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 (St 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 ofHo3+ ions in Y0.998Ho0.002LiF4
Example of a metallic matrix: Ho3+ ions in Y0.999Ho0.001Ru2Si2
OUTLINE
Some classical and quantum aspects of nanomagnetism inmagnetic nanoparticles and molecules
(Brief introduction to the field)
Conclusions and perspectives
Effects of microwave absorption : towards spin qubits
Micro-SQUID magnetometry
10-
4
≈
102
µB
≈ 10-
18
emu
particle
Josephson junctions
stray field
≈ 1 µmM - M
H ~ Hsw
M
Large dB/dt
• fabricated by electron beam lithography
(D. Mailly, LPM, Paris) •
sensitivity :
I Ic
Superc. Normal
W. Wernsdorfer, K. Hasselbach, D. Mailly, B. Barbara, A. Benoit, L. Thomas, JMMM, 145, 33 (1995).
-1
-0.5
0
0.5
1
-150 -100 -50 0 50 100 150
Flux (/ 0)
Ni
Co
H(mT)
CoZrMoNi
Nanometer scale
NanoparticleCluster
20 nm3 nm1 nm 2 nm
Magnetic ProteinSingle Molecule
50S = 10 103 106
Micro-SQUID array
B
crystal
50 µm
• crystal size > few µm• 10-12 to 10-17 emu• temperature 0.03 - 7 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 0
50
100
150
200
250
0°
30°
60°90°
120°
210°
240°270°
300°
330°
oH
sw
(mT
)
FeS, filled nanotubleN. 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
-200
-100
0
100
200
-400 -300 -200 -100 0 100 200 300 400
oH
x(m
T)
oHy(mT)
Hy = const.
0 10 20 30 40 50 60 70t(s)
0.2 K
0.25 K
0.3 K
µoHy = 430.7 mT
106 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) http://www.springer.de
Single phonons shots
Reversal
up, down, up…
Mn(IV)S=3/2
Mn(III)S=2
Total Spin =10
Mn12acetateMn12acetate
Barrier in zero field (symmetrical)H= - DSz
2 - BSz4 - E(S+
2 + S-2) - C(S+
4 + S-4)
spin down spin up
|S,S-2> |S,-S+2>
Ground state tunneling
|S,S-1> |S,-S+1>
|S,S> |S,-S>
SZ
En
erg
y
en
erg
y
magnetic field
²
| S, -m >
| S, m-n >
1 P
1 - P
| S, -m >
| S, m-n >
Thermally activated tunneling
If applied field // -M
non-symmetrical barrierNew resonances at gBHn = 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 Mn12-ac
-1
-0,5
0
0,5
1
-3 -2 -1 0 1 2 3
1.5K
1.6K
1.9K
2.4K
M/M
S
BL (T)
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 …
Ho3+ in Y0.998Ho0.002LiF4
Tetragonal symmetry (Ho in S4); (J = L+S = 8; gJ=5/4)
Dipolar interactions ~ mT << levels separation
Hysteresis loop of Ho3+ ions in YLiF4
-1
-0,5
0
0,5
1
-3 -2 -1 0 1 2 3
1.5K
1.6K
1.9K
2.4K
M/M
S
BL (T)
Comparison with Mn12-ac
dH/dt=0.55 mT/s
-80 -40 0 40 80 120
-1,0
-0,5
0,0
0,5
1,0
200 mK 150 mK 50 mK
M/M
S
0H
z (mT)
-20 0 20 40 60 800
100
200
300
n=0n=3
n=1
n=-1
n=2
dH/dt > 0
1/ 0d
m/d
Hz (
1/T
)
Many steps !
