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

Gaussian absorption lines Important broadening by nuclear spins Loss of coherence  R ~  b ~ 30 kHz    2 ~  ~ 0.2 GHz Rabi oscillations, require larger b. N = B Max /2  =  B  2 /  ~20 Precession ~ 20 turns

Photon assisted tunneling in a SMM (Fe 8 ) Absorption of circular polarized microwaves

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

Photon induced tunnel probability P assisted = P - n ±10 P ±10 TsTs  n=0 n=1 dW/dt = ћ  (1 – n S-1 /N)  ~ ћ  dW/dt = C s dT/dt +C s (T s -T)/  s (  s = spin diffusion time for magnetic excitations) T s = T 0 + ћ  mw  s /C s Sorace et al, PRB (2003)

Environmental effects Central molecule spin Mn 12, Fe 8 Spin-bath Environmental spins Enhance tunneling Mesoscopic spins Decoherence Phonon-bath Spin-phonons transition Bottleneck (T B >>T 1 ) Electromagnetic radiation bath Spin-photons transitions (incoherent) Free carriers Strong decoherence RKKY interactions Kondo, Heavy fermions Central ionic spin Rare-earths Strong hyperfine interactions Coherent dynamics Towards new spin-qubits V 15

Rare-earths ions A new direction Tunneling of the angular momentum J of Ho 3+ ions in Y Ho LiF 4 Example of a metallic matrix: Ho 3+ ions in Y Ho Ru 2 Si 2 Mesocopic nanomagnetism Resonant microwave absorption : towards spin qubits

A new direction: Tunneling of the angular momentum of rare-earths ions A quasi- infinite number of systems for the study of mesoscopic quantum dynamics: - different CF and 4f symmetries - different concentrations - insulating, metallic, semi-conducting … Ho 3+ in Y Ho LiF 4 Tetragonal symmetry (Ho in S4); (J = L+S = 8; g J =5/4) Dipolar interactions ~ mT << levels separation

R. Giraud, W. Wernsdorfer, D. Mailly, A. Tkachuk, and B. Barbara, PRL, 87, (2001) B20 = K, B40 = mK, B44 = mK, B60 =-8.41mK, B64 = mK Sh. Gifeisman et al, Opt. Spect. (USSR) 44, 68 (1978); N.I. Agladze et al, PRL, 66, 477 (1991) Barrier short-cuts Energy barrier ( ~ 10 K) Strong mixing Singlet excited state Doublet ground-state Large  1 (Orbach process) CF levels and energy barrier of Ho 3+ in Y Ho LiF 4

Hysteresis loop of Ho 3+ ions in YLiF 4 Comparison with Mn12-ac dH/dt=0.55 mT/s Many steps ! L.Thomas, F. Lionti, R. Ballou, R. Sessoli, R. Giraud, W. Wernsdorfer, D. Mailly, A.Tkachuk, D. Gatteschi,and B. Barbara, Nature, and B. Barbara, PRL, 2001 Steps at B n = 450.n (mT) Steps at B n = 23.n (mT) Tunneling of Mn 12 -ac Molecules Tunneling of Ho 3+ ion … Nuclear spins…

Ising CF Ground-state + Hyperfine Interactions H = H CF-Z + A{J z I z + (J + I - + J - I + )/2} -7/2 7/2 5/2 3/2 -7/2 Co-Tunneling of electronic and nuclear momenta: Electro-nuclear entanglement The ground-state doublet 2(2 x 7/2 + 1) = 16 states -5/2 5/2 g J  B H n = n.A/2 A = 38.6 mK Avoided Level Crossings between |  , I z  and |  +, I z ’  if  I= (I z -I z ’ )/2= odd

dB/dt ~ 1 mT/s Acceleration of quantum dynamics in a transverse field …. slow sweeping field:  meas >>  bott >  1 Near thermodynamical equilibrium at the cryostat temperature…

n=1 n=2 Case of a metallic matrix: Ho 3+ ions in Y Ho Ru 2 Si 2 n=0 These steps come from tunneling transitions of J+I of single Ho 3+ ions, In a sea of free electrons.

