Nanomagnetism: from atomic clusters to molecules and ions. First microwave experiments in the quantum regime. 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 (S t Petersburg) H. Suzuki (NIMS, Tsukuba, Japan) D. Gatteschi (Florence) A. Müller (Bielefeld) B. Barbara, E. Bonet, W. Wernsdorfer, Nanomagnetism group, Louis Néel Lab., CNRS, Grenoble.

The case of 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 OUTLINE Some classical and quantum aspects of nanomagnetism in magnetic nanoparticles and molecules (Brief introduction to the field) Conclusions and perspectives Effects of microwave absorption : towards spin qubits

Micro-SQUID magnetometry  ≈ 10 2 µB µB ≈ emu M - M H ~ H sw  M Large dB/dt fabricated by electron beam lithography (D. Mailly, LPM, Paris) sensitivity : I I c Superc. Normal W. Wernsdorfer, K. Hasselbach, D. Mailly, B. Barbara, A. Benoit, L. Thomas, JMMM, 145, 33 (1995).

Nanometer scale NanoparticleCluster 20 nm3 nm1 nm2 nm Magnetic ProteinSingle Molecule 50S =

Micro-SQUID array crystal size > few µm to emu temperature 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

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

Effect of a transverse field close to the anisotropy field: Telegraph noise 10 6 spins - 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) Single phonons shots Reversal up, down, up…

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

Barrier in zero field (symmetrical) H= - DS z 2 - BS z 4 - E(S S - 2 ) - C(S S - 4 ) Thermally activated tunneling If applied field // -M non-symmetrical barrier New resonances at g  B H n = nD Landau-Zener Transition at avoided level crossing (isolated system) Tunneling probability: P=1 – exp[-  (  /ħ) 2 /  c] c = dH/dt 

Tunneling of Magnetization in Mn 12 -ac 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…. Resonant tunneling at Hn =450.n mT (Steps)

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…

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 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

R. Giraud, A. Tkachuk, and B. Barbara, PRL (2003). Single-ion level structure E n =  E  g  B H n Tunneling: g  B H n = (n’-n)  E/2 Co-tunneling: g  B H n =(n’-n+1/2)  E/2  E = A) Two-ions Level structure Co-tunneling Biais tunneling Diffusive tunneling

Model of two coupled effective spins 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 - ) + (A/J)  i [ I i z S i z +1/2(I i + S i - + I i - S i + ) ] with  = (J x + J y )/2J  = (J x - J y )/4J This is why dipolar interactions induce multi-tunneling effects B. Barbara et al, ICM’03, JMMM to appear Co-tunnelingDiffusive tunneling This term becomes negligible at T>>2K

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.

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

Absorption of circular polarized microwaves (115 GHz)

Absorption of circularly polarized microwaves (115 GHz)

Absorption of circularly polarized microwaves (95 GHz)

Photon induced tunnel probability P assisted = P - n ±10 P ±10 TsTs  n=0 n=1

Photon induced line-width broadening L. Sorace, W. Wernsdorfer, C. Thirion, A-L. Barra, M. Pacchioni, D. Mailly, and B. Barbara, Phys. Rev. B 68, (2003) Multi—tunneling transitions: R. Giraud, W. Wernsdorfer, D. Mailly, A.Tkachuk, and B. Barbara, PRL, 2001

V 15 : a spin 1/2 molecule with adiabatic LZ transition. Absorption of sub-centimetric waves  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.

Frequency dependence of microwaves absorption in V 15

Resonant absorption at  =  B g ~ 0. 97

Resonant absorption + ~ Field-independent absorption  M / Ms

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

Relatively narrow Resonant absorption ~ 7 mT (15 times smaller) Still ~ 20 precession turns, and Another example: substituted magnetic wheels Fe 5 Ga  R ~  b ~ 30 kHz << 1/  2 ~  ~ 10 MHz A. Cornia, Modena

Multi-photon absorption Cr 7 Ni S = 1/2 G. A. Timco and R. E. P. Winpenny

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 10 5 with access times as short as 0.1 nanoseconds. Quantum computing in molecular magnets …Several ways…

CONCLUSION Ho 3+ in LiYF4 Evidence for tunneling of the total angular momentum J Quasi-isolated Ho 3+ ions (J and I tunnel simultaneously : co-tunneling) Pairs of Ho 3+ 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 (Fe 8 ) Evaluation of coherent precessional time in molecular magnets Most important requirement to observe Rabi oscillations: Radiation Field x 10 4 because spins are small !! Absorption width : 10 2 because of the spin-bath (Stamp, Prokfiev and Tupitsyn, )

Some perspectives Dissipation and decoherence by free carriers on 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 Ho 3+ (dipolar interactions, hyperfine interactions ~1 mK) Spin Qubits manipulated by photons in new molecular and systems.