L.Thomas, F. Lionti, R. Ballou, R. Sessoli, R. Giraud, W. Wernsdorfer, D. Mailly, A.Tkachuk,
D. Gatteschi,and B. Barbara, Nature, 1996. and B. Barbara, PRL, 2001
Steps at Bn = 450.n (mT) Steps at Bn = 23.n (mT)
Tunneling of Mn12-ac Molecules Tunneling of Ho3+ ion
… Nuclear spins…
Ising CF Ground-state + Hyperfine Interactions
H = HCF-Z + A{JzIz + (J+ I- + J- I+ )/2}
-80 -40 0 40 80 120
-1,0
-0,5
0,0
0,5
1,0
200 mK 150 mK 50 mK
M/M
S
0H
z (mT)
-20 0 20 40 60 800
100
200
300
n=0n=3
n=1
n=-1
n=2
dH/dt > 0
1/ 0d
m/d
Hz (
1/T)
-200 -150 -100 -50 0 50 100 150 200
-180,0
-179,5
-179,0
-178,5
I = 7/2
E (
K)
0H
z (mT)
-7/2
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
gJBHn = n.A/2 A = 38.6 mK
Avoided Level Crossings between |, Iz and |+, Iz’ if I= (Iz -Iz
’ )/2= odd
-75 -50 -25 0 25 50 75-1.0
-0.5
0.0
0.5
1.0
T = 30 mKv = 0.6 mT/s
HT=190 mT
HT=170 mT
HT=150 mT
HT=130 mT
HT=110 mT
HT=90 mT
HT=70 mT
HT=50 mT
HT=30 mT
HT=10 mT
M/M
S
0H
z (mT)
dB/dt ~ 1 mT/s
Acceleration of quantum dynamicsin a transverse field
…. slow sweeping field: meas >> bott > 1
Near thermodynamical equilibrium at the cryostat temperature…
-200 -150 -100 -50 0 50 100 150 200
-180,0
-179,5
-179,0
-178,5
I = 7/2
E (
K)
0H
z (mT)
50 mK0.3 T/s
120 160 200 240
0
4
8
-150 -75 0 75 150 225
0
20
40
60
-300 -200 -100 0 100 200 300-1,0
-0,5
0,0
0,5
1,0
-8 -6 -4 -2 0 2 4 6 8 10-180
-120
-60
0
60
120
180
240
n = 6
n = 7n = 8
n = 9
b)
dH/dt<0
n=1
n=0
1/ 0d
m/d
Hz (
1/T
)
0H
z (mT)
a)
M/M
S
0H
z (mT)
integer n half integer n
linear fit
0H
n = n x 23 mT
0Hn (
mT
)
n
Giraud et al, PRL 87, 057203 1 (2001)
Additional steps at fields: Hn = (23/2).n (mT)single Ho3+ tunneling being at avoided level crossings at
Hn = 23.n (mT)
50 mK0.3 T/s
Simultaneous tunneling of Ho3+ pairs (4-bodies entanglement)Two Ho3+ Hamiltonian avoided level crossings at Hn = (23/2).n
R. Giraud, A. Tkachuk, and B. Barbara, PRL (2003).
Single-ion level structure En = E gBHn
Tunneling: gBHn = (n’-n)E/2
Co-tunneling: gBHn=(n’-n+1/2)E/2
E = A)
Two-ions Level structureCo-tunnelingBiais tunnelingDiffusive tunneling
-2000 -1000 0 1000 2000
-180.0
-179.5
-179.0
-178.5
-2000 -1000 0 1000 2000
-360
-359
-358
-357
0 100 200 300 400 500
-360.0
-359.6
n=-9b)
a)
n=-8 n=3/2
. . .
. . .
mI=+5/2
mI=+7/2
mI=+5/2
mI=+7/2
I = 7/2E
ner
gy
(K)
Hz (Oe)
87654
32
1
0
En
erg
y (K
)
Hz (Oe)
n = 0
Hbias
n = 2n = 3/2n = 1/2
n = 1
En
erg
y (K
)
Hz (Oe)
Model of two coupled effective spins
H/J = ijSi
zSjz +
ij(Si
+Sj- + Sj
+Si-)/2 + ij (Si
+Sj+ + Sj
-Si-)
+
(A/J)i[IizSi
z +1/2(Ii+Si
- + Ii-Si
+)] with
= (Jx + Jy)/2J = (Jx - Jy)/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
-1
-0.5
0
0.5
1
-0.08 -0.04 0 0.04 0.08
0.136 mT/s0.068 mT/s0.034 mT/s0.017 mT/s
M/M
s
µ0H (T)
0.04 K
n=1
n=2
Case of a metallic matrix: Ho3+ ions in Y0.999Ho0.001Ru2Si2
n=0
These steps come from tunneling transitions of J+I of single Ho3+ ions,In a sea of free electrons.
