZ = 1 – exp[-p(D/ħ)2/gc] ~ D2/c Spin-bath (Prokofiev and Stamp): PSB~ (D2/w0)e-││/0.n(ED) >> PLZ 0= hyperfine energy = tunnel window Large spins Mesoscopic tunneling (slow) Nuclear spins Observation possible Strong decoherence. D

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