[PPT] - From the atom to magnetic nanoparticles Edgar Bonet Laboratoire PowerPoint Presentation

SLIDE 1

From the atom to magnetic nanoparticles

Edgar Bonet Laboratoire Louis Néel CNRS – Grenoble Brasov, september 2003 S = 102 to 106 S = 1/2 to ~ 30

SLIDE 2

Magnetic scales

S = 1 10 102 103 104 105 106 108 1010 1020

1

1

1

1 M/M

S

µ0 H(T)

Fe8

1K 0.1K 0.7K

giant spin quantum tunneling, quantization quantum interference

1

1

100

100 M/M

S

µ0 H(mT)

single - domain uniform rotation curling

1

1

40
20

20 40 M/M

S

µ0 H(mT)

multi - domain nucleation, propagation and annihilation of domain walls

SLIDE 3

Giant spin molecules

Mn12 (S = 10) V15 (S = ½) Ni12 (S = 12) Fe8 (S = 10)

Single crystals
high intra-molecular couplings
low inter-molecular couplings

Collection of identical quantum systems

SLIDE 4

Giant spin model

SLIDE 5

Giant spin model

SLIDE 6

Landau-Zener tunneling

Oscillation time

|S, m> |S, m> |S, m’> |S, m’>

crossing time
keeps the same state
follows energy level

SLIDE 7

Landau-Zener tunneling

general result for a single level crossing
solution of the Schroedinger equation
L. Landau, Phys. Z. Sowjetunion 2, 46 (1932); C. Zener, Proc. R. Soc. London, Ser. A 137, 696, (1932); E.C.G.

Stückelberg, Helv. Phys. Acta 5, 369 (1932); S. Miyashita, J. Phys. Soc. Jpn. 64, 3207 (1995); V.V. Dobrovitski and A.K. Zvezdin, Euro. Phys. Lett. 38, 377 (1997); L. Gunther, Euro. Phys. Lett. 39, 1 (1997); G.Rose and P.C.E. Stamp, Low Temp. Phys. 113, 1153 (1999); M. Leuenberger and D. Loss, Phys. Rev. B 61, 12200 (2000);

M. Thorwart, M. Grifoni, and P. Hänggi, Phys. Rev. Lett. 85, 860 (2000); …

|S, m> |S, m> |S, m’> |S, m’>

SLIDE 8

1
0.5

0.5 1

1
0.5

0.5 1

v=140 mT/s v=70 mT/s v=14 mT/s v=2.8 mT/s

M/M S µ 0H(T)

40 mK

1
0.5

0.5 1

40
30
20
10

Energy (K) µ0Hz (T)

10
9
8
7

10 9 8 7

Magnetization steps

Fe8

with S = 10, D = 0.27 K, E = 0.046K A.-L. Barra et al. EPL (1996)

S = 10

SLIDE 9

Spin-parity dependent quantum tunneling

Kramers theorem: No matter how unsymmetric the crystal field, a system possessing an odd number of electrons must have a ground state that is at least doubly degenerate, even in the presence of crystal fields and spin-orbit interactions

H. A. Kramers, Proc. Acad. Sci. Amsterdam 33, 959 (1930)

Mesoscopic systems:

M. Enz and R. Schilling R.,J.Phys.C ,19 (1986) L711

J.L. Van Hemmen and S. Süto, Europhys. Lett. 1, 481 (1986)

D. Loss, D.P. DiVincenzo, and G. Grinstein, Phys. Rev. Lett., 69, 3232 (1992)
J. von Delft and C. L. Hendey, Phys. Rev. Lett., 69, 3236 (1992)

Htrans (a.u.) ∆ (a.u.) 1 10

SLIDE 10

Spin-parity dependent quantum tunneling

Environnemental effects

hyperfine interaction (nuclear spins)
dipolar interaction between molecules
exchange interaction between molecules

etc.

