Single-Molecule Magnets: A Molecular Approach to Nanomagnetism

George ChristouDepartment of Chemistry, University of Florida

Gainesville, FL 32611-7200, USA

christou@chem.ufl.edu

Single-Molecule Magnets (SMMs)

Requirements for SMMs:

1. Large ground state spin (S)

2. Negative ZFS parameter (D)

Anisotropy barrier (U) = S2|D| Integer spin

or (S2-1/4)|D| Half- integer spin

ms = -7

ms = -1ms = -2ms = -3

ms = -4

ms = -5

ms = -6

ms = -8

ms = -9

ms = -10

ms = 7

ms = 1ms = 2ms = 3

ms = 4

ms = 5

ms = 6

ms = 8

ms = 9

ms = 10

U

E

ms = 0

ms=10 -10 = ms

9 -9

8 -87 -7

6 -65 -54 -43 -32 -21-1

0

En

erg

y

Magnetization Direction (z)

The barrier to magnetization relaxation in SMMs is not due to inter-spinInteractions, as in traditional magnets, but to Ising (easy-axis) molecular anisotropy. Each molecule is a separate, nanoscale magnetic particle.

Molecular Advantages of SMMs over Traditional Nanoscale Magnetic Particles

truly monodisperse particles of nanoscale dimensions

crystalline, therefore contain highly ordered assemblies well-defined ground state spin, S

truly quantum spin systems

synthesized by room temperature, solution methods

enveloped in a protective shell of organic groups (ligands)

truly soluble (rather than colloidal suspensions) in organic solvents

the organic shell (ligands) around the magnetic core can be easily modified, providing control of e.g. coupling with the environment

Synthesis

Properties

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1

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

M/M

S

µ0H(T)

40 mK

-1 -0.5 0 0.5 1-40

-30

-20

-10

0

En

erg

y (

K)

µ0Hz (T)

-10

-9

-8

-7

10

9

8

7

Hysteresis Loops for an S = 10 SMM

S = 10 21 energy states

MS = -S, -S+1, …, S

Properties of the Mn12 family

S = 10 D = -0.40 to -0.50 cm-1 (-0.58 to -0.72 K) Magnets below 3K

The Mn12 Family of Single-Molecule Magnets (SMMs)

M n4

O 11

O 7

O 12

O 19

M n6

O 10O 3

M n2

O 4O 6

O 2

M n1

O 1O 2a

O 6a

O 1a O 3a

M n2a

O 5a

O 4aO 7a

O 11a

O 13a

O 14a

M n4aO 17a

O 21a

M n7

O 24a

O 24

O 22

O 23

O 18

O 5

O 16

M n5

O 15

M n5a

O 15a

O 16a

O 19aO 22a

O 12a

O 18a

M n6aO 20a

O 23a

O 20

O 14

O 21

O 17

O 10a

O 8a

M n3a

O 9a

O 9

M n3

O 8

O 13

Volume of the Mn12O12 magnetic core ~ 0.1 nm3

[Mn12O12(O2CR)16(H2O)4] (or Mn12)

Mn12-Ac (i.e. R = CH3) has axial symmetry (tetragonal space group I4(bar)), and has therefore been considered the best to study in detail.

Carboxylate Substitution

[Mn12O12(O2CMe)16(H2O)4] + 16 RCO2H [Mn12O12(O2CR)16(H2O)4] + 16 MeCO2H

A Mn12 Complex with Tetragonal (Axial) Symmetry: [Mn12O12(O2CCH2Br)16(H2O)4] (Mn12-BrAc)

[Mn12O12(O2CMe)16(H2O)4] + 16 BrCH2CO2H [Mn12O12(O2CCH2Br)16(H2O)4] + 16 MeCO2H

Mn3

Mn3a

Mn3b

Mn3c

Mn2c

Mn2b

Mn2aMn2

Mn1 Mn1b

Mn1a

Mn1c

--- almost no symmetry-lowering contacts between [Mn12BrAc] and the four CH2Cl2. --- in contrast to Mn12-Ac, where each molecule has strong H-bonding to 0,1, 2, 3 or 4 acetic acid molecules (Cornia et al., P.R.L. 2002, 89, 257201)

crystallizes as [Mn12-BrAc]·4CH2Cl2 tetragonal space group I42d

2 3 4 5 6

Nor

mal

ized

Tra

nsm

issi

on(a

rb. u

nits

–of

fset

)

Magnetic Field (T)

2 – sample #1

2 – sample #2a

2 – sample #2b

1 – parallel to HE

1 – 45º away from HE

A New Mn12 Complex with Tetragonal (Axial) Symmetry: [Mn12O12(O2CCH2But)16(MeOH)4]·MeOH (Mn12-ButAc)

Mn12-Ac Mn12-ButAc

I4(bar) I4(bar)

