Low Temperature Measurements for Detecting Magnetic Spin Interactions
in Transition Metals
Angela Stewart
Department of Physics, Benedict College
July 30, 2003
Abstract
The magnetic properties of inorganic materials compounded with transition metals such
as manganese, iron, copper, and cobalt have been the subject of experimental study this summer.
Determining the magnetic susceptibility as a function of temperature and discovering whether
these samples are liquid crystals have heightened interest on how these materials behave at
temperatures greater than or equal to 2 K. The aim of the present work is to investigate the
magnetic spin interactions in the specimen, thereby determining whether they experience longrange ordering by measuring the magnetism as a function of temperature and magnetic field.
Introduction
An electron in a magnetic field with an electron orbital may be characterized by two
parameters, a spin value and a g value. The spin value denotes the direction of the electron spin
and describes the angular momentum of an electron. The g value describes the combination of
the total momentum, the angular momentum, and the orbital momentum and its effect on the net
magnetic moment [1]. Three spin dimensions for the effective magnetic moment: the Ising, the
XY or planar, and the Heisenberg. The Ising dimension denotes that an electron can only point in
one direction, up or down, whereas the XY dimension indicates that an electron’s movement is
confined to the XY plane. The Heisenberg dimension signifies that an electron can move in
three-dimensional coordinates. The sign of the spin interaction strength J determines whether the
material is ferromagnetic or antiferromagnetic [1].
Liquid crystals are a phase matter whose order is intermediate between that of a liquid
and that of a crystal. A liquid crystal is fluid- like but is anisotropic in its optical and electro-
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magnetic characteristics like a solid [2]. In the crystalline solid state there exists a rigid
arrangement of molecules that stay in a fixed position and orientation with a small amount of
variation from molecular vibration. To maintain this arrangement, large forces hold the
molecules in place, and, therefore, a solid is difficult to deform. In the liquid phase, the
molecules have no fixed position or orientation and are free to move in a random fashion; the
liquid state has less order than the solid state. The random motions of the molecules mean that
the intermolecular attractive forces that kept a solid together are now only strong enough to keep
the liquid molecules fairly close together. A liquid can therefore easily be deformed. The
differences between the states can be attributed to the temperature of the substance [3].
Temperature is a measure of the randomness of the molecules, and therefore less order exists at
higher temperatures. When the liquid crystal is formed from the isotropic state, some amount of
the positional or orientational order is gained. It is this order that accounts for the anisotropies of
the substance. Some examples of liquid crystals are the LCD displays on the faces of watches
and calculators [4]. The purpose of this work, is to investigate the magnetic properties of the
Mn(bipyridine)Cl2, Mn(bipyridine)Br2, and their liquid crystal derivatives.
Materials and Crystal Structures
The samples of Manganese (Mn) provided by Williams College consist of two parent
materials and four derivatives of the parent. The crystal structure of the parent specimen is
shown in Fig. 1, where M is the transition metal, Mn, X is the Bromine (Br) or Chlorine (Cl), and
the complex attached by Nitrogen (N) is Bipyridine (bipy) [5].
2
FIG.1: Crystal structure of parent material provided by Williams College.
The derivatives are similar to the parent in crystal structure except it has a Carbon- 14
(C-14) polymer attached as seen in Fig. 2., where M is the metal Mn, 5-5’ is the position of the
polymer hanging from the parent, and X is the Br or Cl [5].
FIG. 2: Crystal structure of derivatives.
These samples came prepared in powder form for testing. Details of the molecular weight and
appearance were also provided along with nicknames for each sample with indication of the
parent materials as seen in Table I [5].
3
TABLE I : Sample names, labels, molecular weights, and appearances.
SAMPLE
Mn(bipy)Br2
Mn(4-4’C14
bipy)Br2
Mn(5-5’C14
bipy)Br2
Mn(bipy)Cl2
Mn(4-4’C14
bipy)Cl2
Mn(5-5’C14
bipy)Cl2
LABEL MOLECULAR APPEARANCE
WEIGHT
EAM1-16 371.06 g/mol
yellow –green
(Parent)
powder
EAM1-24 1823.13 g/mol
pale gold
powder
EAM1-26
1823.13 g/mol
beige powder
STS1-8
(Parent)
STS1-14
282. 154 g/mol
beige powder
1734.22 g/mol
beige powder
STS1-15
1734.22 g/mol
beige powder
Experimental Measurements
All materials were measured using a device known as a Superconducting Quantum
Interference Device (SQUID). This measurement system is a complex analytical apparatus made
specifically to study the magnetic properties of small experimental samples over a broad range of
temperatures starting at 2 K and magnetic fields from 0 to 7 T. Automatic control and data
collection are provided by a computer and two independent subsystem controllers. Within the
dewar, a cryogenic probe integrates a superconducting magnet with a SQUID detection system
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and a high performance temperature control system. The SQUID provides prompt measurements
over a temperature range of 2 to 300 K, and has an inside coil of 3 cm, a sensing loop, a
superconducting transformer, a SQUID sensor, and control electronics. The coils are designed to
be insensitive to any changes of the uniform field from the superconducting magnet to a
precision of approximately 0.1%, making the SQUID detector relatively insensitive to drifts in
the magnet, even following very large field changes [6].
