Magnetic Properties of One-, Two-, and Three-dimensional Crystal Structures built of
Manganese (III) Cluster-based Coordination Polymers
Kevin J. Little*
Department of Physics, University of Florida
Gainesville, FL 32611-8440
August 2, 2006
Abstract
Magnetization studies, using a SQUID magnetometer operating down to 2 K and
up to 7 T, were performed on one-, two-, and three-dimensional crystal structures
built with Mn3+ cluster-based coordination polymers. All three structures were
found to exhibit strictly paramagnetic behavior with no signs of long-range
ordering down to 2 K. The magnetic properties of the 2D and 3D compounds
were found to be a result of the Mn3+ ions with quantum spin value S = 2 present
in each compound; however, the 1D compound exhibited anomalous magnetic
properties.
*Permanent address: Department of Physics, Taylor University, Upland, IN 46989-1001
1
Introduction
Interest in the synthesis of one-, two- and three-dimensional (1D, 2D, and 3D) crystal
structures using coordination polymers, which are chains of metal ion “nodes” and ligand
“linkers,” has increased in recent years [1]. Some coordination polymer structures have novel
magnetic and electrical properties and may have broad potential for applications in developing
technologies.
When a new chemical compound is fabricated, the magnetic properties of the material
can be an essential element to understanding the atomic properties, intramolecular interactions,
and usefulness of the material. Three new compounds using Mn3+ Schiff-base complexes as the
metal ion nodes (Figure 1) were created by the Department of Chemistry at Wake Forest
University (WFU) and were sent to the Departments of Physics and Chemistry at the University
of Florida (UF) for magnetic analysis.
The low-temperature magnetic properties of the
compounds, such as the type of magnetism, evidence for long-range ordering, and evidence for
any novel magnetic properties, were determined.
SQUID Magnetometer
The magnetic moment of each sample was measured under temperatures ranging from
2 K to 300 K and under external magnetic fields ranging from 0 to 7 T by a Quantum Design
MPMS (Magnetic Properties Measurement System) SQUID (Superconducting QUantum
Interference Device) magnetometer. The MPMS SQUID magnetometer is an automated system
that contains a temperature control system, a superconducting magnet with a maximum field of
7 T, a sample transport system, and a SQUID amplifier system [3]. A sample is connected to a
driving mechanism by a rod and is moved through a second-derivative system of four
2
superconducting coils. A magnetic moment is induced in the sample by the external field H
created by the superconducting magnet. As the sample is moved through the coiled wire, the
magnetic flux Φ through the coils due to the sample’s magnetic moment changes. An electric
v
field E and a current in the coils are created in accordance with Faraday’s Law of Induction,
v
dΦ
v
∫ E ⋅ ds = − dt
,
(1)
v
where ds is an infinitesimal displacement along the boundaries of the line integral and dt is the
infinitesimal of time. The induced current is inductively coupled to the SQUID detector, which
acts as a exceptionally sensitive current to voltage converter due to a quantum tunneling effect
[3]. The voltage is proportional to the magnetic moment of the sample, and this value is
processed and recorded by a computer.
SQUID Measurements Method
Three pairs of empty gel cap tops were prepared. Each gel cap pair was weighed with a
digital scale, placed in the configuration in which it would hold the sample, and mounted in a
drinking straw. The straw was attached to a transport rod which was placed in the SQUID
magnetometer. The gel cap was cooled to 2 K, and its magnetic moment was measured under
external fields ranging from 0 to 7 T. The external magnetic field H was then held constant at
0.1 T, and the magnetic moment was measured as the temperature was swept from 2 K to 300 K.
A sample of each of the three compounds was carefully placed into one of the measured
gel caps and was weighed. The tightly packed gel cap was then mounted in a drinking straw.
The straw was attached to a transport rod and lowered into the bore of the SQUID
magnetometer.
The sample was zero-field cooled (ZFC), i.e., cooled to 2K without the
application of an external magnetic field. At 2 K, a field of 0.1 T was applied. The MPMS
3
SQUID magnetometer then took measurements at temperatures ranging from 2 K to 300 K. The
sample was then cooled in the presence of an external field of 0.1 T, i.e., field cooled (FC).
Measurements were again made in a sweep from 2 K to 300 K. The temperature was then
cooled to 2 K, and measurements of the sample’s magnetic moment were made in external fields
ranging from 0 to 7 T.
Calculations and Results
The SQUID magnetometer measures the magnetic moment for the entire sample, and this
moment can be used to find the molar magnetic susceptibility χm by
χm =
M
,
HN
(2)
where M is the magnetic moment of the sample, H is the applied external field, and N is the
number of moles of the material in the sample. A positive χm value is paramagnetic and a
negative value is diamagnetic. The χm data have been calculated from the magnetic moment data
recorded by the SQUID and adjusted for an intrinsic diamagnetism given in Table I. The results
shown in Figure 2 display similar paramagnetic behavior for all three materials.
