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Low Temperature Capacitance Measurements of a Novel Low-
In order to investigate the structural and electromagnetic properties of novel low-dimensional systems at
low temperatures, we constructed a versatile sample cell for use in a cryogenic probe operating between 1.5 and
300 K. More specifically, the high temperature structural phase transition in (CH3)2NH2CuCI3 (MCCL) has
been studied using a lock-in amplifier to monitor the signal that had been nulled utilizing standard bridge-
balancing techniques. Variations in the temperature dependence of the capacitance, caused by a structural
phase transition, led to observable changes in the nulled signal, which was decomposed into real and
imaginary components. The measurements yielded a transition ranging from 240 ( 243 K.
The discovery of high temperature superconductivity in cuprate materials, consisting of two-
dimensional planes of copper spins, has generated a heightened interest in the investigation of low-
dimensional systems . Current theoretical descriptions have been unable to predict the properties
of high temperature superconductors, so researchers have been focusing on simpler two-dimensional
and one-dimensional materials. We investigated (CH3)2NH2CuCI3, referred to as MCCL, a system of
one-dimensional chains of copper spins. In order to investigate the structural and electromagnetic f...'f
properties of MCCL, we designed a versatile cell that operated over a wide temperature range. The
technique required the design, construction, and operation of an experimental sample cell for a cryogenic probe,
and measurement methods that involved bridge balancing and lock-in detection.
Previous neutron scattering, electron paramagnetic resonance (EPR), and magnetic susceptibility
experiments indicated that MCCL experiences structural phase transitions in the temperature regions near 10
and 240 K [2,3]. The EPR and magnetic susceptibility measurements, which may not distinguish between
magnetic and structural transitions, collected more accurate data in the vicinity of the transition, when compared
to the preliminary neutron scattering work. Our technique was chosen for its sensitivity to structural transitions
. Therefore, to investigate the precise location of the high temperature structural phase transition, and to
search for hysteresis, we monitored changes in a reference signal that was balanced against the capacitance of
The sample cell was designed for use with a pre-constructed, homemade cryogenic probe capable of operating
from 1.5 to 300 K. The cavities of the sample cell became two identical parallel plate capacitors when
assembled [Fig. 1]. Microcrystalline or powdered samples, nominally 2 mg, were placed between the
conducting plates of one cavity to serve as a dielectric medium.
Figure 1. Sample Cell. The powdered MCCL sample is placed in one cavity to act as a dielectric
medium and then the cell is assembled, forming two parallel plate capacitors. The insulators prevent
the signal from being grounded through the sample cell.
Whenever a measurement is made in the laboratory, a corresponding uncertainty places a limit on its accuracy.
In order to maximize the signal to noise ratio, we utilized several voltage techniques to reduce unwanted noise.
The change in the signal occurred on a nanovolt scale, which could have been masked by a large
constant background voltage . In order to prevent the background voltage from concealing evidence of
the structural transition, a bridge circuit was implemented . The bridge circuit divides the signal in two and
passes one portion through a variable element before rejoining them. The variable element is then tuned so that
the meter detector, connected across both signals, reads zero. The meter acts as a null indicator,
or d Capuclior
of a CApaciter
measuring deviations from zero rather than the background voltage. The setup greatly reduces the associated
error; thus allowing for minute transitions in the sample to be clearly observed .
The arrangement used to monitor MCCL [Fig. 2] is based on the same principle. The capacitor, containing MCCL,
is connected to a capacitance-bridge driven by the internal reference signal, 10 kHz, of the lock-in amplifier.
After the signal passes through the capacitance-bridge, it returns to the lock-in, where the X and Y channels
monitor the real (conductance) and imaginary (capacitance) parts of the signal. Adjusting the phase-angle of
the lock-in decouples the channels so that each can be independently nulled. Afterwards, the computer
begins recording both of the signals. The thermometer is connected to a preamplifier, which increases the
signal strength before passing it to the resistance-bridge, and on to the computer. The computer recorded all of
the data using a Lab-View program.
Figure 2. Experimental Configuration. The region in the dotted line is at low temperature.
Low Temperature Techniques
Resistors were used for thermometry due to the ultra-low temperatures. Our resistor was pre-calibrated from 1.5
to 330 K. Current was sent through the resistor creating a voltage drop, which was measured to yield a
resistance. It was necessary to minimize the error associated with the resistance because we were examining
the precise temperature of the transition. Reducing the error was accomplished with a four-wire measurement.
Two leads carried current through the thermometer, while another pair measured the resulting voltage drop.
Thus, the additional resistance from the voltage drop induced by the current in the leads was not measured and
their uncertainty no longer needed to be taken into account .
Careful consideration was required for the cryogenic probe and sample cell to attain the temperature ranges
of interest. The probe contained copper baffles to suppress heat leaks due to thermal radiation. Wires that ran
from room temperature (300 K) to the 1.5 K pot were thermally grounded to reduce the temperature gradient,
and twisted pairs of wires suppressed interference arising from magnetic coupling . We also constructed
the sample cell out of the same material as the base of the probe to prevent damage caused by thermal
contraction. The thermometer was mounted to the probe base using grease that allowed for thermal
conductance without electrical grounding. The heater consisted of a 1 W, 100 W resistor. We chose to use a
metal film resistor because they retain a constant resistance over a wide range of temperatures. An
evaporative cooling technique was previously designed to reach the probe's lowest attainable temperatures. A 1.5
K pot was filled with liquid helium, which was then boiled off by a high vacuum (100 millitorr). The
evaporative process, an endothermic reaction, generates temperatures as low as 1.5 K.
