Initial goal:70’s: Search for « macroscopic » quantum tunneling in magnetism

Measurements on « narrow domain walls », ensemble of nanoparticles…

Outline (Mid 90’s to now)

Single-particles measurements Classical dynamics, phonons bath… quantum effects ?...

Tunneling of ensembles of large spins molecules (Mn12-ac).Slow quantum dynamics and transition to classical dynamicsSome effects of the spin bath (tunneling and decoherence).

Case of a large molecule with spins ½ (V15)A gapped spin 1/2 molecule, phonons bath

Extension to Rare-Earth ions

Role of strong hyperfine coupling, electro-nuclear entanglement,From slow to fast quantum dynamics: towards a new type of spins qubits

Nanomagnetism: From Classical to QuantumNano-particles, atomic clusters, molecules, ions.

_________

Collaborations (Louis Néel lab)

S. Bertaina (Post-doc, LLN)

R. Giraud (LPN), I. Chiorescu (FSU),

E. Bonet (LLN), W. Wernsdorfer (LLN),

L. Thomas (IBM)

Other Collaborations

D. Mailly (LPN), A. Benoit (CRTBT)

S. Gambarelli (DRF-Grenoble), A. Stepanov (Marseille)

B. Malkin, M. Vanyunin (Kazan)

H. Pascard (Palaiseau), A.M. Tkachuk (St Petersbourg), H. Suzuki (Tsukuba),

D. Gatteschi (Florence), G. Cristou (FSU) , A. Müller (Bielefeld)

Tupitsyn, Stamp and Prokof’ev

Micro-SQUID magnetometry

 

particle

Josephson junctions

stray field

≈ 1 µmM - M

H ~ Hsw

I ~ Ic

M

Large dB/dt

• Fabricated by electron beam lithography(D. Mailly, LPM, Paris)

• Sensivity ~ 10-4 0, 10-18 emu, 102 B

Superconducting Normal

W. Wernsdorfer, K. Hasselbach, D. Mailly, B. Barbara, A. Benoit, L.Thomas, JMMM, 145, 33 (1995).

Particles from micrometers to 100 nanometers Obtained by: Lithography, Electro-deposition

Measurements: Micro-Squids

100 nm

50 nm x 1m

1m x 2 m

Small ellipse Large ellipseNanowire

-1

0

1

-40 -20 0 20 40M

/M

S

H(mT)

MULTI – DOMAIN: nucleation, pinning,

propagation and annihilation of domain

walls

-1

0

1

-100 0 100

M/M

S

H(mT)

SINGLE - DOMAINSingle Nucleation

Curling

2(dH/dt,T)

<Hsw(dH/dt,T)>counts

H

0

0.5

1

0°

30°

60°90°

120°

-150°

-120°-90°

-60°

-30°

hn

S < 1

S = 1.3

S = 1.6

S = 2

S = 3

S = 6

0

0.5

1

0°

30°

60°90°

120°

-150°

-120°-90°

-60°

-30°

hsw

S < 1

S = 1.4

S = 2.4

Evidence of the « curling mode » (nanowires)

Frei, Shtrikman, D. Treves et A. Aharoni, 1957

Evidence of the 2-D Stoner-Wohlfarth astroidPhil. Trans. R. Soc.,240, 599 (1948)

5 nm 0

50

100

150

200

250

0°

30°

60°90°

120°

210°

240°270°

300°

330°

oH

sw(m

T)

FeS, filled nanotubleN. Demoncy, H. Pascard, A. Loiseau

W. Wernsforfer, E. Bonet, B. Barbara,N. Demoncy, H. Pascard, A. Loiseau,

JAP, 81, 5543 (1997).

