Diapositive 1

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 ltlt 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 -
n10P10
0.8
n0
Ts
n1
0

0.12
dW/dt ?w(1 nS-1/N)G ?wG dW/dt CsdT/dt
Cs(Ts-T)/ts (ts spin diffusion time
for magnetic excitations)
Ts T0 ?wGmwts /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
(TBgtgtT1)
Coherent dynamics Towards new spin-qubits
7

Mesocopic nanomagnetism
A new direction
Rare-earths ions
Tunneling of the angular momentum J ofHo3 ions
in Y0.998Ho0.002LiF4Example of a metallic
matrix Ho3 ions in Y0.999Ho0.001Ru2Si2
Resonant microwave absorption towards spin
qubits
8
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

• Ho3 in Y0.998Ho0.002LiF4

Tetragonal symmetry (Ho in S4) (J
LS 8 gJ5/4)
Dipolar interactions mT ltlt levels
separation
9
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)
10
Hysteresis loop of Ho3 ions in YLiF4
dH/dt0.55 mT/s
11
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
-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

Acceleration of quantum dynamicsin a transverse
field
. slow sweeping field tmeas gtgt tbott gt
t1 Near thermodynamical equilibrium at the
cryostat temperature
13
Case of a metallic matrix Ho3 ions in
Y0.999Ho0.001Ru2Si2

n2
n0
n1
These steps come from tunneling transitions of
JI of single Ho3 ions, In a sea of free
electrons.
14
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 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
-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 gt t1 gtgt 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-n1/2)A/2
Two-ions Level structure Co-tunneling Biais
tunneling Diffusive tunneling
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

Single-ion level structure En nDE ?
geffmBHn/2 Tunneling gJmBHnn
(n-n)A/2 Co-tunneling gJmBHnn(n-n1/2)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
ICM2003, Rome). S. Bertaina, B. Barbara, R.
Giraud, B. Malkin, M. Vanyunin, A. Takchuk, PRB
submitted.
22
Extension to N gt2 multi-tunneling
gJmBHn(N) nA/2N ? n?-D Multi-mo
lecule resonant tunneling at gmBHn(N) nD/2N ?
n?-D Case of strong coupling (JgtgtD) S S1S2
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 gtgt Dn to
form a SMM The total energy ET ?DnSn2
DT ST2 DT ?DnSn2 / (?Sn)2 ltlt
Dn DnD and SnS DT D/N
gmBHn(N)n(D/N) ? n?-D, as for Weak
C.
Assume
DT
0
N
25

Direct check of hyperfine sublevels from EPR
In HoYLiF4 (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 of hyperfine sublevels (Dm2) 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