RESULTS AND DISCUSSION
The preliminary data indicated a discontinuity in the Y channel, which monitored the capacitance term, arising
from changes in the dielectric constant. These shifts occurred at a temperature that was close to the one observed
in the other experiments monitoring different properties. However, the signal to noise ratio in the Y channel
was three to one. The X channel alone offered no clear indication of a transition.
In order to maximize the signal to noise ratio, both X and Y channels were combined into magnitude (R = X2 +
Y2 ) and phase (q = arctan(X/Y)) data sets. Plotting each set as a function of temperature increased the ratio of
the signal to noise from three to six. The increased signal resolution came from the hidden noise information in the
X channel. Whenever the Y channel shifted, there was a corresponding shift in the X channel that was
partially canceled once the data sets were combined.
While traversing the transition region, the phase angle changed by more than p, thereby necessitating
a straightforward adjustment, which did not affect the magnitude of the signal. A Savitzky-Golay routine
performed on the data sets generated a local polynomial regression to determine the smoothed value for each
data point. The hallmark of this method is that the important data features, such as peek height and width,
which may otherwise diminish when simple adjacent averaging is used, are retained.
The phase as a function of temperature data indicate the transition began at 240 K and continued until 243 K
[Fig. 3]. The slope of the magnitude as a function of temperature data flips sign when the voltage
becomes negative and the transition is revealed at approximately 244 K, where there is a discontinuous jump
20 0 220 230 240 250 260 270 280
jump, 244 K.
210 220 230 240 250 260 270 280
curve appeared to wane.
Figure 3. Magnitude and phase as a function of temperature. The data were collected, while cooling,
from MCCL microcrystals. The arrows in the inset of the lower plot indicate a transition from 240 to
243 K. The arrow in the upper plot also marks the structural phase transition at the discontinuous
jump, 244 K.
Several other techniques were used in an attempt to enhance the signal to noise ratio. The time constant of the
lock-in was increased to average more random noise, although a longer time constant also averaged some of
the transition. We also tried doubling the excitation voltage and using a more sensitive analog lock-in
amplifier. While the transition consistently appeared over numerous runs, the sharpness of the transition
curve appeared to wane.
The reduced signal definition could have been caused from stress on the crystal lattice, which would indicate one
type of history dependence. The transition was also most clearly seen when cooling, rather than while warming,
a second hint of hysteresis. Furthermore, previous runs indicated that MCCL powder reacted with moisture in
the air. The data shown in Fig. 3 were collected from microcrystalline MCCL exposed to air for only several
minutes before being placed under high vacuum. The air in the vacuum can was then evacuated and replaced
with nitrogen, an inert gas. However, more data are needed to investigate the hysteresis.
The current arrangement does not allow for temperatures to be rigorously controlled. Nitrogen was added to
the dewar to cool the sample below its high temperature transition, and 15 VDC were continuously supplied to
the metal film resistor to warm the sample back to room temperature. A temperature controller will be
implemented in future studies to control the temperature. Present studies did not utilize this device because
the temperature controller provided insufficient power to the heater. Nevertheless, a battery-powered amplifier
will offer the needed power without introducing AC noise. The transition range and hysteresis may then be
monitored more carefully
Variations in the temperature dependent capacitance, caused by structural phase transitions, were observed
by monitoring deviations in a nulled signal that was balanced with a capacitance-bridge. The recorded data
were consistent with past measurements, which detected the transition at the same characteristic temperature.
The present data indicate that the current experimental setup offers an expedient way to analyze the
structural transitions of MCCL. Future runs can be extended to study the low temperature transition by using the
1.5 K pot, and detailed investigations of hysteresis will be possible after the addition of a temperature controller
and DC amplifier.
This research was supported, in part, by an Undergraduate Research Fellowship from the UF Center for
Condensed Matter Sciences (CCMS) and the National High Magnetic Field Laboratory (NHMFL) Research
Experience for Undergraduates (REU) program. A sincere thanks is extended to James M. Stock, Brian C.
Watson, and Mark W. Meisel, who contributed to the design of the sample cell, experimental setup, and
cryogenic probe. We also wish to thank the D.R. Talham Group, UF Department of Chemistry, for synthesizing
the compounds used in this research.
1. Elbio Dagotto, Rep. Prog. Phys. 62, 1525 (1999).
2. G. E. Granroth, B. C. Watson, M. W. Meisel, et al., unpublished (2000).
3. B. C. Watson, Quantum Transitions in Antiferromagnets and Liquid Helium-3 (University of Florida,
4. J. W. Hall, W. E. Marsh, R. R. Weller, W. E. Hatfield, Inorg. Chem. 20, 1033 (1981).
5. F. R. Leon and A. F. Hebard, Low-current Noise Measurement Techniques. unpublished (University of Florida,
REU Research Project, 1999).
6. R. E. Simpson, Introductory Electronics for Scientists and Engineers (Allyn and Bacon, Inc., Boston, 1974).
7. R. C. Richardson and E. N. Smith, Experimental Techniques in Condensed Matter Physics at Low
Temperatures (Addison-Wesley, New York, 1988).
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