Muralee Murugesu

--- no symmetry-lowering contacts with the solvent molecules in the crystal --- bulky R group : well separated molecules

Mn12-Ac Mn12-ButAc

-1

-0.5

0

0.5

1

2.5 3 3.5 4 4.5 5 5.5

0.1 K0.6 K0.7 K0.8 K0.9 K1.0 K1.1 K1.2 K1.3 K1.4 K1.5 K1.6 K1.7 K1.8 K1.9 K2.0 K2.1 K2.2 K2.3 K2.4 K

M/M

s

0H (T)

0.002 T/s

Ground statetunneling

Excited statetunneling

-100

-80

-60

-40

-20

0

-5 -4 -3 -2 -1 0 1 2 3 4 5

En

erg

y (

K)

0Hz (T)

Ground statetunneling

Excited statetunneling

The Sharpness of the Hysteresis Loops in Mn12-ButAc allows Steps due to Excited State Tunneling to be seen

Summary: Researchers have thought for over 10 years that axial Mn12-Ac is the best one to study, but it is not. More interesting

physics is now being discovered with cleaner, truly axial Mn12 SMMs

Wernsdorfer, Murugesu and Christou, Phys. Rev. Lett., in press

Spin Injection into Mn12

One - electron additions to Mn12 in bulk

Mn12 + I - [Mn12] - + ½ I2

Mn12 + 2 I - [Mn12] 2- + I2

R E1 (V)a E2(V)b

CHCl2 0.91 0.61

C6H3(NO2)2-2,4 0.74 0.45

C6F5 0.64 0.46

CH2Cl 0.60 0.30

CH2CH3 0.02 -0.50

CH2Cl2 solution vs. ferrocene

Potential (V) -0.40.00.40.81.21.6

50 A

0.86

0.56

0.24

-0.03

0.950.64

0.34

0.91 0.61 0.29

10 A

Cu

rre

nt

CyclicVoltammetry

Differential Pulse Voltammetry

Electrochemistry Redox Potentials

added electrons localized on two Mn S does not change significantly |D| decreases with added electrons barrier decreases with added electrons

Effect of Electron Addition to Mn12

M n4

O 11

O 7

O 12

O 19

M n6

O 10O 3

M n2

O 4O 6

O 2

M n1

O 1O 2a

O 6a

O 1a O 3a

M n2a

O 5a

O 4aO 7a

O 11a

O 13a

O 14a

M n4aO 17a

O 21a

M n7

O 24a

O 24

O 22

O 23

O 18

O 5

O 16

M n5

O 15

M n5a

O 15a

O 16a

O 19aO 22a

O 12a

O 18a

M n6aO 20a

O 23a

O 20

O 14

O 21

O 17

O 10a

O 8a

M n3a

O 9a

O 9

M n3

O 8

O 13

[Mn12]2-

S -D / cm-1 Ueff / K

Mn12 10 0.4 - 0.5 60 - 65

[Mn12]- 19/2 0.3 - 0.4 40 - 50

[Mn12]2- 10 0.2 - 0.3 25 - 40

Also: Quantum Phase Interference and Spin-Parity in Mn12 Single-Molecule MagnetsPhys. Rev. Lett. 2005, 95, 037203

[Mn12]2-

Mn12

[Mn12]-

R = C6F5

19F NMR in solution

-170-170-160-160-150-150-140-140-130-130-120-120-110-110-100-100-90-90-80-80-70-70-60-60

-170-170-160-160-150-150-140-140-130-130-120-120-110-110-100-100-90-90-80-80-70-70-60-60

-170-170-160-160-150-150-140-140-130-130-120-120-110-110-100-100-90-90-80-80-70-70-60-60

o eq(III-III) o ax

(III-IV)

o eq(III-III)

o ax(III-IV)

o eq(III-III)

o ax(III-IV)

m eq(III-III)

m eq(III-III)

p eq(III-III)

p ax(III-IV)

m ax(III-IV)

p ax(III-IV)

p ax(III-III)

m ax(III-III)

p ax(III-III)

p eq(III-III)

p ax(III-IV)

m ax(III-IV)

m eq(III-III)

p ax(III-III)

m ax(III-III) m ax

(III-IV)

p eq(III-III)

m ax(III-III)

Mn4 SMMs with S = 9/2

MnIII

X

MnIV

O

MnIII

OO

MnIII

3Mn3+, Mn4+

C3v virtual core symmetry

Mn3+ Jahn-Teller axial elongations

Core ligands (X): Cl-, Br-, F-, NO3-, N3, NCO-,

OH-, MeO-, Me3SiO-, etc

Advantages

Variation in core X group, for given

organic groups

Variation in organic groups, for a

given Mn4O3X core.

