James Maloney

Journal of Undergraduate Research
Volume 2, Issue 3 - December 2000

Low Temperature Capacitance Measurements of a Novel Low-Dimensional System

ABSTRACT

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)₂NH₂CuCl₃ (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 ˆ 243 K.

INTRODUCTION

James Maloney 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 [1]. 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)₂NH₂CuCl₃, referred to as MCCL, a system of one-dimensional chains of copper spins. In order to investigate the structural and electromagnetic 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 [4]. 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.

EXPERIMENTAL DETAILS

Sample Cell

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.

Measurement Techniques

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 [5]. In order to prevent the background voltage from concealing evidence of the structural transition, a bridge circuit was implemented [6]. 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, 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 [7].

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 [7].

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 [7]. 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 [Fig. 3].

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 V_DC 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

CONCLUSIONS

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.

ACKNOWLEDGEMENTS

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.

REFERENCES

Elbio Dagotto, Rep. Prog. Phys. 62, 1525 (1999).
G. E. Granroth, B. C. Watson, M. W. Meisel, et al., unpublished (2000).
B. C. Watson, Quantum Transitions in Antiferromagnets and Liquid Helium-3 (University of Florida, Dissertation, 2000).
J. W. Hall, W. E. Marsh, R. R. Weller, W. E. Hatfield, Inorg. Chem. 20, 1033 (1981).
F. R. Leon and A. F. Hebard, Low-current Noise Measurement Techniques. unpublished (University of Florida, REU Research Project, 1999).
R. E. Simpson, Introductory Electronics for Scientists and Engineers (Allyn and Bacon, Inc., Boston, 1974).
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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