Influence of pressure on the magnetic response of the low-dimensional quantum magnet
Cu(H2O)2 (C2 H8 N2) SO4
Brandon D. Blasiola*, Marcus K. Peprah, Pedro A. Quintero, Mark W. Meisel
Department of Physics and National High Magnetic Field Laboratory,
University of Florida, Gainesville, FL 32611-8440
and
Alžebeta Orendáčová
Institute of Physics, Faculty of Science, P. J. Šafárik University, Park Angelinum 9,
SK-041 54 Košice, Slovak Republic
End of Project Report for the Summer 2015 UF Physics REU Program
sponsored by the National Science Foundation (NSF) via DMR-1461019
26 July 2015
*Permanent Address: Department of Physics and Astronomy, Eastern Michigan University,
Ypsilanti, MI 48198
Abstract
The influence of pressure on the low-dimensional molecular magnet Cu(H2O)2(en)SO4 (en =
ethylenediamine = C2 H8 N2) has theoretically been shown to affect the exchange interactions of
the material. Herein, the results of an experimental study of pressure effects on the
temperature dependence of the magnetization of Cu(H2O)2(en)SO4 are reported. Using two
different pressure cells, the magnetization measurements were performed between 2 K and
10 K with pressures ranging from ambient to 5.0 GPa. The data suggest, albeit not conclusively,
a possible a shift in the magnetization peak of the material at the lowest temperatures and at
the highest applied pressures.
1
1. INTRODUCTION
Previous theoretical analyses have shown that the molecular magnet Cu(H2O)2(en)SO4
(Fig. 1) has pressure-dependent exchange interactions. By increasing the pressure, the
temperature dependency of its magnetization should be altered. The ability to alter the
magnetic state of a compound is relevant to the
study of high-temperature superconductors and
also may provide insight to quantum states such as
the spin-liquid, which can lead to improvements
for computer memory storage and performance
[2].
w ≅ 0.25 in.
Pressure dependence of the exchange
interactions of Cu(H2O)2(en)SO4 up to 8.2 GPa has
been studied by Legut and Sykora [1]. However,
the effects of pressure on the temperature
Figure 1: A crystal of Cu(H2O)2(en)SO4 is shown along
with its width.
dependency of the magnetization has not been
explored. Here we report experiments that have been conducted on the effects of pressure on
the temperature dependency (between 2 and 10 K) of the magnetization of Cu(H2O)2(en)SO4.
Primary experiments have shown that the magnetization of Cu(H2O)2(en)SO4 has a peak around
2.5 K at ambient pressure. So far, experiments have revealed that the magnetic response at low
temperatures is insensitive to pressures up to 0.6 GPa. Further tests conducted at pressures as
high as 5.0 GPa appeared to show small changes in the temperature dependence of the
magnetization that indicate that the magnetization peak may shift to lower temperatures.
1.1 Crystal Structure and Properties
Materials with triangular lattice structures exhibit frustrated magnetic states that can be
influenced by pressure [3]. One such compound is Cu(H2O)2(en)SO4 ,a low-dimensional,
insulating antiferromagnet with S = 1/2 [4]. The dimensionality of Cu(H2O)2(en)SO4 is
2
unresolved since some studies claim it is quasi-onedimensional [1] and others infer it is quasi-twodimensional [5]. Cu(H2O)2(en)SO4 has the form of a
monoclinic, triangular lattice with unit cell (Fig 2.)
parameters a = 7.232 Å, b = 11.725 Å, c = 9.768 Å,
β = 105.50◦, and Z = 4 [4]. The spins in the lattice are
arranged so that each vertex in the triangular lattice
has one spin. Two of the spins on each triangle will
align antiferromagnetically and be “satisfied”
because they have found the lowest energy state.
The third spin, however, can align itself up or down.
Since both the up-state and the down-state have
the same energy, this spin state is considered to be
frustrated. This frustration leads to degeneracy in
the ground state.
