Single-Molecule Magnets (SMMs):A Molecular (Bottom-up) Approach to Nanoscale

Magnetic Materials

George ChristouDepartment of Chemistry, University of Florida

Gainesville, FL 32611-7200, USA

Lecture 1:The Mn12 Family of Single-Molecule Magnets

Single-Molecule Magnets (SMMs)Molecular Nanomagnets

magnetism intrinsic to the molecule;each molecule is a separate, nanoscale

magnetic particle

Types of Magnetic Materials

MagnetismTraditional Magnets

3D arrays of metal atoms or ions(metals, metal alloys, metal oxides

e.g. magnetite - Fe3O4)

Single-Chain Magnets (SCMs)

magnetism due to 1-D chains

Molecular Magnets

3D arrays of linked, interacting molecules

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�� ��� ����� !��� � �������"�

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

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� ��

�

�� ��� �� � � ��� �����

�

#����$

� �����% ����"��������%�

The barrier to magnetization relaxation in SMMs is not due to intermolecularinteractions (as in traditional magnets) but to zero-field splitting (ZFS).

( ) 44

44

22 ˆBˆˆ OSSE yx +−04

04

2z

ˆBSD O+ HSg B ⋅�

�����������������

HSSSESD BYXZ ⋅+−+= ˆg)ˆˆ(ˆ 222 µH

rm Zeeman te termrhombic termaxial ++=H

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 separations between molecules, coupling with the environment, etc.

Synthesis

Properties

Major Potential Applications of SMMs

Quantum Computing- the use of quantum bits (qubits) rather than classical bits

as in present computation methods.- requires SMMs capable of existing in quantum

superpositions of two (or more) statesi.e. 1 and 0 instead of classical 1 or 0.

- requires SMM to show appropriate quantum properties.

Digital Information Storage- the storage of information at the molecular level as the

orientation direction of the magnetization vector. - each molecule stores one bit of information.- estimated 104 increase in storage density over present

devices.- requires ordered arrays of SMMs, either 2-D surfaces (present technology) or 3-D crystals (future technology).

Frequency-dependent out-of-phaseAC susceptibility signals (�M˝)

Hysteresis loops (with steps due to quantum tunneling of the

magnetization)

Experimental Identification of SMMs

They display the slow magnetization relaxation (reorientation) ratesof single-domain superparamagnets, even though they are much smaller

and the properties arise from a different origin (not long-range co-operativity)

Quantum Tunneling of the Magnetization (QTM)SMM’s are true mesoscale particles. They exhibit the macroscale

property of hysteresis, and the microscale property of QTM through the anisotropy barrier

Barrier (U) = S2|D| for integer S

= (S2-1/4)|D| for half-integer S

Therefore, U < Ueff

Topics for this presentation:

• Crystalline arrays of Mn12 SMMs, and their controlled modification.

• Faster-Relaxing Mn12 SMMs: Jahn-Teller Isomerism

• Electron addition onto Mn12 SMMs, and itseffect on the properties

• New high-quality Mn12 SMMs: the picture comesinto focus.

[Mn12O12(O2CR)16(H2O)4] (Mn12) complexes:

� 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)

Mn4

O11O7

O12

O19

Mn6

O10O3

Mn2

O4O6

O2

Mn1

O1O2a

O6aO1a O3a

Mn2a

O5a

O4aO7a

O11a

O13a

O14a

Mn4aO17a

O21a

Mn7

O24a

O24

O22

O23

O18

O5

O16

Mn5O15

Mn5a

O15a

O16a

O19aO22a

O12a

O18a

Mn6aO20a

O23a

O20

O14

O21

O17

O10a

O8a

Mn3a

O9a

O9

Mn3

O8

O13

Sessoli, Gatteschi, Caneschi, Novak, Nature 1993, 365, 141Gatteschi, Sessoli, Christou, Hendrickson, et al. JACS, 1993,115, 1804

Mn(O2CMe)2 + MnO4- in 60% acetic acid/H2O

[Mn12O12(O2CMe)16(H2O)4]·2AcOH·4H2O(Lis, Acta Cryst. B,1980) [Mn12Ac]

Identified as a SMM in 1993. Mn12Ac has axial symmetry (tetragonal space group I4(bar)), and has therefore been considered the best to study in detail.

