Single-Molecule Magnets: A Molecular
Approach to Nanomagnetism
George Christou
Department of Chemistry, University of Florida
Gainesville, FL 32611-7200, USA
christou@chem.ufl.edu
Single-Molecule Magnets (SMMs)
The barrier to magnetization relaxation in SMMs is not due to inter-spin
Interactions, as in traditional magnets, but to Ising (easy-axis) molecular
anisotropy. Each molecule is a separate, nanoscale magnetic particle.
ms = 0
Requirements for SMMs:
1. Large ground state spin (S)
ms = -1
ms = -2
ms = -3
ms = 1
ms = 2
ms = 3
2.
ms = -4
ms = 4
ms = -5
ms = 5
ms = -6
ms = 6
ms = -7
ms = 7
Negative ZFS parameter (D)
Energy
E
7
8
9
ms=10
6
54 3
0
2 1-1-2
-3 -4
-5
ms = -8
-6
-7
-8
-9
U
ms = 8
ms = -9
ms = 9
ms = -10
ms = 10
-10 = ms
Magnetization Direction (z)
Anisotropy barrier (U) = S2|D| Integer spin
or (S2-1/4)|D|
Half- integer spin
Molecular Advantages of SMMs over
Traditional Nanoscale Magnetic Particles
Properties
 truly monodisperse particles of nanoscale dimensions
 crystalline, therefore contain highly ordered assemblies
 well-defined ground state spin, S
 truly quantum spin systems
Synthesis
 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
1
40 mK
0.5
M/M
S
Hysteresis Loops
for an S = 10 SMM
0
v=140 mT/s
v=70 mT/s
v=14 mT/s
v=2.8 mT/s
-0.5
-1
0-1
-0.5
0
µ 0 H(T)
0.5
1
Energy (K)
-10
-20
S = 10
21 energy states
MS = -S, -S+1, …, S
-7
7
-8
8
-9
9
-10
10
-30
-40
-1
-0.5
0
µ 0 Hz (T)
0.5
1
The Mn12 Family of Single-Molecule Magnets (SMMs)
[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.
O7
O4
O6
O11
O2
O13
O1
O2a
Mn2
O3
Mn1
O1a
O6a
O5a
Mn2a
O5
O3a
O9
O8a
Mn4
O10
Mn6
O10a
O16a
Mn4a
O22
O21
Mn5a
O13a
O23
O21a
O17a
Mn7
O24
O20a
O11a
O14a
Mn6a
 S = 10
 D = -0.40 to -0.50 cm-1 (-0.58 to -0.72 K)
 Magnets below 3K
O18
O15
O9a
O4a
O19
O20
Mn5
O15a
O7a
O14
O17
Mn3
O16
O8
Mn3a
Properties of the Mn12 family
O12
O23a
Volume of the Mn12O12 magnetic
core ~ 0.1 nm3
O24a
O18a
O12a
O19a
O22a
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
crystallizes as [Mn12-BrAc]·4CH2Cl2
tetragonal space group I42d
Mn1c
[Mn12O12(O2CCH2Br)16(H2O)4]
+ 16 MeCO2H
--- 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)
Mn2c
Mn3c
Mn3a
Mn2
Mn2a
Mn3
Mn3b
Mn1
Mn1b
Mn2b
Normalized Transmission
(arb. units – offset)
Mn1a




2 – sample #1
2 – sample #2a
2 – sample #2b
1 – parallel to HE
1 – 45º away from HE
2
3
4
5
Magnetic Field (T)
6
A New Mn12 Complex with Tetragonal (Axial) Symmetry:
[Mn12O12(O2CCH2But)16(MeOH)4]·MeOH (Mn12-ButAc)
