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From a single molecule to an ensemble of molecules at T ~0 :

From a single molecule to an ensemble of molecules at T ~0 : Both tunneling rate and decoherence increase. H= - DS z 2 - BS z 4 - E(S + 2 + S - 2 ) - C(S + 4 + S - 4 ) - g m B S z H z. LZ probability: P LZ = 1 – exp[- p ( D / ħ ) 2 / g c] ~ D 2 /c .

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From a single molecule to an ensemble of molecules at T ~0 :

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  1. 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

  2. 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

  3. Proposal of Morello, Stamp, Tupitsyn

  4. Easy axis Effect of a tilted field (Mn12-ac) BT ө BL B J. Appl. Phys. (1997)

  5. Transverse field with constant transverse field (Fe8) H= - DSz2 - BSz4 - E(S+2 + S-2) - C(S+4 + S-4)- gmBSzHx - gmBSzHz D ~ DS2(┴ / Il)2S/p with ┴<< Il D4 (CS2/D)S/2 D~ D2 (E/D)S D1 (Hx/DS)2S (Parity)

  6. A (small) parity effect on thermally activated tunneling (S=10) n= 0, 2… D4 (E/D)DS/2 0 Mn12-ac S-1 S -(S-1) - S S-1 S -(S-1) - S n=1, 3… -1 0 S-2 S-1 S S-1 S -(S-1) -S -(S-1) -S No effect of S = 9 JMMM (1999)

  7. [Mn12]-2e S = 10  = 0°, n=0 D Large parity effect and quantum phase interference at low temperature (Fe8) W. Wernsdorfer et al, PRL (2005), Science (1999) • = D°cosy  or D= D° siny  y = pgmBHx/[2E(E+D)]1/2 • (e.g. review Tupitsyn, BB)

  8. Dephasing

  9. Chiorescu et al, PRL, 83, 947 (1999) Bn/n = D –B[(m-n)2+n2] . Sharp or continuous transition How the system escapes from the quantum regime (Mn12-ac) Data points and calculated lines Level Scheme

  10. Classical Thermal Activation Tblocking Tc-o Ground-state Tunneling Crossover From Quantum to Classical Regime (Mn12-ac) t ~ t0 exp E(H)/kTB Activated Tunneling Measured ( ) and Calculated ( ) Resonance Fields Barbara et al, JMMM 140-144, 1891 (1995) and J. Phys. Jpn. 69, 383 (2000)

  11. Shorter timescales (ac susceptibility): Tunneling moves to higher temperatures

  12. First relaxation curves (Mn12-ac)

  13. Scaling of the Quantum Dynamics of Mn12-acM/Ms= f(t/t(H,T))Exponential to Square Root Relaxation N. Prokofiev and P. Stamp, PRL 80, 5794 (1998) t/t(T) L. Thomas et al, J. Low Temp. Phys. (1998); PRL (1999). Paulsen et al J. Low Temp (1998).

  14. Sqrt(t) at in H// and H┴ Calculated Energy Spectrum Measured relaxation Chiorescu et al, PRL (2000)

  15. Chiorescu et al, PRL, 83, 947 (1999) Barbara et al, J. Phys. Jpn. 69, 383 (2000) Kent et al, EPL, 49, 521 (2000) Homogeneous broadening of the tunnel window by nuclear spins Weak HF coupling: Broadens the tunnel window (x105) Strong decoherence • Wernsdorfer et al, PRL (1999) Prokofiev and Stamp (1998) Resonance width and tunnel window Effects of magnetic couplings and hyperfine Interactions Inhomogeneous dipolar broadening and the electronic spin-bath Data points and calculated lines Level Scheme 8-0 8-1

  16. Environmental effects Central molecule spin Mn12, Fe8 V15 Spin-bath Environmental spins Enhance tunneling Mesoscopic spins Decoherence Phonon-bath Spin-phonons transition Bottleneck (TB>>T1)

  17. Spins bath Essential Important Phonons bath Depends on T Important

  18. V15 : a large molecule with collective spin ½ 15 spins ½ with AF coupled (DH=215) Time Reversal Symmetry D=0 (Kramers Theorem) Experimentally: D ~80 mK. D ~JDg /g ~ 50mK (Also hyperfine interactions ~20 mK) Diagonalization of the 15-Spin ½ Hamiltoninan H = JijSiSj (I. Tupitsyn) 200 calculated levels. The 8 levels lowest levels frustrated 3-spins ½ triangle Effective hamiltonian: H = |J |(S1S2 + S2S3 + S3S4) – gmBB(S1 + S2 + S3) Measurements of M(H) and (T) confirm this picture Müller, Döring, Angew. Chem. Intl. Engl., 27, 171 (1988)

  19. Dissipative spin reversal in a two-level system ( T<0.1K) Effects of the phonon bath at low temperature Low sweeping rates / Strong coupling to the cryostat M(H): Irreversible LZS transition at Finite Temperature (dissipative) Measured Calculated tbotl > t1 >t meas Hysteresis (≠Orbach process) . Equilibrium (Reversible) M(H)=Msth{H/2kT} Chiorescu et al, PRL 84, 3454 (2000) Abragam and Bleaney (Oxford, 1970)

  20. Spin temperature: n1/n2=exp(DH/kTs) nT= number of phonons with ћw = DH In the presence of a barrier (large spins) Similar phonons emission: Recovery to the ground-state by Inelastic tunneling ? Gine~ pv2aDH3(1+n(DH)) w < 0 w > 0 Ts = T Ts T (n1/n2= constant) Ts << T nTph = nT nTph increases rapidly hole in the phonons density nTph ~ 0 Time-scales: tB >> t1(v = dB/dt) tB=(a/DH2)tanh2(DH/2kT)

  21. Now: fast sweeping rates / weak coupling to the cryostat Adiabatic LZS Spin Rotation is recovered (Ts~0, reversible but out of equilibrium)Fit toM = (1/2)(gmB)2H/[(D2+(gmBH)2)]1/2    80 mK Chiorescu et al PRB, 2003

  22. Fit of M(t) to the Bottleneck model tB (B,T) Relaxation Experiments Inside D Outside D tB << calculated value tB (B,T) ~ calculated value Nuclear spin-bath affects bottleneckBottleneck only

  23. Environmental effects Electromagnetic radiation bath Spin-photons transitions (incoherent) Central molecule spin Mn12, Fe8 V15 Spin-bath Environmental spins Enhance tunneling Mesoscopic spins Decoherence Phonon-bath Spin-phonons transition Bottleneck (TB>>T1)

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