Volume of the Mn12O12 magnetic core ~ 0.1 nm3

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1

M/M

s

µµµµ0H (T)

0.002 T/s

3.6 K

3.2 K

3.0 K

2.8 K

2.6 K

2.5 K

2.4 K

2.3 K

2.2 K

2.1 K

1.3 K

2 K

1.8 K

T [K]2 4 6 8 10

χχ χχ'' M

[cm

3 mol

-1]

0

1

2

3

4

5

0 10 20 30 40

0

5

10

15

20

0.1 T0.5 T1 T2 T3 T4 T5 T6 T7 T

H/T (kG/K)

M/N�

B

S = 10D = - 0.50 cm-1

= - 0.72 K

DC magnetization hysteresis loopsDC magnetization fit

AC out-of-phase signal(50 – 1000 Hz)

Arrhenius Plot

10-5

10-3

10-1

101

103

105

107

109

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

DCAC

ττ ττ(s

)

1/T (1/K)

slope = Ueff

-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

µ 0 H(T)

40 mK

-1 -0.5 0 0.5 1-40

-30

-20

-10

0

Ene

rgy

(K)

µ0 Hz (T)

-10

-9

-8

-7

10

9

8

7

Tunneling Steps in a S = 10 Single-MoleculeMagnet

Field is swept from –1 Tesla to + 1 Tesla. Tunneling transitions are seen as steps, which correspond to asurge in the relaxation rate.

As expected from the Landau-Zener equation, the step size isinversely proportional to thesweep rate.

Modification of the Mn12 Family of SMMs

1) Carboxylate Substitution-- replacement of acetate with other carboxylate groups.-- add RCO2H to Mn12-Ac

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

(J. Am. Chem. Soc. 1993, 115, 1804, and J. Am. Chem. Soc. 1995, 117, 301)

• The substitution is an equilibrium that is driven to 100% reaction by removing the generated acetic acid (MeCO2H) as its toluene azeotrope under vacuum

• Many, many different carboxylate R groups have been used (big vs small, polar vs non-polar, isotopically-labelled, element-labelled (e.g. C6F5), etc

• Allows control of Mn12 solubility, crystallinity, redox potentials, etc

The Faster-Relaxing Variants of Mn12 SMMs

-- even in pure Mn12 crystals, additional signals from a faster-relaxing (LT) species are almost always seen-- in Mn12-Ac, the LT species is ~ 5%. In others, it can be much higher, and in some it is the majority species.

Temperature (K)2 4 6 8 10

0

1

2

31000 Hz250 Hz50 Hz

0

�M

´´(c

m3

mol

-1)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

R = Me R = C6F5

The Ueff typically differ by a factor of two

“Single-molecule magnets: control by a single solvent moleculeof Jahn-Teller isomerism in [Mn12O12(O2CCH2But)16(H2O)4]”

Soler et al. Chem. Commun. 2003, 2672

T (K ) 0 2 4 6 8 1 0 1 2

32 days

18 days

4 days

40 days

Crystals of HT form

Wet crystals of Pure LT form ! The compound crystallizes

from a MeNO2/CH2Cl2 solvent mixture as Mn12.MeNO2.CH2Cl2

The compound crystallizes from a MeCN/CH2Cl2 solvent mixture as Mn12.MeCN.CH2Cl2

triclinic, P�, a = 15.814(2), b = 16.42(2), c = 27.434(3) Å� = 76.900(1), � = 78.220(1), � = 78.210(1)º, Z = 2, V = 6699.08 Å3

triclinic, P�,a = 15.757(1), b = 16.763(1), c = 27.183(1) Å, � = 77.444(1), � = 77.490(1), � = 78.315(1)º, Z = 2, V = 6750.17 Å3