Procedure
A small gelcap and plastic straw were used as the sample holder during the
measurements. The samples were weighed and packed in the gelcap, which was then placed
inside the straw so that measurements could be taken. Magnetizations versus temperature
measurements were taken from 2 to 300 K. The sample was then zero-field cooled to 2 K before
a measuring field of 0.01 T (100 G) was applied. Data were then recorded while the sample was
warmed from the lowest temperature. The sample was then cooled again to 2 K, but in the
presence of a 0.01 T field, and additional field-cooled (FC) data were acquired. Any difference
between the FC and ZFC magnetizations is must arise from long-range ordering. The specimen
was then ZFC to 5 K where a magnetic field was then applied between 0-7 T and the temperature
was fixed at 5 K. The diamagnetic contribution of each sample was estimated from Pascal
constants [7].
5
0.5
χ(emu/mol)
0.4
EAM 1-16 (parent)
Curie - W eiss Fit
0.3
EAM 1-24
EAM 1-26
0.2
0.1
0.0
0
50
100
150
200
250
Temperature (K)
FIG. 3: Magnetic data for the three Mn(Br2) substances, presented as molar
paramagnetic susceptibility versus temperature. A best fit line is also shown to
see if the data fits the Curie-Weiss Law.
Results and Discussion
The salient features of the results of the magnetic susceptibility studies are presented in
Fig. 3, which indicates that all three Mn(Br2) specimens are paramagnetic in nature between 2
and 300K. Fitting the parent data to the Curie-Weiss Law
χ = C/ (T – θ)
(1)
where χ is the magnetic susceptibility, C is the Curie constant, T is the absolute temperature, and
θ is the Weiss temperature in units of temperature suggests that there are no magnetic spin
interactions in the parent material [8]. Fits were also acquired for the derivatives and are typical
to the fit in the parent material; therefore, these fits were not shown. Parameters were extracted
indicating the g value, θ, spin, mass of material, and the mass of the gelcap for each sample as
shown in Table II.
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TABLE II: Data table consisting of the spin, g value, correction term θ, material mass, and gelcap mass.
SAMPLE
LABEL
G VALUE
SPIN
Θ in K
Mn(Bipy)Br2
(Parent)
Mn(4-4’C14Bipy)Br2
Mn(5-5’C14Bipy)Br2
EAM 1-16
2
2.5
EAM 1-24
1.1
2.5
-1.03K
(± .01)
-.46K
(± .03)
EAM 1-26
1.3
2.5
-.17K
(± .01)
MASS OF
MATERIAL
83.29mg
MASS OF
GELCAP
41.63mg
46.34mg
43.74mg
41.35 mg
42.91mg
The values presented are resulting values after the gelcap background and the core diamagnetism
have been subtracted. The gelcap background and core diamagnetism have a minuscule effect on
the results. It has been proven that the derivatives possess a liquid crystal nature at room
temperature and above, whereas the parent material possesses no signs of the liquid crystal state
at any temperature [9]. The Curie constant can be calculated by Eq. (2) [8].
C = Ng2µB2S(S+1)/3kB
(2)
The graph of χT vs T gives visual insight to what the Curie constant is at high temperatures, and
whether long- range ordering is starting to set in. Possibilities of anti-ferromagnetic ordering and
the tendency of different Curie constants can be seen in Fig. 4.
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4.5
4.0
EAM 1-16 (parent)
EAM 1-24
χT (emu K /mol)
3.5
EAM 1-26
3.0
2.5
2.0
1.5
1.0
0.5
0.0
0
50
100
150
200
250
Temperature (K)
FIG. 4: Magnetic data for the three Mn(Br2) substances, presented as molar
paramagnetic susceptibility times temperature versus temperature.
8
0.5
STS 1-8 (parent)
Curie-Weiss Fit
STS 1-14 (4-4')
Curie -Weiss Fit
χ(emu/mol)
0.4
STS 1-15 (5-5')
Curie-Weiss Fit
0.3
0.2
0.1
0.0
0
50
100
150
200
250
300
Temperature (K)
FIG. 5: Magnetic data for the three Mn(Cl2) substances, presented
as molar paramagnetic susceptibility versus temperature.
As has been similarly observed in the Mn(Br2) specimen, paramagnetic behavior is
also present in Mn(Cl2) sample as shown in Fig. 5. Some indication of magnetic
spin interaction is seen from temperatures 100K and below because these three
samples do not fit the Curie-Weiss Law at these temperatures. Parameters were
extracted indicating the g vale, spin value, θ, material mass, and gelcap mass as
shown in Table III.