Mn12-Ac Mn12-ButAc
I4(bar)
I4(bar)
Mn12-Ac
Muralee Murugesu
--- no symmetry-lowering contacts
with the solvent molecules in the
crystal
--- bulky R group : well separated
molecules
Mn12-ButAc
The Sharpness of the Hysteresis Loops in Mn12-ButAc
allows Steps due to Excited State Tunneling to be seen
1
0.5
Excited state
tunneling
-20
M/M s
Energy (K)
0
-40
Ground state
tunneling
-60
Excited state
tunneling
0
Ground state
tunneling
-0.5
-80
-100
-5
-4
-3
-2
-1
0
1
0 Hz (T)
2
3
4
5
-1
2.5
0.002 T/s
3
3.5
4
4.5
0 H (T)
5
0.1 K
0.6 K
0.7 K
0.8 K
0.9 K
1.0 K
1.1 K
1.2 K
1.3 K
1.4 K
1.5 K
1.6 K
1.7 K
1.8 K
1.9 K
2.0 K
2.1 K
2.2 K
2.3 K
2.4 K
5.5
Wernsdorfer, Murugesu and Christou, Phys. Rev. Lett., in press
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
Spin Injection into Mn12
Electrochemistry
Redox Potentials
CyclicVoltammetry
0.03
-
0.24
0.56
Current
0.86
0.34
50 A
0.64
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
R
0.95
Differential Pulse Voltammetry
CH2Cl2 solution vs. ferrocene
0.91 0.61 0.29
10 A
1.6
1.2
0.8
0.4
0.0
Potential (V)
-0.4
One - electron additions to Mn12 in bulk
Mn12 + I -
[Mn12] - + ½ I2
Mn12 + 2 I -
[Mn12] 2- + I2
Effect of Electron Addition to Mn12
O7
O4
O6
O11
O2
O13
O1
O2a
Mn2
O3
Mn1
O1a
O6a
O5a
Mn2a
O5
O3a
Mn4
Mn3a
Mn5
O15a
O7a
O10a
O22
O13a
0.4 - 0.5
60 - 65
[Mn12]-
19/2
0.3 - 0.4
40 - 50
[Mn12]2-
10
0.2 - 0.3
25 - 40
O21
Mn5a
O16a
Mn4a
O18
O15
O9a
O4a
O20
Mn6
O8
10
O19
Mn3
O16
O8a
Ueff / K
Mn12
O14
O17
-D / cm-1
O12
O10
O9
S
O23
O21a
O17a
Mn7
O24
O20a
O11a
O14a
Mn6a
O23a
O18a
O12a
O19a
O22a
[Mn12]2-
O24a
 added electrons localized on two Mn
 S does not change significantly
 |D| decreases with added electrons
 barrier decreases with added electrons
Also: Quantum Phase Interference and Spin-Parity in Mn12 Single-Molecule Magnets
Phys. Rev. Lett. 2005, 95, 037203
19F
R = C6F5
NMR in solution
o eq
(III-III)
Mn12
-60
-70
[Mn12]-
-80
-90
o eq
(III-III)
-60
-70
[Mn12]2-
-80
-70
-80
m ax
-100 -110 -120 -130 p-140
-150 -160 -170
eq (III-III)
(III-III)
m ax
(III-IV)
p ax
(III-III)
p ax
m eq
(III-IV) (III-III)
o ax
(III-IV)
-90
-100 -110 -120 -130 -140 -150 -160 m -170
eq
m ax
(III-III)
(III-III)
m ax
(III-IV)
p
ax
p eq
(III-III) (III-III)
p ax
o ax
(III-IV)
(III-IV)
-90
-100 -110 -120 -130 -140 -150 -160 -170
o eq
(III-III)
-60
p eq
(III-III) m ax
(III-IV)
m ax
p ax
(III-III)
(III-IV)
p ax
o ax (III-III)
m eq
(III-IV)
(III-III)
Mn4 SMMs with S = 9/2
 3Mn3+, Mn4+
X
MnIII
MnIII
O
MnIII
O
O
 C3v virtual core symmetry