A significant difference in the χm values for field cooled (FC) data and zero-field cooled
(ZFC) data would be an indicator of long-range ordering.
Long-range ordering occurs in
ferromagnetic, antiferromagnetic, and ferrimagnetic materials when dipole moments are aligned
throughout relatively distant areas of a material’s structure. The difference between FC and ZFC
data is displayed in the inset graphs of Figure 2. No significant difference within experimental
uncertainties was found for any of the materials.
A plot of χmT vs. T reveals important information about the magnetic properties of a
material. A plot that is a relatively straight, flat line indicates paramagnetism. A plot that curves
4
upward indicates ferromagnetism, and a plot that curves downward at low temperatures indicates
antiferromagnetism. Figure 3 displays χmT vs. T data for all three compounds. While the plots
trend downward at around 50 K, the spins of the Mn3+ ions are most likely not exhibiting
antiferromagnetic coupling. The local molecular structure around the Mn3+ ions suggests that
anisotropy, the tendency for an atom to share its electrons along a preferential axis leading to
distortions in the electron orbitals, may be occurring at low temperatures.
The Curie constant C is equal to χmT and is proportional to the effective magnetic
moment µeff2. The Curie constant C is defined by the equation
χ mT = C =
N A g 2 µ B S (S + 1)
,
3k B
2
(3)
where NA is Avogadro’s number, g is the Landé g-factor or the spectroscopic splitting factor, µB
is the Bohr magneton, kB is the Boltzmann constant, and S is the spin value. By rearranging
Eq. (3), we obtain a method of solving for possible spin values:
S ( S + 1) =
3(χ mT )k B
.
N A g 2 µ B2
(4)
The structural symmetry of the ligands and Nb6 clusters in the three compounds suggested that
the dominant magnetic properties of each compound would be a result of the S = 2 Mn3+ ions.
So, the values of χmT were normalized by the number of Mn ions in the formula unit of each
compound. With the starting value of g = 2 used as an estimate for g, the value of χmT at 300 K
was used to calculate a possible spin. This S value was rounded to a possible quantum spin value
(a multiple of ½) and used to calculate a value for g. The results for each compound are shown
in Table II.
The plots of χ-1 vs. T displayed in the inset graphs of Figure 3 exhibit a linear behavior
over the entire range of data. This behavior is characteristic of paramagnetism. The intercept of
5
all three plots is near the origin, indicating Curie paramagnetism [3]. The data were fit to a
Curie-Weiss Law,
χ m −1 =
(T − θ )
(5)
C
where C is the Curie constant and θ is the Curie-Weiss temperature, which may indicate a
ferromagnetic or antiferromagnetic transition when non-zero.
The results for C and θ are
displayed in Table III. The relation
3k B C
NA
µeff =
(6)
can be used to find the effective magnetic moment. The results are displayed in Table III.
The magnetization per mole of material over a range of external magnetic fields is an
effective indicator of a compound’s magnetic characteristics. The M vs. H data, displayed in
Figure 4, can be fit to the Brillouin function for paramagnetism,

 (2 S + 1)gµ B H
M = nN A gµ B (S + 12 ) ctnh 
2 k BT


 1
 gµ H
 − ctnh  B
 2
 2k BT

 ,

(7)
where M is the molar magnetization, n is the number of interacting spins per formula unit, and
ctnh(x) is the hyperbolic cotangent function [5]. The Brillouin function for paramagnetism is a
model for non-interacting spins with no anisotropy, so the M vs. H data in Figure 4 suggests
some spin interaction or anisotropy occurring in the materials at 2 K.
Discussion and Conclusion
No long-range ordering was observed in the three compounds. The χm-1 vs. T and M vs.
H plots are characteristic of a paramagnetic material.
Deviations from a simple Brillouin
function for paramagnetism suggest that the anisotropy suggested by the χmT data is an important
6
factor in spin behavior at low temperatures. The magnitudes of the values of θ from Curie-Weiss
law fits of χm-1 vs. T data are sufficiently near zero, suggesting paramagnetism. If ordering does
occur, it does so at temperatures that are not within the range of the SQUID magnetometer.
The data from the 2D and 3D compounds suggest that the Mn3+ with S = 2 ions in each
compound are indeed the principal cause of the paramagnetic behavior of the materials. When
the χmT data are normalized for the number of Mn3+ ions per formula unit, the χmT / Mn ion
values are extremely similar (Figure 5). The same is true for the 2D and 3D M vs. H data (Figure
6). The calculated spins from the 300 K χmT values strongly support the Mn3+ ion with S = 2 and
g ≈ 2 as the factor responsible for the compounds magnetic properties. Corroborating evidence
is offered by the Brillouin function fits of the M vs. H data. For the 2D compound, the
parameters S = 2, g ≈ 2, and n ≈ 2 provide a satisfactory fit. For the 3D compound, the
parameters S = 2, g ≈ 2, and n ≈ 3 provide a similarly satisfactory fit.
