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Absorption of microwaves

Absorption of microwaves. G Max ~ 5 s -1. W. Wernsdorfer et al , EPL (2003). . Gaussian absorption lines. Important broadening by nuclear spins Loss of coherence W R ~ g b ~ 30 kHz << 1/ t 2 ~ gs ~ 0.2 GHz Rabi oscillations, require larger b .

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Absorption of microwaves

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  1. Absorption of microwaves G Max ~ 5 s-1 W. Wernsdorfer et al , EPL (2003) .

  2. 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

  3. Photon assisted tunneling in a SMM (Fe8)Absorption of circular polarized microwaves

  4. Absorption of circular polarized microwaves(115 GHz) Sorace et al, PRB 2003

  5. Photon induced tunnel probabilityPassisted = P - n±10P±10 0.8 n=0 Ts n=1 0 0.12 dW/dt = ћw(1 – nS-1/N)G ~ ћwG dW/dt = CsdT/dt +Cs(Ts-T)/ts (ts = spin diffusion time for magnetic excitations) Ts= T0 + ћwGmwts /Cs Sorace et al, PRB (2003)

  6. Environmental effects Electromagnetic radiation bath Spin-photons transitions (incoherent) Free carriers Strong decoherence RKKY interactions Kondo, Heavy fermions Central molecule spin Mn12, Fe8 V15 Spin-bath Environmental spins Enhance tunneling Mesoscopic spins Decoherence Central ionic spin Rare-earths Strong hyperfine interactions Phonon-bath Spin-phonons transition Bottleneck (TB>>T1) Coherent dynamics Towards new spin-qubits

  7. Mesocopic nanomagnetism A new direction Rare-earths ions Tunneling of the angular momentumJ ofHo3+ions inY0.998Ho0.002LiF4Example of a metallic matrix: Ho3+ions inY0.999Ho0.001Ru2Si2 Resonant microwave absorption : towards spin qubits

  8. 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

  9. 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)

  10. 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

  11. 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

  12. 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…

  13. 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.

  14. The resonances fields of Ho3+ ions, in YLiF4 and YCu2Si2 are the same Same resonance fields Many body tunneling events mediated by RKKY interactions ? Multiparticle Kondo ? Screening ? (See Stamp and Prokofiev, 1997) Y0.998Ho0.002LiF4 Ho0.001Y0.999Ru2Si2 Y1-eHoeRu2Si2 e ~ 0.1%

  15. Effect of a transverse field: Step 2 merges with the continuous one

  16. 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

  17. Additional steps at fields: Hn = (23/2).n (mT) single Ho3+ tunneling being at avoided level crossings at Hn = 23.n (mT) Fast measurements: tmeas ~ tbott > t1 >> ts 50 mK 200 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)

  18. Single-ion level structure En = nDE  geffmBHn/2 Tunneling: gJmBHnn’ = (n’-n)A/2 Co-tunneling: gJmBHnn’=(n’-n+1/2)A/2 Two-ions Level structure Co-tunneling Biais tunneling Diffusive tunneling

  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. Single-ion level structure En = nDE  geffmBHn/2 Tunneling: gJmBHnn’ = (n’-n)A/2 Co-tunneling: gJmBHnn’=(n’-n+1/2)A/2 Two-ions Level structure Co-tunneling Biais tunneling Diffusive tunneling

  21. Higher temperatures: cross-spin relaxation through excited singlets • Single-ion tunneling • (LT: spins-bath and phonons-bath ) • - Co-tunneling • (LT: spins-bath, HT: phonons-bath ) R. Giraud et al PRL, 2003 and JMMM (also ICM’2003, Rome). S. Bertaina, B. Barbara, R. Giraud, B. Malkin, M. Vanyunin, A. Takchuk, PRB submitted.

  22. Extension to N >2 multi-tunneling gJmBHn(N) = nA/2N  n-D Multi-molecule resonant tunneling at gmBHn(N) = nD/2N  n-D Case of strong coupling (J>>D): S =S1+S2+…+ SN gmBHn(N)=nD…Wrong! Reason: D decreases when S increases. Multi-tunneling should fill the space between single spins tunneling Profile of (Hz/A) Spin-glass regime

  23. Numerical fits (Malkin, Vanyunin et al, PRB submitted)

  24. Why D decreases when S increases: Take N spins with anisotropy energies: En= DnSn2 Assume they are coupled with J >> Dn to form a SMM: The total energy ET =∑DnSn2 = DT ST2 DT = ∑DnSn2 / (∑Sn)2 << Dn Dn=D and Sn=S DT = D/N gmBHn(N)=n(D/N) n-D, as for Weak C. … AFTER Mn12-ac… Technological applications : Magnetic recording on nm scale Quantum information, Molecular electronic and spintronics,Biomedical applications…….. Incredible impact on molecular and supra-molecular chemistry. Larger and larger molecules DS2 Co cluster Mn30 Mn12 Mn84 Mn4 10 100 1000 1 Classical world Quantum world Assume: DT 0 N

  25. Direct check of hyperfine sublevels from EPR In Ho:YLiF4 (Malkin group) 250 GHz G. Shakurov et al, Appl. Magn. Res. 2005

  26. RPE continue de Ho3+ (9.5 GHz) CaWO4 : Same Structure as YLiF4 Almost no nuclear spins …but too small transition amplitude …

  27. 7 An example of the direct observation of the anticrossing ofhyperfine sublevels (Dm=2) in the EPR spectra (G. Shakurov, B. Malkin, B.Barbara. Appl. Magn. Res. 2005 )

  28. 8 The anticrossings detected in the EPR spectra in LiYF4 (0.1% Ho)

  29. Continuous EPR on Ho3+ (9.5 GHz) CaWO4 : Structure isomorphe à LiYF4 Amost no nuclear spins …but too smal transition amplitude …

  30. CONCLUSION Nanoparticles The Micro-SQUID technique : unique tool for single particles measurements (from micron to nanometer scales) Classical spins dynamics Molecular magnets Quantum Tunneling and quantum dynamics of large spins Effects of environmental degrees of freedom (spin-bath) Very short coherent time in molecular magnets (in « normal » conditions) Rare-Earth in insulating and metalic matrixes Evidence for tunneling of the total angular momentum J Crucial role of hyperfine interactions Multi-tunneling effects Coherent quantum dynamics and new type of spin-qubits

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