The distance between the frustrated spins and
the non-frustrated spins can then be changed by
Figure 2: The crystal structure of Cu(H2O)2 (C2 H8 N2) SO4 is
shown.[5]. (a) A chain of crystals showing the triangular
lattice structure (highlighted by the blue triangles) (b) A
oblique view showing how multiple chains are connected to
form a plane
imposing pressures on this lattice structure. By
altering the unit cell parameters, the spins will interact differently than how they would act at
ambient pressure. Different interactions mean that the overall energy in the crystal lattice is
not the same, which suggests that the temperature dependence of its magnetization should
change.
2. METHODS
2.1 Data Collection and Analysis
2.1.1 The SQUID Magnetometer
All of the data discussed in this paper were collected using a superconducting quantum
interference device (SQUID) magnetometer. The model used was a Quantum Design Magnetic
Property Measurement System (MPMS)-XL7 DC SQUID magnetometer. The MPMS-XL7 can
3
generate fields up to 7 Tesla and can reach temperatures as low as 1.8 K. The MPMS-XL7 is used
since these experiments needed to be conducted between 2 K and 10 K. The SQUID functions
by passing a sample through three superconducting coils. A current is induced in the coils, and
the SQUID measures the longitudinal moment of the sample as a function of temperature.
Samples can be held in a variety of ways and are attached to the end of a transport rod that
slides into the SQUID. A top-mounted motor moves the rod up and down through the coils.
2.1.2 General Data Analysis Techniques
The first data analysis technique used with these data sets was Automatic Background
Subtraction (ABS). This technique has two parts: the first is a run-through of the data collection
sequence with everything except for the sample. The SQUID measures the contribution of these
components and records them. The data collection sequence is then ran with the sample inside
the cell, and ABS is engaged. When ABS is engaged, the SQUID automatically subtracts the
background data that were previously measured from the data it is actively collecting, and
theoretically removes all signals except for the signal from the sample.
A second analysis method used was point-by-point background subtraction; this method
was used for the anvil cell only. For this method, the cell without the sample was run through
the SQUID to obtain a background and a sixth-order polynomial as a function of temperature
was fit to the background data. The background was then
calculated and subtracted point-by-point from the sets.
2.2 Experimental Procedures
2.2.1 The Piston Pressure Cell
The pressures used in these experiments were
achieved by using two types of pressure cell. One type is
the beryllium-copper piston pressure cell that was
custom-designed and machined at the University of
Florida (Fig. 3). Beryllium-copper was chosen because of
its low magnetic signature and its moderate yield strength
4
Figure 3: A schematic of the Piston Pressure Cell
(NOT to scale) [6].
of 1.4 GPa [7]. The signal-to-noise ratio is large due to the low magnetic signature of the BeCu;
this allows for clean data collection. The cell consists of several parts: the sample chamber, two
pistons, two pushers, and two endcaps. The cell has overall dimensions of 1.195 inches in
height by 0.34 inches in diameter. When using this type of pressure cell, the sample is loaded
into a small Teflon can with a pressure medium and a small amount of lead as a manometer.
The sample space inside the Teflon can has dimensions 0.147 inches in height by 0.065 inches in
diameter [6]. The pistons, pushers, and endcaps are assembled into the pressure cell in that
order.
2.2.2 The Anvil Pressure Cell
Due to the structural limitations of the
beryllium copper cell, a second type of pressure cell,
a silicon carbide anvil cell, was used to achieve
higher pressures. This cell is constructed of copper-
Figure 4: The Anvil Pressure Cell compared to a US
penny.
titanium and has two silicon-carbide
culets that are set in counter-threaded
endcaps that face each other; the cell is
tightened like a turnbuckle [6]. Figure 4
shows a picture of the anvil pressure cell
next to a US penny. The sample is loaded
into a 290 µm diameter hole (outlined by
the yellow circle) in a very small gasket
that sits between the faces of the
crystals. The SiC pressure cell can achieve
pressures of about 5 GPa [6]. In order to measure
the pressure inside of this cell, ruby fluorescence is
used.
