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B. Barbara, E. Bonet, W. Wernsdorfer, Nanomagnetism group, Louis Néel Lab., CNRS, Grenoble.

Nanomagnetism: from atomic clusters to molecules and ions . First microwave experiments in the quantum regime. B. Barbara, E. Bonet, W. Wernsdorfer, Nanomagnetism group, Louis Néel Lab., CNRS, Grenoble. PhD students L. Thomas (Versailles, IBM), I. Chiorescu (MSU),

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B. Barbara, E. Bonet, W. Wernsdorfer, Nanomagnetism group, Louis Néel Lab., CNRS, Grenoble.

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  1. Nanomagnetism: from atomic clusters to molecules and ions. First microwave experiments in the quantum regime. B. Barbara, E. Bonet, W. Wernsdorfer, Nanomagnetism group, Louis Néel Lab., CNRS, Grenoble. PhD students L. Thomas (Versailles, IBM), I. Chiorescu (MSU), C. Thirion (Durham), R. Giraud (Würzburg), R. Tiron (LLN) Collaborations with other groups D. Mailly (Marcoussis) A.M. Tkachuk (St Petersburg) H. Suzuki (NIMS, Tsukuba, Japan) D. Gatteschi (Florence) A. Müller (Bielefeld)

  2. OUTLINE Some classical and quantum aspects of nanomagnetism in magnetic nanoparticles and molecules (Brief introduction to the field) A new direction The case of rare-earths ions Tunneling of the angular momentum J ofHo3+ions in Y0.998Ho0.002LiF4Example of a metallic matrix: Ho3+ions in Y0.999Ho0.001Ru2Si2 Effects of microwave absorption : towards spin qubits Conclusions and perspectives

  3. stray field particle ≈ 1 µm Josephson junctions Micro-SQUID magnetometry H ~ Hsw M - M DM Large dB/dt • fabricated by electron beam lithography I Ic Superc. Normal (D. Mailly, LPM, Paris) • sensitivity : 10-4 F0 ≈  102 µB ≈  10-18 emu W. Wernsdorfer, K. Hasselbach, D. Mailly, B. Barbara, A. Benoit, L. Thomas, JMMM, 145, 33 (1995).

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

  5. Micro-SQUID array • crystal size > few µm • 10-12 to 10-17 emu • temperature 0.03 - 7 K • field < 1.4 T and < 20 T/s • rotation of field • transverse field • several SQUIDs at different positions • irradiation with microwaves 0.1 to 345 GHz

  6. Evidence of the 2-D Stoner-Wohlfarth astroid FeS, filled nanotuble N. Demoncy, H. Pascard, A. Loiseau 5 nm W. Wernsforfer, E. Bonnet, B. Barbara, N. Demoncy, H. Pascard, A. Loiseau, JAP, 81, 5543 (1997).

  7. 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

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

  9. Thermally activated tunneling Barrier in zero field (symmetrical)H= - DSz2 - BSz4 - E(S+2 + S-2) - C(S+4 + S-4) Landau-Zener Transition at avoided level crossing (isolated system) D If applied field // -M non-symmetrical barrier New resonances at gmBHn = nD Tunneling probability: P=1 – exp[-p(D/ħ)2/gc] c = dH/dt

  10. Tunneling of Magnetization in Mn12-ac Resonant tunneling at Hn =450.n mT (Steps) ICM’94 Barbara et al JMMM (1995); NATO ASI QTM’94 ed. Gunther and Barbara; Thomas et al Nature (1996); Friedman et al, PRL (1996); Wernsdorfer and Sessoli Science (1999); Tupitsyn and Barbara « Magneto Science, Wiley, NY (review, 2001)… see cond/mat…. ….Slow quantum spin dynamics of molecule magnets….

  11. A new direction:Tunneling of the angular momentum of rare-earthsions A quasi- infinite number of systems for the study of mesoscopic quantum dynamics: - different CF and 4f symmetries - different concentrations - insulating, metallic, semi-conducting … Ho3+ in Y0.998Ho0.002LiF4 Tetragonal symmetry (Ho in S4); (J = L+S = 8; gJ=5/4) Dipolar interactions~ mT << levels separation

  12. Comparisonwith Mn12-ac Many steps ! L.Thomas, F. Lionti, R. Ballou, R. Sessoli, R. Giraud, W. Wernsdorfer, D. Mailly, A.Tkachuk, D. Gatteschi,and B. Barbara, Nature, 1996. and B. Barbara, PRL, 2001 Steps at Bn = 450.n (mT)Steps at Bn = 23.n (mT) Tunneling of Mn12-ac Molecules Tunneling of Ho3+ ion … Nuclear spins… Hysteresis loop of Ho3+ ions in YLiF4 dH/dt=0.55 mT/s

  13. Ising CF Ground-state +Hyperfine InteractionsH =HCF-Z+A{JzIz +(J+I-+ J- I+ )/2} The ground-state doublet 2(2 x 7/2 + 1) = 16 states -7/2 -5/2 5/2 7/2 7/2 5/2 3/2 -7/2 gJmBHn = n.A/2 A = 38.6 mK Avoided Level Crossings between |, Iz and |+, Iz’ if DI= (Iz -Iz’ )/2= odd Co-Tunneling of electronic and nuclear momenta: Electro-nuclear entanglement

