NMR Studies of 3 He Impurities in 4 He in the Proposed Supersolid Phase

Transcription

1 Journal of Low Temperature Physics manuscript No. (will be inserted by the editor) NMR Studies of 3 He Impurities in 4 He in the Proposed Supersolid Phase S. S. Kim 1 C. Huan 1 L. Yin 1 J. S. Xia 1 D. Candela 2 N. S. Sullivan 1 Received: 06/15/09 / Accepted: Abstract Preliminary results are reported for measurements of the NMR relaxation times of very dilute 3 He in samples of solid 4 He in the region where a supersolid phase 1 has been reported. The results were obtained for carefully prepared samples with different 3 He concentrations. The measurements of the spin-spin relaxation time, T 2, show several interesting features. A temperature independent plateau attributed to the exchange motional narrowing is observed down to the lowest temperature studied, and the observed variation of T 2 with 3 He concentration favors the nonlinear theory suggested by Landesman. 2 The best fit to the data is given by T 2 x 1.89±0.1 3 rather than x 1 3. No evidence of an exchange-phonon bottleneck for the spin-lattice relaxation is seen down to 40mK. The vacancy activation energy is determined to be 13.5K for a sample with x 3 = and molar volume 20.9 cm 3. Keywords Supersolid NMR 3He - 4 He mixture Quantum defects PACS g bd d Mc 1 Introduction The recent observation of a nonclassical rotational inertia fraction (NCRIF) at very low temperatures in solid 4 He has stimulated great interest as it can be interpreted as a first observation of a supersolid phase. 1,3,4,5,6 Even though the result has been repeated by a number of research groups, the underlying physics that leads to the observed NCRIFs is still poorly understood from both experimental and theoretical viewpoints. Moreover many experiments have shown that crystal disorder (vacancies, 3 He impurities, grain boundaries, dislocations... ) plays an important role in determining the effects both quantitatively and qualitatively. It is 1: Department of Physics and National High Magnetic Field Laboratory, University of Florida, Gainesville, FL 32611, USA. Tel.: Fax: sungkim@phys.ufl.edu 2: Department of Physics, University of Massachusetts, Hasbrouck Laboratory, University of Massachusetts Amherst, MA 01003, USA.

2 2 therefore important to investigate the microscopic dynamical properties in the region where NCRIF effects are observed and study the role of disorder using methods other than torsional oscillators. NMR measurements on 3 He in solid 4 He are ideally suited to meet this task because of the high sensitivity of NMR to the motion of 3 He impurities. Furthermore, the relevant frequency scale can be changed easily by changing the applied magnetic field and/or field gradient. In this work, we report the results of careful measurements of the temperature dependence of the nuclear spin-spin relaxation times T 2 of 3 He with varying 3 He concentrations. 2 Experimental Method The NMR cell was designed to have a horizontal cylindrical shape with two coils. One is a solenoidal NMR receiving coil wound around the cylindrical sample cell, and the other is a thermally isolated and orthogonal horizontal RF excitation coil for the RF pulses. This crossed coil design offers (i) the conventional reduction of the unwanted pick-up of RF excitation in the receiving coil, and (ii) thermal isolation of the RF-heated excitation coil that can be heat sunk to the still temperature by means of a weak thermal link. The NMR cell was made with polycarbonate. The cell was tested several times with rapid thermal cycling before use in an experiment and was capable of withstanding sample pressures up to 100 bar and remain superfluid leak-tight. One end of the cell was open to a sintered silver plug that provides the required surface area to insure good thermal contact down to mk temperatures. The other end is sealed by an insulating epoxy (Stycast 2585FT) cap through which the capillary filling line passes. Samples were grown by a blocked capillary method. The pressure of the sample during cooling was monitored by a Straty-Adams capacitive pressure gauge which is connected to the NMR cell. After the sample cell was filled to a pressure of 68bar, the cell was cooled from 2.2K to the 1.2K. When the temperature is cooled to meet the the melting curve, the helium pressure follows the melting curve while liquid solidifies, and after 10 min. the pressure of the sample becomes constant indicating that the sample is completely solid. The final pressure of the solid sample at 1.2K was 30±1bars. The molar volume V m of the samples were determined by the PVT data of Grilly and Mills 10 and the equation derived by Mullin 11 V (p,x 3 ) = x 3 V 3 (p) + (1 x 3 )V 4 (p) 0.4x 3 (1 x 3 ) (1) using the measured pressure of the sample cell. Here V 3 and V 4 are the molar volumes of pure 3 He and the 4 He, respectively. In order to enhance the weak NMR sensitivity we constructed a low temperature preamplifier that was placed close to, but thermally isolated from the receiving coil. The circuit design was a simple source follower using pseudomorphic high electron mobility transistors(phemts). Although phemts generate appreciable heating, they have high gain at low temperatures (up to the UHF range) and the planar geometry allows the phemt to be aligned parallel to the magnetic field, 7 eliminating Hall effects. During our experiment the power dissipated by the amplifier was estimated to be less than 0.7 mw. The r.m.s noise amplitude was measured from 1.5K to 250mK and the estimated overall noise temperature was around 1.1K. The 3 He concentrations were determined by dilution of an initial 1000 ppm gas mixture to 500 ppm and 250 ppm by adding 4 He. The spin-spin relaxation times T 2 were measured at the NHMFL High B/T facility using nuclear magnetic resonance spin-echo techniques for a Larmor frequency of f = 2.05MHz.