 Mn3+ Jahn-Teller axial elongations
 Core ligands (X):
MnIV
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
energy
Properties of Mn4 SMMs
 S = 9/2
 D = – 0.65 to – 0.75 K
 U = ΔE = (S2-1/4)|D| = 20 D
E
magnetization orientation
X
OSiMe3
J34 (cm-1)
-34.35
(cm-1)
+13.41
J33
g
1.97
S
9/2
1st ex. state
Mn IV
Mn II I
S1 = 3/ 2
S2 = 2
264 cm-1
S = 9/2
Mn4 SMMs with S = 9/2
Hi = – D Ŝiz2 + Hi trans + g μB μ0 Ŝi H
(2Si + 1) energy states
S = 9/2 : 10 energy states
MS = -S, -S+1, …, S
D = XgµB/kB (X is the step separation)
quantum system
neling in mesoscopic
Supramolecularantiferromagnets
Dimers of Mn4 SMMs:
ds a Exchange-biased
quantum bit Quantum Tunnelling of Magnetization
[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
Pr group
161.71°
W. Wernsdorfer, N. Aliaga-Alcalde,
Quantum Tunnelling in an
[Mn4]2 dimer of SMMs
using [Mn4Pr]2·MeCN (NA3)
D = - 0.50 cm-1 = - 0.72 K
Jintra = - 0.07 cm-1 = - 0.1 K
Wernsdorfer, Christou, et al. Nature 2002, 416,
406
Derivatives of [Mn4O3Cl4(O2CR)3(py-p-R´)3]2 Dimers
R= CH3 (Ac)
R’= H
R= CH2CH3
(Pr)
R’= H
R= CH2CH3
(Pr)
R’= H
R= CH2CH3
(Pr)
R’= D
R3bar
R3bar
R3bar
R3bar
118
130
173
173
NA2
MeCN
NA3
MeCN
NA11
hexane
NA3-D
MeCN
(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
7.630
7.788
7.622
7.750
Nature
Science
Space Group
Temp(°C)
Solvent in the
crystal
Nuria Aliaga-Alcalde
(Å)
···MnIII
MnIII
Variation of Exchange-bias and Fine-structure
in [Mn4]2 SMM Dimers
[Mn4Ac]2 · MeCN
[Mn4Pr]2 · MeCN (Nature)
1
1
NA2
NA3
0.5
0.04 K
0
0.035 T/s
0.017 T/s
0.008 T/s
0.004 T/s
-0.5
-1
-1
-0.5
0.04 K
M/M s
M/M s
0.5
0
µ 0 H (T)
0.5
1
0
0.140
0.070
0.035
0.017
0.008
0.004
-0.5
-1
-1.2
-0.8
-0.4
0
0.4
µ 0 H (T)
T/s
T/s
T/s
T/s
T/s
T/s
0.8
1.2
[Mn4Pr]2 · hexane (Science)
Two effects:
2) Variation in fine structure (Jinter)
0.5
M/M s
1) Variation in exchange-bias (Jintra)
1
NA11
0.04 K
0
0.140 T/s
The properties of [Mn4]2 are very
sensitive to the ligands and the solvent
in the crystal
0.070 T/s
-0.5
0.035 T/s
0.017 T/s
0.008 T/s
-1
-1
-0.5
0
µ 0 H (T)
0.5
1
Quantum Superpositions in Exchange-coupled
[Mn4]2 Dimers
-- with [Mn4Pr]2 · hexane (NA11)
Jz
Jx, Jy
Hill, Edwards, Aliaga-Alcalde, Christou, Science 2003, 302, 1015
Hysteresis evidence for inter-dimer exchange interactions
↓
J´
↓
J´
J´
↓
↓
(↓ ↓ ↓)
(↑ ↓ ↓)
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
[Mn12O12(O2CR)16(H2O)4] + MnO4- in MeOH/MeCO2H
The structure consists of six Mn14 units
i.e. [Mn14]6
Tasiopoulos et al. Angew. Chem.