  14. dB/dt~ 1 mT/s Acceleration of quantum dynamicsin a transverse field …. slow sweeping field: tmeas >> tbott > t1 Near thermodynamical equilibrium at the cryostat temperature…

  15. Additional steps at fields: Hn = (23/2).n (mT) single Ho3+ tunneling being at avoided level crossings at Hn = 23.n (mT) 50 mK 0.3 T/s 50 mK 0.3 T/s Simultaneous tunneling of Ho3+ pairs (4-bodies entanglement) Two Ho3+ Hamiltonian avoided level crossings at Hn = (23/2).n Giraud et al, PRL 87, 057203 1 (2001)

  16. R. Giraud, A. Tkachuk, and B. Barbara, PRL (2003). Single-ion level structure En = DE  gmBHn Tunneling: gmBHn = (n’-n)DE/2 Co-tunneling: gmBHn=(n’-n+1/2)DE/2 (DE = A) Two-ions Level structure Co-tunneling Biais tunneling Diffusive tunneling

  17. Model of two coupled effective spins H/J = ijSizSjz + ij(Si+Sj- + Sj+Si-)/2 + bij(Si+Sj+ + Sj-Si-) + (A/J)i[IizSiz +1/2(Ii+Si- + Ii-Si+)] with a = (Jx + Jy)/2J b = (Jx - Jy)/4J This term becomes negligible at T>>2K Diffusive tunneling Co-tunneling This is why dipolar interactions induce multi-tunneling effects B. Barbara et al, ICM’03, JMMM to appear

  18. Case of a metallic matrix: Ho3+ ions in Y0.999Ho0.001Ru2Si2 n=2 n=0 n=1 These steps come from tunneling transitions of J+I of single Ho3+ ions, In a sea of free electrons.

  19. Spin tunneling assisted by photons: Irradiation of a single crystal of Fe8 by circularly polarized electromagnetic radiations DM=±1 Effects of photons and of phonons can be differenciated

  20. Absorption of circularly polarized microwaves(115 GHz)

  21. Photon induced tunnel probabilityPassisted = P - n±10P±10 0.8 Ts n=0 n=1 0.12 0

  22. V15 : a spin 1/2 molecule with adiabatic LZ transition Absorption of sub-centimetric waves G Max ~ 5 s-1 I. Chiorescu, W. Wernsdorfer, A. Müller, H. Boggë, and B. Barbara et al, PRL (2000) W. Wernsdorfer, D.Mailly, A. Müller, and B. Barbara, EPL, to appear. .

  23. Resonant absorption at n = gB g ~ 0. 97

  24. Gaussian absorption lines • Important broadening by nuclear spins Loss of coherence • WR ~ gb ~ 30 kHz << 1/t2~ gs~ 0.2 GHz Rabi oscillations, require larger b. N = BMax/2ps = gBt2/2p ~20 Precession ~ 20 turns

  25. Another example: substituted magnetic wheels Fe5Ga A. Cornia, Modena Relatively narrow Resonant absorption ~ 7 mT (15 times smaller) Still ~ 20 precession turns, and WR ~ gb ~ 30 kHz << 1/t2 ~ gs ~ 10 MHz

  26. Multi-photonabsorption Cr7Ni S = 1/2 G. A. Timco and R. E. P. Winpenny

  27. Quantum computing in molecular magnets…Several ways… Leuenberger & Loss, NATURE, 410, 791 (2001) • implementation of Grover's algorithm • storage unit of a dynamic random access memory device. • fast electron spin resonance pulses can be used to decode and read out stored numbers of up to 105 with access times as short as 0.1 nanoseconds.

  28. CONCLUSION Ho3+ in LiYF4 Evidence for tunneling of the total angular momentum J Quasi-isolated Ho3+ ions (J and I tunnel simultaneously : co-tunneling) Pairs of Ho3+ions (four-body entanglement) Relevant quantum number (Kramers,..) : I+J at T < 2K Crucial role of the anisotropic character of dipolar interactions Metals: spin tunneling in the presence free carriers Molecular magnets Hidden multi-tunneling effects Tunneling assisted by photons: Highly non-linear effects (Fe8) Evaluation of coherent precessional time in molecular magnets Most important requirement to observe Rabi oscillations: Radiation Field x 104because spins are small !! Absorption width : 102because of the spin-bath (Stamp, Prokfiev and Tupitsyn, 1996-2004)

  29. Some perspectives Dissipation and decoherence by free carrierson spin tunneling in metals (Kondo, heavy fermions, spintronics) Higher order many-body tunneling and decoherence by the environment (quantum phase transitions) Rabi oscillations and spin-echo experiment on electronic states of - Molecular magnets (intra-molecules hyperfine interactions ~10 mK) - Entangled E-N pairs of Ho3+ (dipolar interactions, hyperfine interactions ~1 mK) Spin Qubits manipulated by photons in new molecular and systems.

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