Phys. Rev. B 65,

180403 (2002)

S = 9/2 Ha = 4.6 T ∆0 = 1.9*10-7 K S = 8 Ha = 5.1 T ∆0 = 0.28*10-7 K S = 10 Ha = 4.0 T ∆0 = 0.94*10-7 K

SLIDE 11

Quantum phase interference (Berry phase) in single-molecule magnets

0.2 0.4 0.6 0.8 1 1.2 1.4 0.1 1 10 Tunnel splitting ²(10 -7 K) Transverse field (T) M = -10 10 ϕ - 90° ϕ - 0° ϕ - 7° ϕ - 20° ϕ - 50°

Z Y X

easy axis hard axis easy plane YZ

Htrans ϕ

SLIDE 12

Quantum phase interference (Berry phase) in single-molecule magnets

W. Wernsdorfer and R. Sessoli, Science 284, 133 (1999)

Theory: A. Garg, Europhys. Lett. 22, 205 (1993)

0.2 0.4 0.6 0.8 1 1.2 1.4 0.1 1 10 Tunnel splitting ²(10 -7 K) Transverse field (T) M = -10 10 ϕ - 0° ϕ - 7° ϕ - 20° ϕ - 50° ϕ - 90°

Z Y X

easy axis hard axis easy plane YZ

SLIDE 13

Quantum phase interference (Berry phase) in single-molecule magnets

W. Wernsdorfer and R. Sessoli, Science 284, 133 (1999)

Theory: A. Garg, Europhys. Lett. 22, 205 (1993)

Z Y X Htrans

easy axis hard axis easy plane

0.2 0.4 0.6 0.8 1 1.2 1.4 0.1 1 10 Tunnel splitting ²(10 -7 K) Transverse field (T) M = -10 10 ϕ - 0° ϕ - 7° ϕ - 20° ϕ - 50° ϕ - 90°

SLIDE 14

Parity of level crossings

W. Wernsdorfer and R. Sessoli, Science 284, 133 (1999)

0.1 1 10 100

1
0.5

0.5 1 ² (10

7 K)

µ0Hx (T) M = -10 10 M = -10 9 M = -10 8

SLIDE 15

Intermolecular interactions

(dipolar and exchange)

J/D

SMM “ideal” MM 0.001 0.01 0.1 1 10 100 [Mn4]2 Mn4 (SB1) Fe8 Mn12ac doped Fe6 Fe5Ga ? spin chains, etc.

SLIDE 16

R. Tiron,W. Wernsdorfer, C. Thirion, R. Giraud, E. Bonet, B. Barbara (LLN,

CNRS, Grenoble, France), A. Benoit (CRTBT, CNRS, Grenoble, France), D. Mailly (LPN, CNRS, Marcoussis, France), N. Aliaga, S. Bhaduri, C. Boskovic, C. Canada,

M. Soler, G. Christou (Dept. of Chemistry, Uni. of Florida, USA), E. Yang,
E. M. Rumberger, D. N. Hendrickson (Dept. of Chemistry, Uni. of California at San

Diego, USA)

Molecular dimers

SLIDE 17

Single molecule vs. Dimer

Hi = −D Si,z

2 + H i trans + gµ Bµ0

r S

i

r H

(2Si + 1) energie states Si = 9/2 : 10 levels mi = -Si, -Si+1, …, Si

H = H1 + H2 + J r S

1

r S

2

(2S1 + 1)(2S2 + 1) energie states Si = 9/2 : 100 levels m1 = -S1, -S1+1, …, S1 m2 = -S2, -S2+1, …, S2

SLIDE 18

Zeeman Diagram for the S = 9/2 dimer

Hi = −D Si,z

2 + H i trans +gµ Bµ0

r S

i

r H H = H1 + H2 + J r S

1

r S

2

100 energy states (m1,m2)

SLIDE 19

Exchange bias

bias fixed

SLIDE 20

Anisotropy & intermolecular coupling

D = g * µB/kB * X1 = 2 * 0.928/1.38 * 0.58 = 0.75 K Jtot = g * µB/kB * X2 / S = 2 * 0.928/1.38 * 0.34 / 4.5 = 0.10 K D = anisotropy constant; Jtot = coupling constant

1
0.5

0.5 1

1
0.5

0.5 1 M/M s µ0H (T) 0.04 K 0.14 T/s x1 x2

40
35
30
25
20
15
1.2
0.8
0.4

0.4 0.8 1.2 Energy(K) µ0Hz (T)

