Work done with

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
100 nm
50 nm x 1mm
1mm x 2 mm
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
50
S 10
103
106
Nanoparticle
Cluster
Magnetic Protein
Single Molecule

20 nm
3 nm
1 nm
2 nm
5
The molecules are regularly arranged in the
crystal
6
Mn12acetate
Mn(III) S2
Mn(IV) S3/2
Total Spin 10
7
Barrier in zero field (symmetrical)H - DSz2 -
BSz4 - E(S2 S-2) - C(S4 S-4)

Spin in a spin-bath
Isolated Spin


D
Molecule magnets large spins give extremely
small splittings Tunneling probability PLZ1
exp-p(D/h)2/gc c dH/dt
Tunneling probability PSB D2 e-?/?0
n(ED)/E0 gtgt 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
ICM94 Barbara et al, JMMM (1995) NATO-ASI,
QTM94 ed. Gunther and Barbara Thomas et al
Nature (1996) Friedman et al, PRL (1996) .
Slow quantum spin dynamics of molecule
magnets.
9
Resonance width and tunnel window Effects of
magnetic couplings and hyperfine Interactions
Data points and calculated lines
Level Scheme

• Chiorescu et al, PRL, 83, 947 (1999)
• Barbara et al, J. Phys. Jpn. 69, 383 (2000)
• Kent et al, EPL, 49, 521 (2000)

Weak HF coupling Broadens the tunnel window
(105) Decoherence mechanisms
10
Tunneling of the angular momentum of
rare-earths ions An extention of the slow
quantum dynamics studies of SMM to the cases of
strong spin-orbit and hyperfine coupling

• 0.2 Ho3 in substitution of Y3
• In YLiF4

Tetragonal symmetry (Ho in S4) (J
LS 8 gJ5/4)

Dipolar interactions 20 mK ltlt 200 mK
(levels separation)
11
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)

• R. Giraud, W. Wernsdorfer, D. Mailly, A. Tkachuk,
  and B. Barbara, PRL, 87, 057203-1 (2001)

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
Hysteresis loop of weakly interacting Ho3 ions
in YLiF4

dH/dt0.55 mT/s
Nuclear spins
13

Quasi-Ising CF Ground-state Hyperfine
Interactions H HCF-Z AJzIz (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
-5/2
-7/2
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 gtgt
tbott gt 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
T0 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-n1/2)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 S1/2 Dipolar
interactions 103 times smaller but
I7/2
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, with
gz /gx gtgt 1

• H/J ?ijSizSjz ??ij(SiSj- SjSi-)/2
  b?ij (SiSj Sj-Si-)
• with
• a (Jx Jy)/4J
  b (Jx - Jy)/4J

Co-tunneling
Diffusive 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 ltlt 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 LS 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 IJ (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).