Single-Molecule Magnets: A Molecular Approach to Nanomagnetism
George ChristouDepartment of Chemistry, University of Florida
Gainesville, FL 32611-7200, USA
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' >