The µeff value for the 2D data found from the Curie-Weiss law Curie constant (7.38µB) is
close to the 7.34µB value of [Me4N]2{[Mn(salen)]2[Nb6Cl12(CN)6]}, a similar material [2]. The
µeff value calculated for the 3D data (8.98µB) is near the 8.84µB value of a similar material,
Na{[Mn(salen)]3[Re6Se8(CN)6]} [2].
While the 1D and 2D compounds display a 2:3 relationship for M vs. H and χmT vs. T,
the data of the 1D compound appear anomalous. Since the 1D compound contains only one
Mn3+ ion, its molar magnetization and χmT values should be similar to the normalized 2D and 3D
data if all significant magnetism is due to the S = 2 Mn3+ ion. However, these values are too
large by a factor of two to support this conclusion.
For a more complete analysis, the cause of this anomaly needs to be investigated. A
likely possibility is that excess Mn ions were present in the sample. The compound may have
7
contained excess or residued Mn ions, or a structure containing two Mn3+ ions instead of one
may have been created.
Acknowledgements
I would like to thank Mark W. Meisel for his instruction and patience this summer. I
would like to thank Norman Anderson and Daniel Pajerowski for their enlightening discussions
and coaching. I would also like to thank James Ch. Davis for his initial data measurements and
instruction. Funding was provided by the National Science Foundation grant DMR-0552726
through the Physics Research Experience for Undergraduates program at the University of
Florida and by DMR-0305371 (MWM). Samples were created by Huajun Zhou and Abdessadek
Lachgar at the Wake Forest University Department of Chemistry under grant DMR-0446763.
References
[1] K. Uemura, R. Matsuda, and S. Kitagawa, J. Solid State Chem. 178, 2420 (2005).
[2] H. Zhou, et al., “One-, Two-, and Three-dimensional frameworks built of Octahedral Metal
clusters and manganese(III) complexes,” preprint (2006).
[3] M. McElfresh, Fundamentals of Magnetism and Magnetic Measurements Featuring
Quantum Design’s Magnetic Properties Measurement System (Quantum Design, Inc.,
San Diego, CA, 1994).
[4] H. Zhou, Email correspondence, 15 July 2006. The following corrections were made:
diamagnetic contribution and temperature independent paramagnetic contribution of the
Nb6 cluster using J.G. Converse and R.E. McCarley, Inorg. Chem. 9, 1361 (1970); and
8
diamagnetic contributions of inner chlorides and cyanide ligands from the cluster units
and ligands using O. Kahn, Molecular Magnetism (Wiley-VCH, New York, 1993).
[5] C. Kittel, Introduction to Solid State Physics, 5th Ed. (John Wiley & Sons, New York, 1976).
9
Molecular Formula
Molar Mass
(g/mol)
Sample
Mass (mg)
Intrinsic Diamagnetism
(emu/mol) [4]
1D
[Me4N]3{{Mn(L1)}{Nb6Cl12(CN)6]}
1799.77
6.2
-180.8 x 10
-6
2D
[Me4N]2{[Mn(L2)]2[Nb6Cl12(CN)6]} · 2.0 MeOH
2049.92
14.1
-382.8 x 10
-6
3D
[Me4N]{[Mn(L3)]3[Nb6Cl12(CN)6]} · 0.6 MeOH
2069.41
13.2
-548.8 x 10
-6
(L1 = 5-MeO-salen = C18H18N2O4; L2 = 7-Me-salen = C18H18N2O2; and L3 = acacen = C12N2O2H18)
TABLE I. Properties of measured materials.
1D
2D
3D
Possible spin
3
2
2
2
calculated g
2.11
2.98
2.12
2.11
TABLE II. Rounded estimated spins and g values for compound / Mn ion.
1D
C
(emu K/mol)
(±0.02)
6.78
2D
6.81
0.2
7.38
3D
10.09
-2.1
8.98
θ (K)
(±0.2)
µeff (µB)
-1.2
7.36
TABLE III. Curie constant and Curie-Weiss temperature found from fit of Curie-Weiss law to
χm-1 vs. T. Calculated µeff given in Bohr magnetons.
10
(a)
(b)
FIG. 1. (a) 1D, (b) 2D, and (c) 3D crystal structures [2]. Blue:
Nb; Magenta: Mn; Green: Cl; Cyan: N; Red: O; Grey: C.
Molecular formulas are given in Table I.