Observation of 3D Stoner-Wohlfarth astroidand origin of the magnetic anisotropy

Josephson junctions

Co clusters (3 nm)

Interface anisotropy

M. Jamet et al, J. Magn.Magn.Mat. 237, 293-301 (2001); PRL, 86, 10 (2001) 281.

clusters

Co (20 nm) and BaFeO (10 nm)

Shape anistropy + Surface anisotropy

E. Bonet, W. Wernsdorfer, B. Barbara, A. Benoit, D. Mailly, A. Thiaville, PRL, 83, 20, 4188 (1999).

Temperature dependence of the switching fields of a 3nm Co cluster

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

-0.3 -0.2 -0.1 0 0.1 0.2 0.3

0H

z (

T)

0Hy (T)

0.04 K

1 K2 K

4 K8 K

12 K

TB 14 K ∆t ≈ 1 s

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…

2

H sw

p(H)

0

0.4

0.8

1.2

-45° 0° 45° 90° 135°

E( )

h > 0

T ° 0 K

²E kT

activation thermique

Néel-Brown model

M ~ (Min- Meq)e-t/eq

t

0e-E0(1-H/H0)3/2/kT

HMP ~ H0 [1 – (kT/E0)

2/3.(ln(/ 0vH))2/3]H(t)~ (2H0/3)(kT/E0)2/3.(ln(0T/ vH))

-1/3

- J. Kurkijärvi, PRB 6, 832 (1972)- L. Gunther and B. Barbara, PRB 49, 3926 (1994)

H

M

Hsw

Two types of measurements

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

-300 -200 -100 0 100 200 300

Flux()

H(mT)

A

AB

B

0

20

40

60

80

100

no

mb

re

HSW

2

Switching field Measurements of

the 20 nm Co particle

One switch

20nm Co particle embeeded in Carbone

-W. Wernsdorfer, E. Bonet, K. Hasselbach, A. Benoit, B. Barbara, N. Demoncy, A. Loiseau, H. Pascard, D. Mailly, Phys. Rev. Lett., 78, 1791 (1997).- B. Barbara, W. Wernsdorfer, E. Bonet, K. Hasselbach, D. Mailly, A. Benoit, M.P. Pileni, Proc. Mat. Res. Symp. 475, 265 (1997).

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

-300 -200 -100 0 100 200 300

Flux()

H(mT)

A

AB

B

0

0.2

0.4

0.6

0.8

1

0.1 1 10

T = 4 K

P(t)

t(s)

141.953 mT= 6.1 s

141.922 mT= 33.8 s

141.983 mT= 1.7 s

142

142.2

142.4

142.6

142.8

143

0 5 10 15 20[Tln(105T/(v 1/2 ))] 2/3

0.14K

2K

0.9K

1.5K

3K

H

sw

(mT

)

5K

4K

Most probable switching field Exponential relaxation and Arrhenius law

E0 ≈ 2.2 10 5 K ≈ (20 nm)3

0 ~ 4 10-9 s

D. MaillyN. Demoncy, A. Loiseau, H. Pascard

Hysteresis measurements of ferromagnetic nanoparticles made by the micro-Squid technique (last decade)Obtained by: Lithography, Electro-deposition, Arc discharge, LECBD

100 nm50 nm x 1m1m x 2 m

-1

0

1

-40 -20 0 20 40

M/M

S

H(mT)

-1

0

1

-100 0 100

M/M

S

H(mT)

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

-300 -200 -100 0 100 200 300

Flux()

H(mT)

A

AB

B

20 nm

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

-150 -100 -50 0 50 100 150

Flux()

H(mT)

Hw

0

0.2

0.4

0.6

0.8

1

0.01 0.1 1 10

T = 0.13 K

P(t)

t(s)

64.22 mT= 5.4 s

= 0.64

64.34 mT= 1.0 s

= 0.67

64.09 mT= 21.8 s

= 0.6

0

0.2

0.4

0.6

0.8

1

0.01 0.1 1 10

T = 6 K

P(t)

t(s)

62.38 mT= 0.97 s

= 1.69

62.51 mT= 0.24 s

= 1.67 62.25 mT= 8.6 s

= 1.62

62.12 mT= 40.7 s

= 1.32

Waiting time measurements

Non-exponential single particle relaxation:

Low T: < 1 Nucleation-creep Propagation (surface)

High T: > 1 Nucleation-coalescence

Macroscopic Quantum Tunneling of 105 B ?