Figure 5: (Left) A picture (Taken from the top of the
cell before being pressurized) of the sample inside the
anvil cell. The gasket is the bronze region and the
sample is the bluish region The sample in this cell was
a single crystal of Cu(H2O)2(en)SO4. The cell is backlit
and differences in the thickness of the crystal cause
the sample to appear different shades of blue. A
pressure medium (for hydrostatic pressure) and ruby
particles (for manometry) are also present.
(Right): A drawing of the anvil cell showing the
counter-threaded endcaps, SiC anvils, gasket, and
sample.
5
2.3 Superconducting Transition of
0.04
(a)
The piston pressure cell that
was used to hold the samples has no
means to read the internal pressure
mechanically. The compactness of the
cell leaves no room for any type of
Magnetization (10-3 emu G)
Lead as a Manometer
0.02
Tc_min = 6.725 K
Tc_max = 6.8 K
Pmax= 1.2 GPa
Pmin= 0.98 GPa
P  Tc
0.00
0.405
Tc = 6.75 K
P = 1.1 GPa
-0.02
-0.04
conventional pressure gage,
6.4
necessitating a different method.
6.5
6.6
6.7
6.8
6.9
7.0
7.1
7.2
7.3
7.4
T (K)
The element lead, Pb, when
experiencing atmospheric pressure,
undergoes a superconducting transition at
7.2 K [8], meaning that it suddenly
becomes strongly diamagnetic. This
transition manifests as a change in sign of
the magnetization, a clear example of
which can be seen in Figure 6b. When
under pressure, the critical temperature
of Pb is decreased. The pressure in the cell
can then be calculated by finding the
difference between the atmospheric
critical temperature and the high-pressure
Figure 6: (a): The superconducting transition of lead is shown.
The transition temperature estimate was incorrect, thus, some
graphical analysis was necessary. The green line at 6.75 K is
where the lead was found to transition for P = 1.1 GPa. The red
line extends the non-superconducting state and the blue curve
extends the superconducting state. (b): The superconducting
transition of Pb for three different pressures is shown. These
data were collected by Marcus Peprah and used with his
permission [6].
critical temperature using the linear relation
ΔT/ΔP = 0.405 K/GPa [9].
The Pb transition is measured by the SQUID by sweeping the temperature over the
anticipated transition temperature range, beginning first by cooling down to near 6 K and
warming up. Warming measurements are done to prevent false data from supercooling. A small
region where we expected the transition to happen was selected to have a higher resolution of
6
data points. As can be seen in Figure 6a, we had estimated incorrectly. Because we had placed
the high-resolution temperature sweep incorrectly, finding the approximate critical
temperature required graphical analysis. We know that the critical temperature has to lie
between the last point in the paramagnetic phase and the first point in the diamagnetic phase.
A linear fit was applied to the high-temperature data, continuing the line where more data
points would have been collected if the lead did not have a superconducting transition. A
parabolic curve was fit to the few data points in the low temperature end, extending the line
where data points would have been if the transition occurred at a much higher temperature.
The region in which the critical temperature can be found lays between where these two curves
intersect and the last data point on the high-temperature data. This range was found to have
upper and lower limits of 1.2 GPa and 0.98 GPa, respectively. These data can be seen in Figure
6a. A graph showing a high-resolution Pb transition can be seen in Figure 6b.
2.4 Ruby Fluorescence
The sample space for the anvil pressure cell is
approximately two orders of magnitude smaller than
the piston pressure cell, so Pb manometry cannot be
used. Instead, we used the ruby fluorescence scale.
Minute particles of Cr3+-doped ruby are placed in the
sample space; these are the tiny dark spots in Figure
7. A violet laser with wavelength λ = 405 nm is used
to irradiate the sample space. The Cr3+ is energized and
Figure 7: A picture of the ruby particles inside
the anvil cell. This picture was taken from the
bottom of the cell prior to it being pressurized.
emits light of wavelength, λ = 694.15 nm, at room
temperature. The Cr3+ will emit light at a higher
wavelength when under pressure, and the new
pressure can be determined by the relation
P  
0.365
[10].