Mn6

O18

O85

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1

M/M

s

µ0Hz (T)

0.004 T/s

3.0 K3.2 K

3.4 K

2.8 K

2.6 K

2.4 K

2.2 K

2.0 K

3.6 K1.8 K

1.6 K

1.4 K

-1

-0.5

0

0.5

1

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

M/M

s

µ0Hz (T)

0.008 T/s

1.8 K

1.7 K

1.6 K

1.5 K

1.4 K

1.3 K

1.2 K

1.05 K

0.9 K0.8 K

0.7-0.04 K

Pure LT formMn12.MeNO2.CH2Cl2

Pure HT formMn12.MeCN.CH2Cl2

2. Site-Selective, Partial Carboxylate Substitution

[Mn12O12(O2CR)16(H2O)4] + x HL [Mn12O12(O2CR)16-x(L)x (H2O)4]

Examples: [Mn12O12(O2CR)12(NO3)4 (H2O)4] [Mn12O12(O2CR)8(O2CR’)8 (H2O)4]

[Mn12O12(O2CR)8(O3SPh)8 (H2O)4] [Mn12O12(O2CR)8(O2PPh2)8 (H2O)4]

Inorg. Chem. 2001, 40, 4199 Dalton Trans. 2003, 2243-2248

O4O13

O1

O38

O39

S8O2

O12

S3

Mn2

O3

O6O11

Mn3

O7

O8

O10 S2

O14O9

O57

Mn10

O45O49

O42

O37

O36

O29O30 S5

Mn1

O46

O31

Mn7

Mn8O40

O56

O5Mn9

O43

O34O32

O48S7O33

O28

O25

O35 O26

O27

O24

O20

O21O23

O19

O15

S4

O51

O16

Mn4O18Mn11

O50

O55O53 O44

Mn12

O52

S6

Mn5

Mn6

S1

10-5

10-3

10-1

101

103

105

107

109

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

DCAC

ττ ττ (s

)

1/T (1/K)

τ0 = 6.6 x 10 -9 s

Ueff = 67 K

3. Electron Addition (Spin Injection)Carboxylate variation alters the Mn12 redox potentials (E),

(related to the thermodynamic Gibbs free energy by �Gº = -nFEºi.e. ease of addition (or removal) of

electrons)-- determined by electrochemistry

0.300.60CH2Cl

-0.500.02CH2CH3

0.460.64C6F5

0.450.74C6H3(NO2)2-2,4

0.610.91CHCl2

E2(V)bE1 (V)aR

DPV

in CH2Cl2 solution vs. ferrocenePotential (V)

-0.40.00.40.81.21.6

50 µA

0.860.56

0.24

-0.03

0.950.64

0.34

0.91 0.61 0.29

10 µA

Cur

rent

CV

a. First e- additionb. Second e- addition

Electrochemical data for[Mn12O12(O2CR)16(H2O)4]

[Mn12O12(O2CR)16(H2O)4] + I- [Mn12O12(O2CR)16(H2O)4]- + ½ I2[Mn12]-

[Mn12O12(O2CR)16(H2O)4] + 2 I- [Mn12O12(O2CR)16(H2O)4]2- + I2[Mn12]2-

-- products can be made in multi-gram amounts, and isolated as pure, crystalline solids.

Electron Addition to Mn12 : Bulk Isolation of Products

-- using iodide (I-) as a one-electron donor

JACS 1995, 117, 301, and JACS, 2003, 135, 3576

Crystal Structures of Mn12 and [Mn12]-

H2O ( )H2O ( )