(c)
11
1D χm vs. T
1.6
4.0
H = 0.1 T
ZFC
FC
0.8
0.0
-1.0
0.6
2.0
1.0
-2
1.0
χm (emu/mol)
χm (emu/mol)
1.0
3.0
∆χ (emu x 10 /mol)
2.0
2.0
-2
1.2
4.0
H = 0.1 T
ZFC
FC
2.5
3.0
∆χ (emu x 10 /mol)
1.4
2D χm vs. T
0
25
0.4
50
75
100
1.5
0.0
-1.0
-2.0
-3.0
1.0
-4.0
0
25
T (K)
50
75
100
T (K)
0.5
0.2
0.0
0
50
100
150
200
250
0.0
300
T (K)
.
0
50
100
150
200
250
300
T (K)
(b)
(a)
3D χm vs. T
6.0
H = 0.1 T
ZFC
FC
5.0
4.0
∆χ (emu x 10 /mol)
3.0
χm (emu/mol)
-2
2.5
2.0
1.5
3.0
2.0
FIG. 2. χm vs. temperature with ∆χ vs. temperature inset.
∆χ = χ FC − χ ZFC with uncertainties propagated from the
standard deviations of SQUID measurements and an estimated
mass uncertainty of 0.1 mg. All measurements performed at
0.1 T. (a) 1D, (b) 2D, (c) 3D.
1.0
0.0
-1.0
-2.0
-3.0
-4.0
-5.0
1.0
0
25
50
75
100
T (K)
0.5
0.0
0
50
100
150
200
250
300
T (K)
(c)
12
1D χmT vs. T
7.0
6.5
2D χmT vs. T
7.0
H = 1 kG
ZFC
FC
H = 1 kG
ZFC
FC
-1
4.5
20
-1
4.0
30
10
40
-1
Curie-Weiss Fit χ = (T-θ)/C
6.0
5.5
3.5
20
0
0
50
100
150
200
250
300
0
T (K)
50
100
150
200
50
100
150
200
250
300
T (K)
2.5
0
30
10
0
3.0
H = 1 kG
ZFC
FC
-1
-1
Curie-Weiss Fit χ = (T-θ)/C
5.0
-1
χ vs. T
50
χ (mol/emu)
40
6.5
H = 1 kG
ZFC
FC
χmT (emuK/mol)
5.5
χ (mol/emu)
χmT (emuK/mol)
χ vs. T
50
6.0
250
5.0
300
0
T (K)
50
100
150
200
250
300
T (K)
(a)
(b)
3D χmT vs. T
10
H = 1 kG
ZFC
FC
-1
χ vs. T
30
25
H = 1 kG
ZFC
FC
FIG. 3. χmT vs. temperature with χm-1 vs. temperature inset. A
Brillouin function was fit to the χmT vs. T data. A Curie-Weiss
Law was fit to the χm-1 vs. T data. (a) 1D, (b) 2D, (c) 3D.
-1
Curie-Weiss Fit χ = (T-θ)/C
χ (mol/emu)
8
-1
χmT (emuK/mol)
9
7
20
15
10
5
0
0
50
100
150
200
250
300
T (K)
6
0
50
100
150
200
250
300
T (K)
(c)
13
2D M vs. H
1D M vs. H
5
4
M (emuG x 10 /mol)
T=2K
UP
DOWN
Brillouin Fit
S
2
N
1.87685
g
2
2
1
3
T=2K
UP
DOWN
Brillouin Fit
S
2
n
1.71912
g
2.12192
4
3
4
M (emuG x 10 /mol)
4
±0
±0.02194
±0
2
1
±0
±0.06345
±0.06361
0
0
0
1
2
3
4
5
6
0
7
1
2
3
4
5
6
7
H (Tesla)
H (Tesla)
(b)
(a)
3D M vs. H
6
4
4
M (emuG x 10 /mol)
5
T=2K
UP
DOWN
Brillouin Fit
S
2
N
2.90149
g
1.71933
3
2
1
FIG. 4. Molar magnetization vs. external magnetic field with a
Brillouin function fit to the data. (a) 1D, (b) 2D, (c) 3D.
±0
±0.106
±0.04997
0
0
1
2
3
4
5
6
7
H (Tesla)
(c)
14
Comparison of χmT / Mn ion vs. T
Comparison of M / Mn ion vs. H
7.0
6
1D
2D
3D
6.0
M / Mn ion (emuG x 10 /mol)
6.5
5.5
5.0
5
4
χmT / Mn ion (emuK/mol)
1D FC
2D FC
3D FC
4.5
4.0
3.5
3.0
2.5
4
3
2
1
0
2.0
0
50
100
150
200
250
0
300
1
2
3
4
5
6
7
H (Tesla)
FIG. 6. M vs. H data normalized for the number of Mn3+ ions
per formula unit in each compound.
T (K)
FIG. 5. χmT vs. T field cooled data normalized for the number of
Mn3+ ions per formula unit in each compound.
15