The intensity curves of the ruby fluorescence for these experiments are shown in Figure 8.
7
500
P=0
P = 2.5 GPa
P = 5.0 GPa
Intensity (Counts)
400
300
200
100
0
690
691
692
693
694
695
696
697
698
699
700
Wavelength (nm)
Figure 8: The black, red, and blue curves show the intensity peaks for
pressures of 0, 2.5, and 5.0 GPa, respectively. As pressure is increased,
the peak red-shifts. This phenomenon is linear for the pressures used in
these experiments [10]
3. RESULTS AND DISCUSSION
3.1 Crystal Response
The sample alone has the
peak at low temperatures shows
where the quantum state of the
crystal is the spin liquid. The purpose
of this research has been to see
Magnetization (10-3 emu G)
signal shown in Figure 9. The small
1.2
whether or not the position of the
1.0
0.8
Crystal Only in 1 kG
0.6
peak, and more specifically, the
0
1
2
3
4
5
6
7
8
9
Temperature (K)
temperature dependency, can be
Figure 9: The signal from an isolated crystal is
shown. The peak of the magnetization can be
seen around 2.5 K.
changed with pressure.
8
10
3.2 Data Table
Table 1, Summary of data collected between March 2015 and July 2015
Measurement Sample
Mounting
Pressure
Figure Comments
Mass
1
4 mg
Piston cell
0 GPa
11a
Peak at 2.5 K
2
4 mg
Piston cell
0.6 GPa
11a
Peak at 2.5 K
3
4 mg
Piston cell
1.1 GPa
11c
More prominent peak at 2.5 K
4
3 mg
straw
ambient
10
Crystal only
5
~4µg
Anvil cell
0 GPa
15
No discernable peak, too noisy
6
~4µg
Anvil cell
2.5 GPa
15
No peak, but trend toward peak
for T < 2 K
7
~4µg
Anvil cell
5.0 GPa
15
No peak, but trend toward peak
for T < 2 K
8
0
Anvil Cell
0 GPa
9
12
Background only, no sample
3.3 Data collected in the Piston Pressure Cell.
Data were collected in this cell in pressures ranging from ambient to 1.1 GPa using
automatic background subtraction and point-by-point background subtraction. The data that
show the pressure in the cell are shown in Figure 10. Figure 10a and 10b use ABS. The data
from the ambient pressure and 0.6 GPa runs are shown in Figure 10a. At first look, they appear
to differ by only a vertical shift. Figure 10b shows the ambient data shifted vertically. The inset
shows the difference between each point. It can be said that there is no significant change in
temperature dependence between ambient pressure and 0.6 GPa.
Magnetization (10-3 emu G)
(a)
1.4
1.2
1.0
0.6 GPa
Ambient
Magnetization (10-3 emu G)
0.8
(b)
1.4
1
1.2
2
3
4
5
6
Temperature (K)
1.0
0.6 GPa
Ambient (normalized)
(d)
1.5
1.0
1.1 GPa data shifted by a constant
0.5
0.6 GPa
1.1 GPa
(e)
4.4
Diff. between 0.6
and 1.1 GPa
Trendline
4.2
D = (2 x 10-5 )*T + (6.01 x 10-4)
Blasiola 2015 July 09
4.0
0.8
2.0
Magnetization (10-3 emu G)
Magnetization (10-3 emu G)
2.0
0.0
0.17
0.16
0.15
0.14
0.13
0.12
0.11
0.10
0
Difference (10-4 emu G)
Magnetization (10-3 emu G)
1.6
(c)
1.5
1.0
0.5
0.6 GPa
1.1 GPa
0.0
2.0
(f)
1.5
1.0
0.5
0.6 GPa
1.1 GPa
0.0
0
1
2
3
4
5
6
7
8
9
10
Temperature (K)
0
1
2
3
4
5
6
7
8
9
10
Temperature (K)
Figure 10 (All data collected in 1 kG): (a) Ambient pressure data and 0.6 GPa data, (b) Showing the vertical shift, inset: The difference between
ambient ant 0.6 GPa, (c) 0.6 and 1.1 GPa data, (d) 1.1 GPa shifted up by a constant to compare to (b), (e) Fitting a line to the difference
between 1.1 GPa and 0.6 GPa at high temperature, (f) The linear fit from (e) applied to the 1.1 GPa data.