Eppley et al. JACS, 1995, 117, 301

Mn4

O11O7

O12

O19

Mn6

O10O3

Mn2

O4O6

O2

Mn1

O1O2a

O6aO1a O3a

Mn2a

O5a

O4aO7a

O11a

O13a

O14a

Mn4aO17a

O21a

Mn7

O24a

O24

O22

O23

O18

O5

O16

Mn5O15

Mn5a

O15a

O16a

O19aO22a

O12a

O18a

Mn6aO20a

O23a

O20

O14

O21

O17

O10a

O8a

Mn3a

O9a

O9

Mn3

O8

O13

Crystal Structure of [Mn12]2-

--- added electrons are localized on opposite sides of the Mn12 molecule

--- the neutral H2O ligands bind preferentially to the MnII atoms

1H NMR Spectra of [Mn12]2- in CD3CN Solution

60 50 40 30 20 10 0 -10

ax(III-III)

eq

eq

eqax

(III-IV)

ax(III-IV)

ax(III-IV)ax

(III-III)

ax(III-III)

C

C

S

S

*

S

*

*a

*

00101020203030404050506060

00101020203030404050506060

00101020203030404050506060

ax(III-III)

ax(III-IV)

*

ax(III-IV)

ax(III-IV)

eq(III-III)

eq(III-III)

eq(III-III)

ax(III-III)

ax(III-III)

C

*

*

* *

S

S

*

[Mn12O12(O2CCHCl2)16(H2O)4]z

������

������

������

[Mn12O12(O2CCH2Cl)16(H2O)x]z

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������

������

sc

Effective solution symmetry D2d

Magnetic Properties of [Mn12]1- , 2-

32 57 66 Ueff (K)

-0.39-0.49-0.65D (K)

1019/210S

[Mn12]2-[Mn12]1-[Mn12]R = CHCl2

H/T (kG/K)0 10 20 30 40 50

10

12

14

16

18

20

7T6T5T4T3T2T1T

M/N

µ B

DC Reduced Magnetization

S = 10D = - 0.27 cm-1

= - 0.39 K

AC Susceptibility

T(K)0 2 4 6 8 10 12 14

0

1e-5

2e-5

3e-5

4e-5

5e-5

χ” (e

mu)

[Mn12]2-

)

0.1 0.2 0.3 0.4 0.5

10-4

10-3

10-2

10-1

Ueff = 53 K

Ueff = 28 K

Ueff = 64 K

�(s

)

1/T (K-1)

[Mn12][Mn12]1-

[Mn12]2-

R = C6F5

χ M"

(cm

3m

ol-1

)

Mn12

χM" peak at 6 - 8 K

[Mn12]-

χM" peak at 4 - 6 K

[Mn12]2-

χM" peak at 2 - 4 K

T (K)1.5 2.0 2.5 3.0 3.5 4.0 4.5

1000 Hzχ" (e

mu)

Out-of-Phase AC Susceptibility for Mn12, [Mn12]- and [Mn12]2-

- dried solids

wet crystals

Soler, et al., JACS, 2003, 135, 3576

T (K)

1.5 2.0 2.5 3.0 3.5 4.0 4.5

χ" (e

mu)

8e-5

1e-4

1e-4

1e-4

2e-4

2e-4

2e-4

2e-4

2e-4

3e-4

1000 Hz

Out-of-phase AC Magnetic Susceptibility for(PPh4)2[Mn12O12(O2CCHCl2)16(H2O)4]

(PPh4)2[Mn12]•4CH2Cl2•H2O (PPh4)2[Mn12]•6CH2Cl2triclinic P�V = 6969.79 Å3

Monoclinic P21/cV = 7468.51Å3

Arrhenius → Ueff = 18.5 K Arrhenius → Ueff = 30.2 K

Peak at 3.6 KPeak at 2.4 K

(PPh4)2[Mn12]•4CH2Cl2•H2O (PPh4)2[Mn12]•5CH2Cl2

(PPh4)2[Mn12]•4CH2Cl2•H2O (plates)

• SMM below TB =2.0 K• Tunneling steps • D = - 0.28 cm-1

• Ueff = 21.0cm-1 = 30.2K

(PPh4)2[Mn12]•6CH2Cl2 (needles)

