From a single molecule to an ensemble of molecules at T ~0 :

1
From a single molecule to an ensemble of
molecules at T 0 Both tunneling rate and
decoherence increase

H - DSz2 - BSz4 - E(S2 S-2) - C(S4 S-4) -
gmBSzHz
LZ probability PLZ 1 exp-p(D/h)2/gc
D2/c

Spin-bath (Prokofiev and Stamp) PSB
(D2/w0)e-?/?0.n(ED) gtgt PLZ ?0 hyperfine
energy tunnel window Large spins
Mesoscopic tunneling (slow) Nuclear
spins Observation possible
Strong decoherence.
D
2
Barrier in zero field (symmetrical)H - DSz2 -
BSz4 - E(S2 S-2) - C(S4 S-4)
Coexistence of tunneling and hysteresis
Landau-Zener transition at avoided level
crossing (single molecule)
Thermally activated tunneling
D
H // -M New resonances at gmBHn nD (B0)
Tunneling probability P1 exp-p(D/h)2/gc
c dH/dt
3
Proposal of Morello, Stamp, Tupitsyn
4
Easy axis
Effect of a tilted field (Mn12-ac)
BT
?
B
BL
J. Appl. Phys. (1997)
5
Transverse field with constant transverse field
(Fe8)
H - DSz2 - BSz4 - E(S2 S-2) - C(S4 S-4) -
gmBSzHx - gmBSzHz
D DS2(- / Il)2S/p with - ltlt Il
D4 ? (CS2/D)S/2
D
D2 ? (E/D)S
D1 ? (Hx/DS)2S
(Parity)
6
A (small) parity effect on thermally activated
tunneling (S10)
n 0, 2
D4 ? (E/D)DS/2
0
Mn12-ac
S-1 S
-(S-1) - S
S-1 S
-(S-1) - S
n1, 3
-1
0
S-2 S-1 S
S-1 S
-(S-1) -S
-(S-1) -S
No effect of S 9
JMMM (1999)
7
Large parity effect and quantum phase
interference at low temperature (Fe8)
Mn12-2e S 10
? 0, n0
D
W. Wernsdorfer et al, PRL (2005), Science (1999)

• D ?cosy ? or D D ?siny ??
• y pgmBHx/2E(ED)1/2
• (e.g. review Tupitsyn, BB)

8

Dephasing
9
How the system escapes from the quantum regime
(Mn12-ac)
Data points and calculated lines
Level Scheme

• Chiorescu et al, PRL, 83, 947 (1999)

10

Crossover From Quantum to Classical Regime
(Mn12-ac)

t t0 exp E(H)/kTB
Activated Tunneling
Measured ( ) and Calculated ( )
Resonance Fields Barbara et al, JMMM 140-144,
1891 (1995) and J. Phys. Jpn. 69, 383 (2000)
11
Shorter timescales (ac susceptibility)
Tunneling moves to higher temperatures
12




First relaxation curves (Mn12-ac)
13
Scaling of the Quantum Dynamics of
Mn12-acM/Ms f(t/t(H,T)) Exponential to Square
Root Relaxation N. Prokofiev and P. Stamp, PRL
80, 5794 (1998)
t/t(T)
L. Thomas et al, J. Low Temp. Phys. (1998) PRL
(1999). Paulsen et al J. Low Temp (1998).
14
Sqrt(t) at in H// and H-
Calculated Energy Spectrum
Measured relaxation
Chiorescu et al, PRL (2000)
15
Resonance width and tunnel window Effects of
magnetic couplings and hyperfine Interactions
Inhomogeneous dipolar broadening and the
electronic spin-bath
Data points and calculated lines
Level Scheme
8-0
8-1

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

16




Environmental effects
Central molecule spin Mn12, Fe8
V15
Spin-bath Environmental spins Enhance
tunneling Mesoscopic spins Decoherence
Phonon-bath Spin-phonons transition Bottleneck
(TBgtgtT1)
17
Spins bath Essential
Important Phonons bath
Depends on T Important
18
V15 a large molecule with collective spin ½
15 spins ½ with AF coupled (DH215)
Time Reversal
Symmetry D0 (Kramers Theorem) Experimentally
D 80 mK. D JDg /g 50mK (Also hyperfine
interactions 20 mK)
Diagonalization of the 15-Spin ½ Hamiltoninan H
?JijSiSj (I. Tupitsyn) 200 calculated
levels. The 8 levels lowest levels
frustrated 3-spins ½ triangle Effective
hamiltonian H J ?(S1S2 S2S3 S3S4)
gmBB(S1 S2 S3) Measurements of M(H) and
?(T) confirm this picture

Müller, Döring, Angew. Chem. Intl. Engl., 27,
171 (1988)
19
Dissipative spin reversal in a two-level system
( Tlt0.1K) Effects of the phonon bath at low
temperature
Low sweeping rates / Strong coupling to the
cryostat
M(H) Irreversible
LZS transition at Finite Temperature
(dissipative)
Measured Calculated
tbotl gt t1 gt t meas Hysteresis (?Orbach
process) .
Equilibrium (Reversible) M(H)MsthH/2kT
Chiorescu et al, PRL 84, 3454 (2000) Abragam and
Bleaney (Oxford, 1970)
20
Spin temperature n1/n2exp(DH/kTs)
nT number of phonons with ?w DH
In the presence of a barrier (large
spins) Similar phonons emission Recovery to the
ground-state by Inelastic tunneling ? Gine
pv2aDH3(1n(DH))
w lt 0
w gt 0
Ts T
Ts ? T (n1/n2 constant)
Ts ltlt T
nTph nT
nTph increases rapidly
hole in the phonons density
nTph 0
Time-scales tB gtgt t1 (v dB/dt)
tB(a/DH2)tanh2(DH/2kT)
21
Now fast sweeping rates / weak coupling to the
cryostat
Adiabatic LZS Spin Rotation is recovered (Ts0,
reversible but out of equilibrium) Fit to
M (1/2)(gmB)2H/(D2(gmBH)2)1/2 ? ? ?
80 mK

Chiorescu et al PRB, 2003
22
Relaxation
Experiments

• Fit of M(t) to the Bottleneck model ? tB (B,T)

Inside D
Outside D
tB ltlt calculated value
tB (B,T) calculated
value Nuclear
spin-bath affects bottleneck
Bottleneck only
23




Environmental effects
Electromagnetic radiation bath Spin-photons
transitions (incoherent)
Central molecule spin Mn12, Fe8
V15
Spin-bath Environmental spins Enhance
tunneling Mesoscopic spins Decoherence
Phonon-bath Spin-phonons transition Bottleneck
(TBgtgtT1)