Soluble and crystalline

Mn4O3X core volume ~ 0.01 nm3

Properties of Mn4 SMMs

magnetization orientation

en

erg

y

S = 9/2

D = – 0.65 to – 0.75 K

U = ΔE = (S2-1/4)|D| = 20 D

E

X OSiMe3

J34 (cm-1) -34.35

J33 (cm-1) +13.41

g 1.97

S 9/2

1st ex. state 264 cm-1

S = 9/2

MnIV

MnIII

S1 = 3/2

S2 = 2

Mn4 SMMs with S = 9/2

(2Si + 1) energy statesS = 9/2 : 10 energy states

MS = -S, -S+1, …, S

Hi = – D Ŝiz2 + Hi trans + g μB μ0 Ŝi H

D = XgµB/kB (X is the step separation)

[Mn4Pr]2

Hexagonal R3(bar)

(S6 symmetry)

Distances

C…Cl 3.71 Å

C-H…Cl 2.67 Å

Cl…Cl 3.86 Å

Angle

C-H…Cl 161.71°

Supramolecular Dimers of Mn4 SMMs:

Exchange-biased Quantum Tunnelling of Magnetization

Pr group

Quantum Tunnelling in an [Mn4]2 dimer of SMMs

using [Mn4Pr]2·MeCN (NA3)

Wernsdorfer, Christou, et al. Nature 2002, 416, 406

D = - 0.50 cm-1 = - 0.72 KJintra = - 0.07 cm-1 = - 0.1 K

R= CH3 (Ac)

R’= H

R= CH2CH3 (Pr)

R’= H

R= CH2CH3 (Pr)

R’= H

R= CH2CH3

(Pr)R’= D

Space Group R3bar R3bar R3bar R3bar

Temp(°C) 118 130 173 173

Solvent in the crystal

NA2MeCN

NA3MeCN

NA11hexane

NA3-DMeCN

(Å)Cl ··· Cl 3.739(13) 3.858(12) 3.712(10) 3.844(7)

(Å)Cl ··· C 3.600 3.706 3.664 3.721

(°)C-H··· Cl 158.15 158.00 151.94 157.36

(Å)MnIII ···MnIII 7.630 7.788 7.622 7.750

Derivatives of [Mn4O3Cl4(O2CR)3(py-p-R´)3]2 Dimers

Nuria Aliaga-Alcalde

Nature Science

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1

0.140 T/s

0.070 T/s

0.035 T/s

0.017 T/s

0.008 T/s

M/M

s

µ0H (T)

NA11

0.04 K

-1

-0.5

0

0.5

1

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

0.140 T/s0.070 T/s0.035 T/s0.017 T/s0.008 T/s0.004 T/s

M/M

s

µ0H (T)

0.04 K

NA3

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1

0.035 T/s0.017 T/s0.008 T/s0.004 T/s

M/M

s

µ0H (T)

0.04 K

NA2

Variation of Exchange-bias and Fine-structure in [Mn4]2 SMM Dimers

[Mn4Ac]2 · MeCN [Mn4Pr]2 · MeCN (Nature)

[Mn4Pr]2 · hexane (Science)

Two effects:

1) Variation in exchange-bias (Jintra)

2) Variation in fine structure (Jinter)

The properties of [Mn4]2 are very sensitive to the ligands and the solvent in the crystal

Quantum Superpositions in Exchange-coupled [Mn4]2 Dimers

-- with [Mn4Pr]2 · hexane (NA11)

Hill, Edwards, Aliaga-Alcalde, Christou, Science 2003, 302, 1015

JJzz J Jxx, J, Jyy

J´ J´

J´

Hysteresis evidence for inter-dimer exchange interactions

0

2

4

6

8

10

-0.4 0 0.4 0.8 1.2

dM

/dH

µ 0 H (T)

(-9/2,-9/2)

(-9/2,9/2)

(-9/2,-9/2)

(-9/2,7/2)

(-9/2,9/2)

(-9/2,9/2)

(9/2,9/2)

(-9/2,-9/2)

(-9/2,5/2)

(-9/2,7/2)

(-9/2,9/2)

(-9/2,9/2)

(7/2,9/2)

(9/2,9/2)

0

2

4

6

8

10

-0.4 0 0.4 0.8 1.2

dM/d

H

µ 0 H (T)

(-9/2,-9/2)

(-9/2,9/2)

(-9/2,-9/2)

(-9/2,7/2)

(-9/2,9/2)

(-9/2,9/2)

(9/2,9/2)

(-9/2,-9/2)

(-9/2,5/2)

(-9/2,7/2)

(-9/2,9/2)

(-9/2,9/2)

(7/2,9/2)

(9/2,9/2)

(↓ ↓ ↓)

(↑ ↓ ↓)

(↑ ↑ ↓)

(↑ ↑ ↑)