(-9/2,-9/2) (-9/2,9/2) (-9/2,7/2) (-7/2,9/2) (9/2,9/2) (9/2,7/2) (-9/2,5/2)

x2 x1

SLIDE 21

(1) (-9/2,-9/2) ? (-9/2, 9/2) ; (2) (-9/2,-9/2) ? (-9/2, 7/2) relaxes ? (-9/2, 9/2) ; (3) (-9/2, 9/2) ? ( 9/2, 9/2) ; (4) (-9/2,-9/2) ? (-9/2, 5/2) relaxes ? (-9/2, 9/2) ; (5) (-9/2, 9/2) ? ( 7/2, 9/2) relaxes ? ( 9/2, 9/2). Transitons

Tunneling in the dimer

3 3 4 4 5 5 2 2 1 1

(1) and (3) are symmetric relative to the origin;

SLIDE 22

1
0.5

0.5 1

1
0.5

0.5 1

0.560 T/s 0.140 T/s 0.035 T/s 0.008 T/s

M/M s µ0 H (T) NA11 0.04 K

1
0.5

0.5 1

1.2
0.8
0.4

0.4 0.8 1.2

0.280 T/s 0.140 T/s 0.035 T/s 0.008 T/s 0.004 T/s 0.002 T/s

M/M s µ0 H (T) 0.04 K

Inter Inter-

molecular coupling is stronger in NA11 than in NA3;

molecular coupling is stronger in NA11 than in NA3; Easier to resolve resonances (2) from (3) and (4) from (5) Easier to resolve resonances (2) from (3) and (4) from (5)

45
40
35
30
25
20
15
10
1
0.5

0.5 1 Energy (K) µ0 H z(T) 5 1 3 2 4

(-9/2,-9/2) (9/2,9/2) (9/2,7/2) (-9/2,5/2) (-7/2,9/2) (-9/2,7/2) (-9/2,9/2)

1 2 3 4 5

2x 2x Mn Mn4O O3Cl Cl4(O (O2CEt) CEt)3(py) (py)3

3 NA3

NA3

2x 2x Mn Mn4O O3Cl Cl4(O (O2CH2Cl2) )3(py) (py)3

3 NA11

NA11

SLIDE 23

0.6
0.4
0.2

0.2 0.4 0.6

0.6
0.4
0.2

0.2 0.4 0.6 Energy (K) µ0H (T)

1/2

1/2

S = 1/2

1
0.5

0.5 1

0.6
0.4
0.2

0.2 0.4 0.6 M/M s µ0 H (T) 0.04 K

Absorption of microwaves

1
0.5

0.5 1

0.6
0.4
0.2

0.2 0.4 0.6

0 s 0.1 ms 0.5 ms 1 ms 2 ms 3 ms

M/M s µ0 H (T) 0.04 K 11 GHz 0.001 T/s

period: 10 ms

V15 S = 1/2 h ν

SLIDE 24

Frequency dependence of the absorption of microwaves in V15

0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 M/M s µ0H (T)

16 GHz

0.04 K 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 M/M s µ0H (T)

15 GHz

0.04 K 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 M/M s µ0H (T)

14 GHz

0.04 K 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 M/M s µ0H (T)

13 GHz

0.04 K 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 M/M s µ0H (T)

12 GHz

0.04 K 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 M/M s µ0H (T)

11 GHz

0.04 K 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 M/M s µ0H (T)

10 GHz

0.04 K 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 M/M s µ0H (T)

9 GHz

0.04 K 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 M/M s µ0H (T)

8 GHz

0.04 K 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 M/M s µ0H (T)

7 GHz

0.04 K 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 M/M s µ0H (T)

6 GHz

0.04 K 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 M/M s µ0H (T)

5 GHz

0.04 K 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 M/M s µ0H (T)

4 GHz

0.04 K 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 M/M s µ0H (T)

3.5 GHz

0.04 K 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 M/M s µ0H (T)

3 GHz

0.04 K 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 M/M s µ0H (T)

2.5 GHz

0.04 K 0.2 0.4 0.6 0.8 1 0.1 0.2 0.3 0.4 0.5 0.6 M/M s µ0H (T)

2 GHz

0.04 K

SLIDE 25

Reducing intermolecular couplings

1
0.5

0.5 1

0.4
0.3
0.2
0.1

0.1 0.2 0.3 0.4

0.280 T/s 0.140 T/s 0.070 T/s 0.035 T/s 0.017 T/s

M/M s µ0 Hz (T)

