Experiments on the spin-bath in spin-tunneling systems B. Barbara

1. Experiments on the spin-bath in spin-tunneling systems B. Barbara Louis Néel Lab., CNRS, Grenoble. Work done with W. Wernsdorfer (LLN), L. Thomas (IBM), I. Chiorescu (FSU), R. Giraud (LPN) Collaborations with other groups B. Malkin (Kazan) A.M. Tkachuk (St Petersburg) D. Gatteschi (Florence) A. Müller (Bielefeld) D. Mailly (LPN, Marcoussis)

2. 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

3. Temperature dependence of the switching field distribution of a single nanoparticle (Co, 25 nm) s ~ T2/3 Low temperature noise: energy barrier fluctuations: « free » spins, nuclear spins. PRL, 78, 1791 (1997).

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

5. The molecules are regularly arranged in the crystal

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

7. Thermally activated tunneling Barrier in zero field (symmetrical)H= - DSz2 - BSz4 - E(S+2 + S-2) - C(S+4 + S-4) Spin in a spin-bath Isolated Spin D Molecule magnets: large spins give extremely small splittings Tunneling probability: PLZ=1 – exp[-p(D/ħ)2/gc] c = dH/dt Tunneling probability: PSB = D2 e-││/0 n(ED)/E0>> PLZ 0= tunnel window = hyperfine energy If applied field // -M non-symmetrical barrier New resonances at gmBHn = nD

8. Tunneling of magnetization in Mn12-ac: « Technical » hysteresis loop + resonant tunneling Steps at Hn =450.n mT 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); ….Slow quantum spin dynamics of molecule magnets….

9. Chiorescu et al, PRL, 83, 947 (1999) Barbara et al, J. Phys. Jpn. 69, 383 (2000) Kent et al, EPL, 49, 521 (2000) Inhomogeneous dipolar broadening and the electronic spin-bath 8-0 8-1 Homogeneous broadening of the tunnel window by nuclear spins: • Wernsdorfer et al, PRL (1999) Prokofiev and Stamp (1998) Resonance width and tunnel window Effects of magnetic couplings and hyperfine Interactions Data points and calculated lines Level Scheme Weak HF coupling: Broadens the tunnel window (105) Decoherence mechanisms

10. Tunneling of the angular momentum of rare-earthsionsAn extention of the slow quantum dynamics studies of SMM to the cases of strong spin-orbit and hyperfine coupling Tetragonal symmetry (Ho in S4); (J = L+S = 8; gJ=5/4) 0.2 % Ho3+ in substitution of Y3+ In YLiF4 Dipolar interactions ~ 20 mK << 200 mK (levels separation)

11. R. Giraud, W. Wernsdorfer, D. Mailly, A. Tkachuk, and B. Barbara, PRL, 87, 057203-1 (2001) CF levels and energy barrier of Ho3+ in Y0.998Ho0.002LiF4 Strong mixing Barrier short-cuts Singlet excited state + Doublet ground-state + Large t1 (Orbach process) Energy barrier ( ~ 10 K) B20 = 0.606 K, B40 = -3.253 mK, B44 =- 42.92 mK, B60 =-8.41mK, B64 =- 817.3mK Sh. Gifeisman et al, Opt. Spect. (USSR) 44, 68 (1978); N.I. Agladze et al, PRL, 66, 477 (1991)

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 Hysteresis loop of weakly interacting Ho3+ ions in YLiF4 dH/dt=0.55 mT/s … Nuclear spins…

13. Quasi-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 -5/2 gJmBHn = n.A/2 A = 38.6 mK, Linewidth ~ 10 mK ~ Dip. Int. Avoided Level Crossings between |, Iz and |+, Iz’ if DI= (Iz -Iz’ )/2= odd Co-Tunneling of electronic and nuclear momenta: Electro-nuclear entanglement

14. Application of a transverse magnetic field: Cross-over between « classical » and quantum paramagnet (slow sweeping field: tmeas >> tbott > t1, near thermodynamical equilibrium at the cryostat temperature) Acceleration of quantum dynamics Vanishing of the remanent magnetization: Mechanism for the QPT: strong single-ions mixing quantum fluctuations in the spin-bath destroy the local moment (C/Q paramagnet) At lowT/high concentration, M should vanish when D= -Z 0, leading to T=0 collective fluctuations above the GS, destroying LR order Nature of the mixing: entangled electro-nuclear states (other types of mixings in QPT with heavy fermions, cupratres, 2D elctron gas, …)

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 due to dipolar interactions (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)A/2 Co-tunneling: gmBHn=(n’-n+1/2)A/2 (A= Ho hyperfine constant) Two-ions Level structure Electronic Spin-bath: Co-tunneling Biais tunneling Diffusive tunneling Nuclear spin-bath (Li, F, Y): Linewidths

17. . G. Shakurov, B. Malkin, B.Barbara, Appl. Magn. Res. 2005 Ho-dimer satellites in the EPR signal in 7LiYF4 (1% Ho): Bias-tunneling transitions Boris Malkin group, Kazan In the 7Li 0.1% sample the width of single ions ~3.5 mT and of dimers ~ 2mT

18. V15 , a molecule with S=1/2 Dipolar interactions 103 times smaller but I=7/2 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, 2004 .

19. Toy model of two coupled effective spins, withgz /gx >> 1 H/J = ijSizSjz + ij(Si+Sj- + Sj+Si-)/2 + bij(Si+Sj+ + Sj-Si-) with a = (Jx + Jy)/4J b = (Jx - Jy)/4J Diffusive tunneling Co-tunneling This is why dipolar interactions induce co-tunneling

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

21. CONCLUSION Molecular magnets Coexistence of classical hysteresis loop and resonant tunneling (Landau-Zener, spin-bath) Observation of tunneling possible and strong decoherence: due to the spin-bath Observation of Rabi oscillations and manipulations of molecule spins will require ns synchronized pulses Highly diluted Ho3+ in LiYF4 Evidence for tunneling of the total angular momentum J = L+S of Ho3+ ions Quasi-isolated Ho3+ ions: J and I tunnel simultaneously (in a metal also: Ho in YSi2Ru2). Relevant quantum number of Ho3+ is not J but I+J (Kramers, QPT…). Co-tunneling, bias-tunneling, spin-diffusion in Ho3+ dimmers (four-body entanglements) Co-tunneling of distant dimmers is observed. Crucial role of the anisotropic character of dipolar interactions. Microscopic basis for the study of QPT (concentrated systems) and coherent quantum dynamics (highly diluted).