Spin tunneling assisted by photons:Irradiation of a single crystal of Fe8
by circularly polarized electromagnetic radiations
-1 -0.5 0 0.5 1-40
-30
-20
-10
0
En
erg
y (
K)
µ0Hz (T)
²M = ±1
-10
-9
-8
-7
10
9
8
7
M=±1
Effects of photons and of phonons can be differenciated
Absorption of circularly polarized microwaves(115 GHz)
-1
-0.5
0
0.5
1
-1 -0.5 0 0.5 1
0
0.119
0.1510.190
0.237
0.256
0.3200.458
M/M
s
µ0Hz (T)
60 mK115 GHz
0.007 T/s
P/P 0 =
Photon induced tunnel probabilityPassisted = P - n±10P±10
10-7
10-6
10-5
10-4
10-3
10-2
10-1
0.001 0.01 0.1
P_EPRB
B
PEP
R
(au)
n = 1n = 0
Ts
0.12
0.8
n=0
n=1
V15 : a spin 1/2 molecule with adiabatic LZ transition
1
1
)(21
)(2
)(
)(
B
B
BM
BM
eq
-1
-0.5
0
0.5
1
-0.6 -0.4 -0.2 0 0.2 0.4 0.6
0 s0.1 ms0.5 ms1 ms2 ms3 ms
M/M
s
µ0H (T)
0.04 K11 GHz
0.001 T/s
period: 10 ms
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.
0
5
10
15
20
25
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
f (GHz)
f (G
Hz)
µ0Hz (T)
Resonant absorption at = B
g ~ 0. 97
Gaussian absorption lines
Important broadening by nuclear spins Loss of coherence
R ~ b ~ 30 kHz2~ ~ 0.2 GHz
Rabi oscillations, require larger b.
N = BMax/2 = B2/ ~20
Precession ~ 20 turns
tbBbB
bP 2
1222
22
2
)(2
1sin
)()(
)(
)()(4
2LL Bfb
Relatively narrow
Resonant absorption ~ 7 mT (15 times smaller)
Still ~ 20 precession turns, and
-1
-0.5
0
0.5
1
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4
8 dB6 dB5 dB0.140 T/sM
/Ms
µ0Hz (T)
0.04 K
0.00001 T/s
20 GHz
-0.4 -0.2 0 0.2 0.4-5
-4
-3
-2
-1
0
1
En
erg
y (
K)
µ0Hz (T)
-5/2 5/2
-3/2
-1/2
3/2
1/2
D = 0.5 K
Another example: substituted magnetic wheels Fe5Ga
R ~ b ~ 30 kHz << 1/2 ~ ~ 10 MHz
A. Cornia, Modena
Multi-photonabsorption
0
0.1
0.2
0.3
0.4
0.5
0.6
0 0.02 0.04 0.06 0.08 0.1
M/M
s
µ0H (T)
0 s0.2 s
0.5 s
1 s
2 s
3 s
10 s
20 s
50 s
100 s
0.587 GHz
0 0.02 0.04 0.06 0.08 0.1
-1
0
1En
erg
y (
GH
z)
B (T)
ms = -1/2
ms = 1/2
1 x h2 x h
3 x h
Cr7Ni 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 105 with access times as short as 0.1 nanoseconds.
Quantum computing in molecular magnets…Several ways…
CONCLUSION
Ho3+ in LiYF4
Evidence for tunneling of the total angular momentum J Quasi-isolated Ho3+ ions (J and I tunnel simultaneously : co-tunneling)
Pairs of Ho3+ ions (four-body entanglement)
Relevant quantum number (Kramers,..) : I+J at T < 2KCrucial 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 (Fe8) Evaluation of coherent precessional time in molecular magnets
Most important requirement to observe Rabi oscillations: Radiation Field x 104 because spins are small !!
Absorption width : 102 because of the spin-bath (Stamp, Prokfiev and Tupitsyn, 1996-2004)
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 Ho3+ (dipolar interactions, hyperfine interactions ~1 mK)
Spin Qubits manipulated by photons in
new molecular and systems.