Initial goal: 70’s: Search for « macroscopic » quantum tunneling in magnetism Measurements on « narrow domain walls », ensemble of nanoparticles… Outline (Mid 90’s to now) Single-particles measurements Classical dynamics, phonons bath… quantum effects ?... Tunneling of ensembles of large spins molecules (Mn 12 -ac). Slow quantum dynamics and transition to classical dynamics Some effects of the spin bath (tunneling and decoherence). Case of a large molecule with spins ½ (V 15 ) A gapped spin 1/2 molecule, phonons bath Extension to Rare-Earth ions Role of strong hyperfine coupling, electro-nuclear entanglement, From slow to fast quantum dynamics: towards a new type of spins qubits Nanomagnetism: From Classical to Quantum Nano-particles, atomic clusters, molecules, ions. _________

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

Micro-SQUID magnetometry M - M H ~ H sw I ~ I c  M Large dB/dt Fabricated by electron beam lithography (D. Mailly, LPM, Paris) Sensivity ~  0, emu, 10 2  B Superconducting Normal W. Wernsdorfer, K. Hasselbach, D. Mailly, B. Barbara, A. Benoit, L.Thomas, JMMM, 145, 33 (1995).

Particles from micrometers to 100 nanometers Obtained by: Lithography, Electro-deposition Measurements: Micro-Squids 100 nm 50 nm x 1  m 1  m x 2  m Small ellipseLarge ellipseNanowire MULTI – DOMAIN: nucleation, pinning, propagation and annihilation of domain walls SINGLE - DOMAIN Single Nucleation Curling

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

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

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

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

Effect of a transverse field close to the anisotropy field: Telegraph noise 10 6 spins - 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) Single phonons shots Reversal up, down, up…

Néel-Brown model M ~ (M in - M eq )e -t/   eq t  0 e -E0(1-H/H 0 ) 3/2 /kT H MP ~ H 0 [1 – (kT/E 0 ) 2/3.(ln(    /  0 v H )) 2/3 ] H(t)    ~  (2H 0 /3)(kT/E 0 ) 2/3.(ln(  0 T/ v H )) -1/3 - J. Kurkijärvi, PRB 6, 832 (1972) - L. Gunther and B. Barbara, PRB 49, 3926 (1994) H M H sw Two types of measurements

Switching field Measurements of the 20 nm Co particle One switch

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). Most probable switching field Exponential relaxation and Arrhenius law E 0 ≈ K ≈ (20 nm) 3  0 ~ s D. MaillyN. Demoncy, A. Loiseau, H. Pascard

Hysteresis measurements of ferromagnetic nanoparticles made by the micro-Squid technique (last decade) Obtained by: Lithography, Electro-deposition, Arc discharge, LECBD 100 nm 50 nm x 1  m1  m x 2  m 20 nm

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

Macroscopic Quantum Tunneling of 10 5  B ? Easy axis Barium ferrite Insulating ferri. nanoparticle (10 nm) 3D - astroid W. Wernsdorfer, E. Bonet, K. Hasselbach, A. Benoit, D. Mailly, O. Kubo, H. Nakano, and B. Barbara, PRL, 79, 4014, (1997)

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

Nanometer scale NanoparticleCluster 20 nm3 nm1 nm2 nm Magnetic ProteinSingle Molecule 50S =

Single Molecule Magnets The molecules are regularly arranged in the crystal

Tunneling of Magnetization in Mn 12 -ac, S=10 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 …. Resonances at H n = nD/g  B = 450.n mT Magnetic relaxation

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

fig2 Magnetization of a single crystal of Mn12-ac Tupitsyn and Barbara, review, Wiley-VCH (2001) D H =

Barrier in zero field (symmetrical) H= - DS z 2 - BS z 4 - E(S S - 2 ) - C(S S - 4 ) H // -M New resonances at g  B H n = nD (B=0) Thermally activated tunneling Landau-Zener transition at avoided level crossing (single molecule) Tunneling probability: P=1 – exp[-  (  /ħ) 2 /  c] c = dH/dt  Coexistence of tunneling and hysteresis

 From a single molecule to an ensemble of molecules at T ~0 : Both tunneling rate and decoherence increase  LZ probability: P LZ = 1 – exp[-  (  /ħ) 2 /  c] ~  2 /c Spin-bath (Prokofiev and Stamp): P SB ~ (  2 /  0 )e -│  │/  0.n(E D ) >> P LZ  0 = hyperfine energy = tunnel window Large spins Mesoscopic tunneling (slow) Nuclear spins Observation possible Strong decoherence. H= - DS z 2 - BS z 4 - E(S S - 2 ) - C(S S - 4 ) - g  B S z H z