Hysteresis Loops for (PPh4)2[Mn12O12(O2CCHCl2)16(H2O)4]

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1

M7065M6055

M/M

s

µ 0 Hz (T)

1.5 K0.07 T/s

plates

needles

• SMM below TB = 1.5 K• Tunneling steps • D = - 0.17 cm-1

• Ueff = 12.9cm-1 = 18.5K

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1

M/M

s

µ0 Hz (T)

0.07 T/s

0.6 K

0.7 K

0.8 K

1.2

1.5 K

0.5 K

0.9

1.0

1.10.4 K

0.3 K0.2 K0.04 K

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1

M/M

s

µ0 Hz (T)

0.07 T/s

0.6 K

0.7 K

0.8 K

1.2

2.0 K

0.5 K

0.9

1.0

1.8 K

0.4 K0.3 K0.2 K0.04 K

1.6 K

1.4 K

Topics for this presentation:

• Crystalline arrays of Mn12 SMMs, and their controlled modification.

• Faster-Relaxing Mn12 SMMs: Jahn-Teller Isomerism

• Electron addition onto Mn12 SMMs, and itseffect on the properties

• New high-quality Mn12 SMMs: the picture comesinto focus.

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

crystallizes as [Mn12BrAc]·4CH2Cl2

tetragonal space group I42d

--- single type of molecule in the crystal.

--- in contrast to Mn12Ac, where each molecule has strong H-bonding to 0,1, 2, 3 or 4 acetic acid molecules of crystallization (Cornia et al., Phys. Rev. Lett. 2002, 89, 257201)

Nicole Chakov

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

• Better even than Mn12BrAc

• Less solvent of crystallization

• Bulky R group : well separated molecules

• Well aligned with cell axes

I42d

Mn12BrAc

I4(bar)I4(bar)

Mn12ButAcMn12Ac

Muralee Murugesu

H/T [kG/K]

0 10 20 30 40

M/N

µµ µµB

0

2

4

6

8

10

12

14

16

18DC Magnetization fit

S = 10D = - 0.51 cm-1

= - 0.73 K

AC Susceptibility

(1/T)/K-1

0.14 0.16 0.18 0.20 0.22

ln( ττ ττ

−1−1 −1−1// //s

−1−1 −1−1)) ))

3

4

5

6

7

8

9

10

T [K]2 4 6 8 10

χχ χχ'' M

[cm

3 mol

-1]

0

1

2

3

4

5

Magnetic Properties of [Mn12O12(O2CCH2But)16(MeOH)4](Mn12ButAc) Dr. Muralee Murugesu

Arrhenius Plot

Ueff = 67.8 K�0 = 5.58 x 10-8s

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1

M/M

s

µµµµ0 H (T)

0.002 T/s

3.6 K

3.2 K

3.0 K

2.8 K

2.6 K

2.5 K

2.4 K

2.3 K

2.2 K

2.1 K

1.3 K

2 K

1.8 K

Single-Crystal 55Mn NMR Spectra of Mn12Ac vsMn12BrAc with S4 (Axial) Symmetry

Mn3

Mn3a

Mn3b

Mn3c

Mn2c

Mn2b

Mn2aMn2

Mn1 Mn1b

Mn1a

Mn1c

Mn12-Ac: tetragonal space group I4(bar) Mn12-BrAc: tetragonal space group I42d

Mn12BrAcMn4+

Mn3+Mn3+

N. S. Dalal, S. O. Hill, G. Christou, et al.Inorg. Chem. 2005, 44, 2122.

JACS, 2006, 128, 6975

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

I4(bar)I4(bar)

Mn12-tBuAcMn12-Ac

Wernsdorfer, Murugesu, and Christou, P. R. L., 2006, 96, 057208

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

Mn12-Ac Mn12-tBuAc

-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

µµµµ0 H (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

Ene

rgy

(K)

µµµµ0 Hz (T)

Ground statetunneling

Excited statetunneling

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

Summary: Researchers have thought for over 13 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., 2006, 96, 057208