10
Figure 10c shows the raw data from 0.6 GPa and 1.1 GPa. It appears that there may be a
difference in the low-temperature dependence. The data were shifted vertically so that the 10K
data points overlie. This step is shown in Figure 10d. Assuming the high-temperature data (8 K 10 K) have properties independent of pressure, a fit was found that brought the 8 K -10 K data
from 1.1 GPa into agreement with 0.6 GPa. This fit was then applied to the entire 1.1 GPa data
set. The final outcome of this analysis is shown in Figure 10f. While the peak has not shifted up
or down the temperature scale, the temperature dependence is different. At 1.1 GPa, the
curve has a steeper curvature. These data indicate that pressure may influence the prominence
of the peak.
3.4 Data Collected in the Anvil
The raw data that were collected
in the anvil pressure cell under pressures
between 0 and 5.0 GPa are shown in
Figure 11. While a potential change in
Magnetization (10-4 emu G) )
3.2
Pressure Cell
temperature dependence cannot be
3.0
2.8
2.6
P = 5.0
P = 2.5
P=0
Background
2.4
2.2
determined from these data, it can be
0
1
2
3
noted that the overall strength of the
cell. Because of this constraint, the
signal from the cell dominates the signal
from the sample. The first attempt to
7
8
9
10
2.9
Magnetization (10-4 emu G)
than the amount that fit into the piston
6
3.0
The amount of sample that was able to
almost two orders of magnitude less
5
Figure 11: The raw data collected in the anvil
cell are shown.
response is increased with pressure.
be put in the anvil pressure cell was
4
Temperature (K)
2.8
2.7
2.6
2.5
2.4
Background
Fit
2.3
2.2
remove the background came from
0
fitting a sixth-order polynomial (Fig. 12)
1
2
3
4
5
6
7
8
9
Temperature (K)
Figure 12: The background data collected from the
Anvil Cell and the polynomial curve fitted to it.
to the background data since the
11
10
temperature data for each run are not
background subtractions performed
from the fit equation. Many variations
are present and are partially due to the
Magnetization (10-5 emu G)
exactly the same. Figure 13 shows the
0.00
P = 0 GPa
-0.05
-0.10
-0.15
-0.20
-0.25
-0.30
uncertainties subtract to get a very
small number with a big uncertainty.
In order to fix this issue, the
data were normalized by calculating
the percent difference between the
raw data and the background data. The
normalized data can be easily analyzed
P = 2.5 GPa
1.65
1.60
1.55
1.50
1.45
1.40
Magnetization (10-5 emu G)
two large numbers with big
Magnetization (10-5 emu G)
-0.35
nature of the background subtraction:
P = 5.0 GPa
2.30
2.25
2.20
2.15
2.10
2.05
0
since this method puts the
1
2
3
4
5
6
7
8
9
10
Temperature (K)
Figure 13: The raw data from the anvil cell with background
subtracted. Since the subtraction was with two big numbers
with big uncertainties, we are left with a small number with a
big uncertainty. No conclusions can be drawn from these data
because they are too noisy.
magnetization data into arbitrary units.
The normalization data are shown in Figure 14.
The 2.5 GPa data and the 5.0 GPa data
-2
toward low temperatures. The P = 0
data, however, does not appear to show
any trend. No conclusions can be drawn
from the P = 0 data set because it is too
noisy; the data are a line within the
noise. The trends that are present in the
2.5 GPa and 5.0 GPa data sets are barely
Magnetization (Arb. Units)
sets both show somewhat of a trend
Anvil P=5.0 GPa
Anvil P=2.5 GPa
Anvil P=0 GPa
-3
-4
-5
-6
-7
0
outside of the noise.