Easy axis

Barium ferrite Insulating ferri. nanoparticle (10 nm)

3D - astroid

W. Wernsdorfer, E. Bonet, K. Hasselbach, A. Benoit, D. Mailly, O. Kubo, H. Nakano, and B. Barbara, PRL, 79, 4014, (1997)

0

0.02

0.04

0.06

0.08

0 0.5 1 1.5 2 2.5 3

Hy=250mT

Hy=180mT

Hy=0mT

particle II

T(K)

odH/dt = 10 mT

(mT)

263

263.2

263.4

263.6

263.8

264

264.2

0 2 4 6 8 10[Tln(2*10 6T/(v 1/2 ))] 2/3

0.13K 0.3K

0.5K

H

sw

(mT

)1.3K

0.9K

= 79°

0.2K

0.13-0.3K

0.5K

1.3K

0.9KT = T*

0

50

100

150

200

250

300

50 50.1 50.2 50.3 50.4 50.5 50.6

cou

nts

µoHsw(mT)

2 K1.3 K

0.9 K

0.5 K

0.15 K

N = 2000

0.2

0.4

0.6

0.8

1

1.2

0° 15° 30° 45° 60° 75° 90°

Tc(

)/T

c(4

5°)

angle

Tc=0.31 K

Teff

T

Tc() 0Ha 1/4 cot 1/ 61 cot 2/3 1

E. Chudnovsky, PRB 54, 389 (1996)

Quantum description

W. Wernsdorfer, E. Bonet, K. Hasselbach, A. Benoit, D. Mailly, O. Kubo, H. Nakano, and B. Barbara, PRL, 79, 4014, (1997)

Hy=250 mT

Hy=180 mT

Hy= 0 mT

Bigger particle

Nanometer scale

NanoparticleCluster

20 nm3 nm1 nm 2 nm

Magnetic ProteinSingle Molecule

50S = 10 103 106

Single Molecule Magnets

The molecules are regularly arranged in the crystal

Tunneling of Magnetization in Mn12-ac, S=10

-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)

Thomas et al Nature (1996); Friedman et al, PRL (1996). Barbara et al (ICM’94)

NATO ASI workshop QTM’94 Chichilianne and Grenoble (B.Barbara, L.Gunther, N.Garcia, A. Leggett).

…….

…. Slow quantum dynamics of molecule magnets spins ….

Resonances at Hn= nD/gB= 450.n mT

102

104

106

-2 -1 0

(s

ec)

H (T)

(sec

)

T(K)103

105

2 3

0 T0.44 T0.6 T0.88 T1.32 T1.76 T2.2 T2.64 T

Magnetic relaxation

Mn(IV)S=3/2

Mn(III)S=2

Total Spin =10

Mn12acetateMn12acetate

fig2

Magnetization of a single crystal of Mn12-ac

Tupitsyn and Barbara, review, Wiley-VCH (2001)

DH= 108 21

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 >

H // -M

New resonances at gBHn = nD (B=0)

Thermally activated tunneling

Landau-Zener transition at avoided level crossing

(single molecule)

Tunneling probability:

P=1 – exp[-(/ħ)2/c]

c = dH/dt

Coexistence of tunneling and hysteresis

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

ener

gy

magnetic field

²

| S, -m >

| S, m-n >

1 P

1 - P

| S, -m >

| S, m-n >

LZ probability:PLZ = 1 – exp[-(/ħ)2/c] ~ 2/c

Spin-bath (Prokofiev and Stamp):

PSB ~ (2/0)e-││/0

.n(ED) >> PLZ

0= hyperfine energy = tunnel window

Large spins Mesoscopic tunneling (slow)

Nuclear spins Observation possible Strong decoherence.

H= - DSz2 - BSz

4 - E(S+2 + S-

2) - C(S+4 + S-

4) - gBSzHz