3 3 3 Results and Discussion The temperature dependence of T 2 observed for different 3 He concentrations is shown in Fig.1. At high temperatures a well-known strong temperature dependence is observed and is attributed to the thermal activation of highly mobile vacancies. 8 The minimum at T = 1.1K is the familiar BPP minimum 9 when the Larmor frequency is close to the vacancy modulation frequency. From the slope of the temperature dependence and the value of the minimum value of T 2 we can determine the vacancy formation energy E vac and the frequency ω vac with which a vacancy moves through the lattice. This analysis yielded E vac = 13.5 K and ω vac = s 1 for a 500 ppm sample with a molar volume V m = 20.9 cm x x x10 3 T2(ms) 1.0x x x x x /T(K -1 ) Fig. 1 (Color online) Observed temperature dependence of the nuclear spin-spin relaxation time, T 2, for 3 He in solid 4 He at a molar volume V m = 20.9cm 3 for three different fractional concentrations: 10 3, and At temperatures below 0.7 K, we observe temperature independent plateaus of T 2 for all samples studied. This region previously studied down to 0.4K 12 is interpreted as resulting from the quantum tunneling of the 3 He atoms through the 4 He lattice. What has not been well-determined from earlier studies is the concentration dependence. This is important because there is an appreciable lattice distortion around the 3 He impurities due to the difference in the zero-point motion of the two isotopes. This distortion has been described by a relatively long range interaction, 2 V (R jk ) = V o (a/r jk ) 3 (1 3cos 2 ξ ) (2) where a is the near neighbor distance, ξ the angle between R jk and the trigonal axis. This leads to a reduced effective exchange interaction J e f f = J 2 34 /V o where J 34 is the bare exchange frequency. 2 The T 2 measurements determine J e f f which scales as x 4/3 in the simplest model compared to a simple x 1 dependence if the lattice distortion is neglected. These two different dependences are compared in Figure 2. The results clearly show a concentration dependence closer to the value predicted by Landesman. 2 For the lowest concentration

4 / T2 (ms -1 ) ,000 1,200 1,400 x 3 (Concentration of 3 He, ppm) Fig. 2 (Color online) Concentration dependence of the nuclear spin-spin relaxation time T 2 in the temperature independent region. The two lines refer to the fitting based on two different theories : (i) T 1 2 x 3 (red solid line) and (ii) T 1 2 x 4/3 3 (brown broken line). Our data were fitted best by (iii) T 1 2 x3 1.89±0.1 (blue dotted line). studied there is a small temperature dependence greater than the experimental uncertainties and possibly due to variations in the effect of the lattice distortions. We therefore analysed the results for different temperatures and the results are given in Table 1. The analysis show a stronger concentration dependence than expected x 4/3 and points to a shorter range interaction than that given by Eqn 2. Although these series of systematic measurements have been limited to T 250 mk so far, we did carry out one rapid cooling to 40 mk by turning off the pre-amplifier, waiting for 1h and then rapidly measuring the NMR signal. The observed response showed that the relaxation time was considerably less than 10 3 s showing that the expected phonon bottleneck for the relaxation had not been reached. Table 1 Fitting parameters of concentration and temperature dependence of T 2. ( T 1 2 = A x α ). Temp. 250mK 300mK 350mK 400mK 450mK 650mK α A 1.29E E E E E E-8 4 Conclusion Careful measurements of T 2 for 3 He impurities in solid 4 He as a function of temperature show the existence of a temperature independent plateau down to 250 mk for three different

5 5 concentration(250 ppm, 500 ppm and 1000 ppm). From the observed concentration dependence of the data at low temperatures, we conclude that the behavior is best described by a non-linear concentration dependence as predicted by the crystal field interaction model of Landesman. 2 The observed concentration dependence of x 1.89±0.1 is appreciably stronger than the value of x 4/3 predicted by Landesman and suggests that the dominant interaction may have shorter range than that given by Eqn 2, and is better understood in terms of an R 6 dependence. Further measurements at lower concentrations are needed to resolve this issue, and to determine the role played by 3 He impurities in the supersolid region. Acknowledgements We gratefully acknowledge the assistance of L. Phelps in assembling the low temperature amplifiers. This research was carried out at the NHMFL High B/T Facility which is supported by NSF Grant DMR and by the State of Florida. This project was supported in part by an award from the Collaborative Users Grant Program of the NHMFL. References 1. E. Kim and M. W. H. Chan, Science, 305, 1941 (2004). 2. A. Landesman, Phys. Lett. 54A, 137 (1975). 3. E. Kim and M. W. H Chan, Nature 427, 225 (2004). 4. E. Kim and M. W. H. Chan, J. Low Temp. Phys. 138, 1941 (2005). 5. E. Kim and M. W. H. Chan, Phys. Rev. Lett. 97, (2006). 6. A. C. S. Ritter and J. D. Reppy, Phys. Rev. Lett. 97, (2006). 7. J. Bodart, B. M. Garcia, L. Phelps and N.S. Sullivan, Rev. Sci. Instr. 69, 319 (1998). 8. H. A. Reich, Phys. Rev. 129, 630 (1963). 9. N. Bloembergen, E. M. Purcell, and R. V. Pound, Phys. Rev. 73, 679 (1948). 10. E. R. Grilly and R. L. Mills, Ann. Phys.(N.Y.) 18, 250 (1962). 11. W. J. Mullin, Phys, Rev. Lett. 20, 254 (1968). 12. A. R. Allen, M. G. Richards, and J. Schratter, J. Low Temp. Phys., 47, 289 (1982).