1
2
3
4
5
6
7
8
9
10
Temperature (K)
12
Figure 14: The normalized high-pressure data are shown.
Trends are visible in the 2.5 and 5.0 GPa data, but the 0 GPa
data is a line within the noise. The orange lines represent a
centerline for the data. The gray data lie within the noise, but
the maroon and blue data lie just outside the noise. The black
bars on each orange line represent 2σ for each data set..
-1
temperature appear to have peaks
at lower temperatures than the
M (Arb. Units)
The trends that appear at low
peak at ambient pressure. If the
removed, the peak is removed, but
the trend toward a peak is still
-3
-4
-5
-6
-7
Piston P=0.6 GPa
Piston P=0 GPa
Crystal Only
1.4
M (10-3 emu G)
lowest-temperature data point is
Anvil P=5.0 GPa
Anvil P=2.5 GPa
Anvil P=0 GPa
-2
present. Because the removal of
1.2
1.0
0.8
0.6
0
1
2
3
that single data point removes the
confidence of a peak being at 2 K,
the presence of this peak cannot be
unambiguously established. However, a
general trend does seem to be present and
4
5
6
7
8
9
10
Temperature (K)
Figure 15: The normalized high-pressure data compared to
the data collected in the piston cell. While the highpressure data from the anvil cell appears to peak around 2
K, if that last point is removed, the peak is removed.
Nevertheless, the trend remains that the high-pressure
data may have a magnetization peak at a temperature
lower than 2.5 K.
suggests, albeit it not conclusively, the data possess a peak at a temperature less than 2.5 K.
The comparison among the high-pressure data from the anvil pressure cell and the lowerpressure data from the piston pressure cell is shown in Figure 15.
4. CONCLUSIONS
It has been shown theoretically that Cu(H2O)2(en)SO4 has some pressure-dependent
properties such as its exchange interactions [1], but experiments on the influence of pressure
have not been studied previously. The experiments conducted here have suggested that it may
be possible to alter the temperature dependence of the magnetization of Cu(H2O)2(en)SO4 with
pressure. Data collected at 1.1 GPa show a small change in the temperature dependence such
that the peak is more prominent under pressure than at ambient. The temperature at which
the peak exists was not changed for experiments up to 1.1 GPa in the piston pressure cell. Data
collected in the anvil cell have exhibited trends that may indicate that the temperature at which
the magnetization peaks can be shifted by pressure. The data collected at 2.5 GPa and 5.0 GPa,
while not definitive, suggest that the magnetization has a peak at a lower temperature.
13
These experiments, while not extensive, have shown that it may be possible to alter the
magnetization of Cu(H2O)2(en)SO4 with pressure. There are two main reasons that the data
were not definitive: small signal strength and the structural limitations on the cells. The amount
of sample that can be fit into the anvil cell is very small. However, the anvil cell was the only cell
present that could achieve higher pressures. For further studies on the magnetization of
Cu(H2O)2(en)SO4 , a different type of pressure cell will need to be designed. A cell that can hold
a large amount of sample and also achieve pressures greater than 2.5 GPa would be key. Also,
according to the data presented, the magnetization peak may exist below 2 K. The SQUID used
in these experiments can only reach 1.8 K, so a different SQUID that can achieve temperatures
less than 1 K or a different data collection process would need to be implemented in order to
obtain definitive data.
Acknowledgements
This work was supported, in part, by the National Science Foundation (NSF) via DMR1202033 (MWM), DMR-1157490 (NHMFL), and DMR-1461019 (UF Physics REU Program).
Contributions to general laboratory practices by co-REU student Jaynise Peréz Valentíne are
recognized, and assistance from Derrick VanGennep of the Hamlin group are gratefully
acknowledged.
14
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