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.