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Table III: Data table consisting of the spin values, g values, correction term θ,
material mass, and gelcap mass
SAMPLE
LABEL
G VALUE
SPIN
VALUE
Θ (K)
Mn(Bipy)Cl2
(Parent)
Mn(4-4’C14Bipy)Cl2
Mn(5-5’C14Bipy)Cl2
STS 1-8
2
2.5
STS 1-14
1.1
2.5
1.5
(± .02)
-.5
(± .05)
STS 1-15
1.4
2.5
-1
(± 1)
MASS OF
MATERIAL
(mg)
67.22
MASS OF
GELCAP
(mg)
45.29
58.00
43.42
61.40
42.41
The values presented are resulting values after the gelcap background and the core diamagnetism
have been subtracted. The gelcap background and core diamagnetism have a minuscule effect on
the results as seen in the Mn(Cl2). Similarly, the derivatives possess a liquid crystal nature at
room temperature and above, whereas the parent material possesses no signs of the liquid crystal
state at any temperature [9]. The Curie constant can again be calculated by Eq, (2) [8].
For this sample, C was calculated to be 4.3 emu K / mol. χT vs T gives a visual approximation
of the Curie constant and how it remains a constant at high temperatures as seen in Fig.6. C is
approximately equal to 4 emu K / mol at high temperatures also seen in Fig. 6.
10
XT (emu K / mol)
9
8
7
6
5
4
3
2
1
STS 1-8 (parent)
STS 1-14
STS 1- 15
0
50
100
150
200
250
300
Temperature (K)
FIG. 6: Magnetic data for the three Mn(Cl2) substances, presented
paramagnetic susceptibility times temperature versus temperature.
M ( emu G / mol)
2500
2000
1500
STS 1-8 (parent)
Brillouin Fit
1000
500
0
0
1
2
3
4
5
6
B (Tesla)
FIG7:7:Magnetization
Magnetizationversus
versusMagnetic
magneticField
field.
FIG
As the applied field increases the magnetic moment increases as shown in Fig. 7. This M vs B plot
is typical of all Mn samples tested, therefore those graphs are not shown. A Brillouin fit was done
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to determine the g-value of the materials. The spin value, S, was fixed at 5/2 and the temperature
was fixed at 5 K. The experimental g–value is 2 with an error of ±.02.
Conclusion
These results are typical and expected of Mn2+ because the spin value is usually 5/2 which
produces a strong magnetic signal even at temperatures greater than or equal to 2 K. The Mn
produces standard paramagnetic behavior with some possibilities of magnetic spin interactions and
long range ordering. All samples proved to be antiferromagnetic with the exception of the
Mn(bipy)Cl2. This material proved to be ferromagnetic, a result that is consistent in the
literature (10). More accurate results of the low temperature behavior of these samples can be
obtained by testing a sample of the C-14 polymer alone between 2 and 300 K.
Acknowledgements
I would like to thank the National Science Foundation and the University of Florida for
funding my research this summer. I would like to thank Dr. Kevin Ingersent and Dr. Alan Dorsey
for giving me the opportunity for a new experience. I would especially like to thank Dr. Mark W.
Meisel for allowing me to collaborate with him this summer. Last but not least, I would like to
thank Dr. Dan Talham, Ju-Hyun Park, Erik Cizmar, David Elam, and James Davis for their
invaluable help and Williams College for supplying the samples and literature. These people made
my summer both enjoyable and educational.
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References
[1]
C. Kittel, Solid State Physics, 5th ed. (John Wiley and Sons, New York, 1976),
pp. 435-440.
[2]
Akira Isihara, Condensed Matter Physics (Oxford University Press, Oxford, 1991),
pp. 285 –287.
[3]
P.M. Chaikin and T.C. Lubensky, Principles of Condensed Matter Physics,
(Cambridge University Press, Cambridge, 1995), pp. 58 –71.
[4]
Mark W. Meisel (private communication).
[5]
Lee Y. Park, Department of Chemistry, Williams College, Williamstown,
Massachusetts 01267 (private communication).
[6]
Magnetic Property Measurement System, Hardware Reference Manual (Quantum
Design, San Deigo 1996), pp. (1-1), (1-8).
[7]
Olivier Kahn, Molecular Magnetism, (Wiley-VCH Inc. New York, 1993), pp.3-4.
[8]
Richard Carlin, MagnetoChemistry, (Springer-Verlag, New York, 1986), pp. 10 –12.
[9]
L. Park and J.M. Rowe, Chem Mater. 10, 1069, (1998).
[10]
B. W. Dockum and W. M. Reiff, Inorg. Chem. 21, 2613, (1982).
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