0.04 K

0.4
0.2

0.2 0.4

5
4
3
2
1

1 Energy (K) µ0 Hz (T)

5/2

5/2

3/2
1/2

3/2 1/2

D = 0.5 K

Fe6 wheels: S = 0 Doping with Ga Fe5Ga : S = 5/2

SLIDE 26

1
0.5

0.5 1

0.4
0.3
0.2
0.1

0.1 0.2 0.3 0.4

8 dB 6 dB 5 dB 0.140 T/s

M/M s µ0 Hz (T)

0.04 K

0.00001 T/s

20 GHz

0.4
0.2

0.2 0.4

5
4
3
2
1

1 Energy (K) µ0 Hz (T)

5/2

5/2

3/2
1/2

3/2 1/2

hω D = 0.5 K

Reducing intermolecular couplings

Fe6 wheels: S = 0 Doping with Ga Fe5Ga : S = 5/2

SLIDE 27

Photon assisted tunneling

Absorption of circular polarized microwaves

10
5

5 10 Energy quantum number m

? M = +1

tunneling

? M = -1

H = 0

1
0.5

0.5

40
30
20
10

Energy (K) µ0Hz (T)

? M = ±1

10
9
8
7

10 9 8 7

h? h? h?

SLIDE 28

Absorption of circular polarized microwaves (115 GHz)

1
0.5

0.5 1

1
0.5

0.5 1 0.091 M/M s µ0H (T)

0.007 T/s

P/P0 =

1
0.5

0.5 1

1
0.5

0.5 1 0.119 M/M s µ0H (T)

0.007 T/s

P/P0 =

1
0.5

0.5 1

1
0.5

0.5 1 0.131 M/M s µ0H (T)

0.007 T/s

P/P0 =

1
0.5

0.5 1

1
0.5

0.5 1 0.151 M/M s µ0H (T)

0.007 T/s

P/P0 =

1
0.5

0.5 1

1
0.5

0.5 1 0.167 M/M s µ0H (T)

0.007 T/s

P/P0 =

1
0.5

0.5 1

1
0.5

0.5 1 0.190 M/M s µ0H (T)

0.007 T/s

P/P0 =

1
0.5

0.5 1

1
0.5

0.5 1 0.207 M/M s µ0H (T)

0.007 T/s

P/P0 =

1
0.5

0.5 1

1
0.5

0.5 1 0.237 M/M s µ0H (T)

0.007 T/s

P/P0 =

1
0.5

0.5 1

1
0.5

0.5 1 0.256 M/M s µ0H (T)

0.007 T/s

P/P0 =

1
0.5

0.5 1

1
0.5

0.5 1 0.292 M/M s µ0H (T)

0.007 T/s

P/P0 =

1
0.5

0.5 1

1
0.5

0.5 1 0.320 M/M s µ0H (T)

0.007 T/s

P/P0 =

1
0.5

0.5 1

1
0.5

0.5 1 0.366 M/M s µ0H (T)

0.007 T/s

P/P0 =

1
0.5

0.5 1

1
0.5

0.5 1 0.458 M/M s µ0H (T)

0.007 T/s

P/P0 =

1
0.5

0.5 1

1
0.5

0.5 1 0.568 M/M s µ0H (T)

0.007 T/s

P/P0 =

1
0.5

0.5 1

1
0.5

0.5 1 0.693 M/M s µ0H (T)

0.007 T/s

P/P0 =

1
0.5

0.5 1

1
0.5

0.5 1 0.841 M/M s µ0H (T)

0.007 T/s

P/P0 =

1
0.5

0.5 1

1
0.5

0.5 1 1 M/M s µ0H (T)

0.007 T/s

P/P0 =

SLIDE 29

Absorption of circular polarized microwaves (115 GHz)

1
0.5

0.5 1

1
0.5

0.5 1

0.119 0.151 0.190 0.237 0.256 0.320 0.458

M/M s µ0Hz (T)

60 mK 115 GHz 0.007 T/s P/P0 =

SLIDE 30

Absorption of circular polarized microwaves (95 GHz)

1
0.5

0.5 1

1
0.5

0.5 1

0.10 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55

M/M s µ0Hz (T)

60 mK 95 GHz 0.007 T/s