Int. Ed. 2004, 43, 2117
~4.3 nm
Side-view
~1.9 nm
~1.2 nm
Front-view
Mn84_xtals_str1_wet sample_July 29
6
0.035 T/s
55
S/molecule
45
XM' (cm 3 mol -1 K)
4
cM′T vs T
50
40
35
30
25
500 Hz
250 Hz
50 Hz
25 Hz
10 Hz
5 Hz
S=6
20
2
4
6
8
10
0.1 K
0.3 K
0.5 K
0.7 K
1.0 K
1.5 K
0
-2
-4
-6
15
0
2
12
-3
T, K
3.0
-1
0
0 H (T)
1
2
3
109
cM′′T vs T
2.5
500 Hz
250 Hz
50 Hz
25 Hz
10 Hz
5 Hz
2.0
107
105
1.5
103
1.0
t (s)
XM" (cm 3 mol -1)
-2
0.5
101
Ueff = 18 K
τ0 = 5.7 x 10-9 s
DC
AC
10-1
0.0
1.5
2.0
2.5
3.0
3.5
T, K
4.0
4.5
5.0
10-3
10-5
0
5
10
1/T (1/K)
15
20
Comparison of Sizes and Néel Vectors
Mn4
1
Mn12
Mn30
3 nm Co nanoparticle
Mn84
Quantum world 10
Molecular (bottom-up) approach
100 Classical world 1000
N
Classical (top-down) approach
A meeting of the two worlds of nanomagnetism
Tasiopoulos et al. Angew. Chem. Int. Ed. 2004, 43, 2117
A Mn70 Torus
EtOH yields a smaller torus of five units i.e. [Mn14]5
1.4 nm
Alina Vinslava
Anastasios Tasiopoulos
3.7 nm
~ 3.7 nm
~ 1.4 nm
109
107
105
t (s)
Ueff = 23 K
τ0 = 1.7 x 10-10 s
103
101
~ 1.2 nm
10-1
DC
10-3
10-5
0
5
10
15
1/T (1/K)
20
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
→
MnCl2 + pdmH2 + N3- + base
[Mn25O18(OH)2(N3)12(pdm)6(pdmH)6]2+
MnIV, 18 MnIII, 6 MnII
N
OH
OH
pdmH2
green, MnIV; purple, MnIII; yellow, MnII; red, O; blue, N
A
A
B
S = 51/2, D = - 0.022 cm-1
C
B
C
S = 15/2 + 0 + 21/2 + 0 + 15/2 = 51/2
A
B
C
B
A
Murugesu et al., JACS, 2004, 126, 4766
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
Acknowledgements
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)
$$ NSF and NSF/NIRT $$
Magnetic Properties of [Mn12O12(O2CCH2But)16(MeOH)4]
(Mn12ButAc)
AC Susceptibility
DC Reduced Magnetization fit
18
c''M [cm3 mol-1]
5
16
14
M/NB
12
10
S = 10
D = - 0.51 cm-1
= - 0.73 K
8
6
4
4
3
2
1
0
2
4
6
2
8
10
T [K]
Arrhenius Plot
0
0
10
20
30
40
10
H/T [kG/K]
9
[Mn12
S
10
10
D (K)
-0.72
-0.73
8
ln(ts
[Mn12Ac]
ButAc]
7
6
5
Ueff (K)
64
68
4
Ueff = 67.8 K
τ0 = 5.58 x 10-8s
3
0.14
Muralee Murugesu
0.16
0.18
(1/T)/K
0.20
-1
0.22
Landau-Zener Tunnelling (1932)
Tunnelling probability at an
avoided level crossing
| S, m >
| S, m' >
1-P
energy

2 
P  1 expc

dH
/dt


²
1
c

2 g B m  m'  0
P
| S, m >
| S, m' >
magnetic field