View down S6 axes

↓

↓ ↓

↓

R. Tiron, W. Wernsdorfer, N. Aliaga-Alcalde, and G. Christou, Phys. Rev. B 2003, 68, 140407(R)

A New Generation of Mn Clusters: A Mn84 Torus

Tasiopoulos et al. Angew. Chem. Int. Ed. 2004, 43, 2117

[Mn12O12(O2CR)16(H2O)4] + MnO4- in MeOH/MeCO2H

The structure consists of six Mn14 units i.e. [Mn14]6

~ 4 .3 n m~ 4 .3 n m

~ 1 .9 n m

~1.2 nm

Side-view

Front-view

10-5

10-3

10-1

101

103

105

107

109

0 5 10 15 20

DCAC

-6

-4

-2

0

2

4

6

-3 -2 -1 0 1 2 3

0.1 K0.3 K0.5 K0.7 K1.0 K1.5 K

S/m

ole

cule

0H (T)

0.035 T/s

(s)

1/T (1/K)

Ueff = 18 Kτ0 = 5.7 x 10-9 s

M′T vs T

M′′T vs T

S = 6

Mn4

Mn30Mn12

1 10 100 1000N

Quantum world Classical world

Mn84

Comparison of Sizes and Néel Vectors

Molecular (bottom-up) approach Classical (top-down) approach

3 nm Co nanoparticle

A meeting of the two worlds of nanomagnetism

Tasiopoulos et al. Angew. Chem. Int. Ed. 2004, 43, 2117

1.4 nm

A Mn70 Torus EtOH yields a smaller torus of five units i.e. [Mn14]5

3.7 nm

Alina VinslavaAnastasios Tasiopoulos

~ 3.7 nm

~ 1.2 nm

~ 1.4 nm

10-5

10-3

10-1

101

103

105

107

109

0 5 10 15 20

DC

(s)

1/T (1/K)

Ueff = 23 Kτ0 = 1.7 x 10-10 s

Compare Mn84: Ueff = 18 K, τ0 = 5.7 x 10-9 s

A Mn25 SMM with a Record S = 51/2 Spin for a

Molecular Species

Murugesu et al., JACS, 2004, 126, 4766A B C

S = 51/2, D = - 0.022 cm-1

green, MnIV; purple, MnIII; yellow, MnII; red, O; blue, N

S = 15/2 + 0 + 21/2 + 0 + 15/2 = 51/2 A B C B A

A B C

MnCl2 + pdmH2 + N3- + base → [Mn25O18(OH)2(N3)12(pdm)6(pdmH)6]2+

N

OHOH

pdmH2

MnIV, 18 MnIII, 6 MnII

Summary and Conclusions

• Mn12 and many other SMMs can be easily modified in various ways; this is one of

the major advantages of molecular nanomagnetism

• Two more Mn12 SMMs, Mn12BrAc and Mn12ButAc, with tetragonal (axial) symmetry

have been studied, and they exhibit data of far superior quality than Mn12Ac

“All tetragonal Mn12 complexes have axial symmetry, but some are

more axial than others” (with apologies to George Orwell, Animal

Farm)

• The techniques of molecular and supramolecular chemistry can be used to

modify the quantum properties of SMMs

• Giant SMMs represent a meeting of the two worlds of nanoscale magnetism, the

traditional (‘top-down’) and molecular (‘bottom-up’) approaches

Dr. Tasos Tasiopoulos (Mn84, Mn12)

Dr. Muralee Murugesu (Mn25)

Dr. Philippa King (Mn12, Mn18)

Nuria Aliaga (Mn4, [Mn4]2)

Nicole Chakov (Mn12)

Alina Vinslava (Mn84, Mn70)

Khalil Abboud (U. of Florida, X-ray)

Naresh Dalal (Florida State Univ) Stephen Hill (U. of Florida, Physics)

Ted O’Brien (IUPUI) Wolfgang Wernsdorfer (Grenoble)

$$ NSF and NSF/NIRT $$

Acknowledgements

[Mn12Ac] [Mn12ButAc]

S 10 10

D (K) -0.72 -0.73

Ueff (K) 64 68

DC Reduced Magnetization fit

S = 10D = - 0.51 cm-1 = - 0.73 K

AC Susceptibility

Magnetic Properties of [Mn12O12(O2CCH2But)16(MeOH)4] (Mn12ButAc)

Arrhenius Plot

Ueff = 67.8 Kτ0 = 5.58 x 10-8s

Muralee Murugesu

Landau-Zener Tunnelling (1932)

Tunnelling probability at an avoided level crossing

c

2 gB m m' 0

P 1 exp c2

dH /dt

en

erg

y

magnetic field

²

| S, m >

| S, m' >

1 P

1 - P

| S, m >

| S, m' >