Y Ho LiF 4 Ho Y Ru 2 Si 2 The resonances fields of Ho 3+ ions, in YLiF 4 and YCu 2 Si 2 are the same Y 1-  Ho  Ru 2 Si 2  ~ 0.1% Same resonance fields Many body tunneling events mediated by RKKY interactions ? Multiparticle Kondo ? Screening ? (See Stamp and Prokofiev, 1997)

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

Ising CF Ground-state + Hyperfine Interactions H = H CF-Z + A{J z I z + (J + I - + J - I + )/2} -7/2 7/2 5/2 3/2 -7/2 Co-Tunneling of electronic and nuclear momenta: Electro-nuclear entanglement The ground-state doublet 2(2 x 7/2 + 1) = 16 states -5/2 5/2 g J  B H n = n.A/2 A = 38.6 mK Avoided Level Crossings between |  , I z  and |  +, I z ’  if  I= (I z -I z ’ )/2= odd

50 mK 0.3 T/s Giraud et al, PRL 87, (2001) Additional steps at fields: H n = (23/2).n (mT) single Ho 3+ tunneling being at avoided level crossings at H n = 23.n (mT) 50 mK 200 mK 0.3 T/s Simultaneous tunneling of Ho 3+ pairs (4-bodies entanglement) Two Ho 3+ Hamiltonian avoided level crossings at H n = (23/2).n Fast measurements:  meas ~  bott >  1 >>  s

Single-ion level structure E n = n  E  g eff  B H n /2 Tunneling: g J  B H nn’ = (n’-n)A/2 Co-tunneling: g J  B H nn’ =(n’-n+1/2)A/2 Two-ions Level structure Co-tunneling Biais tunneling Diffusive tunneling

Toy model of two coupled effective spins, with g z /g x >> 1 H/J =  ij S i z S j z +  ij (S i + S j - + S j + S i - )/2 +  ij (S i + S j + + S j - S i - ) with  = (J x + J y )/4J  = (J x - J y )/4J This is why dipolar interactions induce co-tunneling Co-tunnelingDiffusive tunneling

Single-ion level structure E n = n  E  g eff  B H n /2 Tunneling: g J  B H nn’ = (n’-n)A/2 Co-tunneling: g J  B H nn’ =(n’-n+1/2)A/2 Two-ions Level structure Co-tunneling Biais tunneling Diffusive tunneling

Higher temperatures: cross-spin relaxation through excited singlets 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. -Single-ion tunneling (LT: spins-bath and phonons-bath ) - Co-tunneling (LT: spins-bath, HT: phonons-bath )

Extension to N >2 multi-tunneling g J  B H n (N) = nA/2N  n  -D Multi-molecule resonant tunneling at g  B H n (N) = nD/2N  n  -D Case of strong coupling (J>>D): S =S 1 +S 2 +…+ S N g  B H n (N)=nD …Wrong! Reason: D decreases when S increases. Multi-tunneling should fill the space between single spins tunneling Spin-glass regime Profile of  (H z /A)

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

Why D decreases when S increases: Take N spins with anisotropy energies: E n = D n S n 2 Assume they are coupled with J >> D n to form a SMM: The total energy E T =∑D n S n 2 = D T S T 2 D T = ∑D n S n 2 / (∑S n ) 2 << D n D n =D and S n =S D T = D/N g  B H n (N)=n(D/N)  n  -D, as for Weak C. … Quantum world Classical world Mn 4 Mn 12 Mn 84 Mn 30 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 DS 2 AFTER Mn 12 -ac… Co cluster Assume: DTDT N 0

Direct check of hyperfine sublevels from EPR In Ho:YLiF 4 (Malkin group) G. Shakurov et al, Appl. Magn. Res GHz

…but too small transition amplitude … RPE continue de Ho 3+ (9.5 GHz ) CaWO 4 : Same Structure as YLiF4 Almost no nuclear spins

An example of the direct observation of the anticrossing of hyperfine sublevels (  m=2) in the EPR spectra (G. Shakurov, B. Malkin, B.Barbara. Appl. Magn. Res ) 7

8 The anticrossings detected in the EPR spectra in LiYF 4 (0.1% Ho)

…but too smal transition amplitude … Continuous EPR on Ho 3+ (9.5 GHz ) CaWO 4 : Structure isomorphe à LiYF4 Amost no nuclear spins

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