Pis'ma v ZhETF, vol. 95, iss. 6, pp. 355 - 360
© 2012 March 25
Phase diagram of superfluid 3He in "nematically ordered" aerogel
R. Sh. Askhadullin+, V. V. DmitrievD. A. Kiasnikhin, P. N. Maitynov+, A. A. Osipov+, A. A. Senin, A. N. Yuclin
Kapitza Institute for Physical Problems of the RAS, 119334 Moscow, Russia
+ Leypunsky Institute for Physics and Power Engineering, 249020 Obninsk, Russia Submitted 13 February 2012
Results of experiments with liquid 3He immersed in a new type of aerogel are described. This aerogel consists of A1203-H20 strands which are nearly parallel to each other, so we call it as a "nematically ordered" aerogel. At all used pressures a superfluid transition was observed and a superfluid phase diagram was measured. Possible structures of the observed superfluid phases are discussed.
1. Introduction. An asymmetry of a volume filled by superfluid 3He can influence on resulting pairing states. For example, in the case of a restricted geometry, boundaries of the container can suppress some components of the superfluid order parameter [1]. This distortion persists over a distance of the order of the temperature dependent superfluid correlation length £ = £(T), which diverges at the superfluid transition temperature. Theory predicts, that restricted geometry may stabilize superfluid phases which do not occur in bulk liquid 3He [2, 3]. In superfluid 3He inside a narrow gap (or in 3He film) a planar type distortion is expected for the B phase in agreement with results of recent experiments [4, 5]. A spatially inhomogeneous order parameter with polar core may be realized in a narrow channel. This prediction has not been unambiguously confirmed by experiments, however measurements of mass supercurrent in narrow channels indicate a possible phase transition at the temperature just below the superfluid transition temperature [6, 7]. It is probable that these observations are associated with the transition into such kind of polar-type superfluid phase.
Another way to introduce the anisotropy into super-fluid 3He is to use 3He confined in a globally anisotropic aerogel. It is known that the high porosity silica aerogel does not completely suppress the superfluidity of 3He [8, 9]. It is also established that superfluid phases of 3He in aerogel (A-like and B-like phases) are similar to superfluid phases of bulk 3He (A- and B phases respectively) if the anisotropy of the aerogel is weak or if it corresponds to the squeezing deformation [10-14]. In this case the anisotropy of the aerogel influences only on the orientation of the 3He superfluid order parameter and on its spatial structure [12, 13, 15]. However, recent theoretical investigations [16] show that the stretching anisotropy of the aerogel should result in a polar dis-
1 ^ e-mail: dmitriev@kapitza.ras.ru
tortion of the -4-like phase of superfluid 3He in aerogel. Moreover, if the anisotropy is large enough then, in some range of temperatures just below the superfluid transition temperature, the pure polar phase may be more favorable than the A phase. Unfortunately silica aerogels are rather fragile, therefore in practice the stretching anisotropy can be obtained only in process of aerogel preparation [17] and the large value of this anisotropy is hardly achievable.
In this paper we present results of nuclear magnetic resonance (NMR) studies of liquid 3He confined in a new type of aerogel [18]. This aerogel consists of AI2O3 • H20 strands with a characteristic diameter ~5011111 and a characteristic separation of ~200nm (see Fig. 1 and the SEM-photo in [19]). The remarkable feature of this aero-
Fig. 1. The SEM-photo of "nematically ordered" aerogel
gel is that its strands are oriented along nearly the same direction at a macroscopic distance (~3-5 mm), i.e., this aerogel may be considered as almost infinitely stretched.
To emphasize this property we call it as "nematically ordered" aerogel.
2. Experimental setup. Our experimental chamber was made of epoxy resin Stycast-1266 and had two cylindric cells (see Fig. 2). Two aerogel samples with dif-
Fig. 2. The sketch of the experimental chamber: 1 - the denser sample; 2 - the less dense sample; 3 - quartz tuning fork; 4 - heater
ferent porosities were placed freely in the cells. Samples had a form of a cylinder with the diameter ~4 mm and with the heights 2.6 mm (the denser sample) and 3.2 mm (the less dense sample). Axes of the cylinders were oriented along aerogel strands (z-axis). Each cell was surrounded by transverse NMR-coil (not shown in Fig. 2) with the axis along x. Experiments were carried out in magnetic fields H from 106 up to 346 Oe (the range of NMR-frequencies was from 344 kHz up to 1.12 MHz) and at pressures from s.v.p. up to 29.3 bar. We were able to rotate H by any angle /t in the y^z-plane. Additional gradient coils were used to compensate an in-homogeneity of H and to apply the controlled field gradient. Residual inhomogeneity of H was ~ 4 • 10-5 for H = 0 and ~ 4 • 10-4 for /t = 90°. About 30% of the cell volumes were filled with the bulk liquid, but usually it was easy to distinguish the signal of superfluid 3He in aerogel from bulk 3He signal. Necessary temperatures were obtained by a nuclear demagnetization cryostat and were determined either by NMR in the A phase of bulk 3He (when it was possible) or using a quartz tuning fork calibrated by measurements of the Leggett frequency in bulk 3He-B. To avoid paramagnetic signal from solid 3He aerogel samples have been
preplated by ~2.5 atomic monolayers of 4He. The aerogel strands have bends and their surface is rough so we assume that, in spite of the preplating, a scattering of 3He quasiparticles on the strands is diffusive.
The described setup has been used also for measurements of spin diffusion in normal liquid 3He in the same aerogel samples [19]. The spin diffusion was found to be anisotropic in the limit of low temperatures. Quasiparticles effective mean free paths determined by aerogel strands were found to be: Ay « 850 nm, Aj_ ~ « 450 nm (for the denser sample) and Ay « 1600 nm, Aj_ ~ 1100nm (for the less dense sample). Here Ay and A i are the mean free paths along and normal to the aerogel strands respectively.
Most of the experiments described below were done with the denser sample and the presented results were obtained using this sample if not specially mentioned.
3. Phase diagram. On cooling from the normal phase we observed a superfluid transition of 3He in both aerogel samples. The transition was detected by continuous wave (CW) NMR with H parallel to the aerogel strands (¡j, = 0): at the transition temperature (Tca) a positive NMR-frequency shift (Aw) from the Larmor value appears. The transition temperature is suppressed in comparison with the superfluid transition temperature in bulk 3He (Tc) and the suppression was found to be ~2 times less in the less dense sample than in the denser sample. The pressure dependence of the suppression in terms of the superfluid coherence length £0 is shown in Fig. 3.
Fig. 3. The suppression of Tca of 3He in "nematically ordered" aerogel versus £o/A±. o - the less dense sample, • - the denser sample. The line is the best fit by y = Ax with A = 0.51
Fig. 4 shows the measured phase diagram of super-fluid 3He in "nematically ordered" aerogel. The filled
Phase diagram of superfluid 3He in "nematically ordered" aerogel
357
0.70 0.75
0.85 0.90 0.95
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Fig. 4. The phase diagram of liquid 3He in "nematically ordered" aerogel obtained on cooling from the normal phase. Note that the temperature is normalized to the superfluid transition temperature in bulk 3He. See text for explanations
circles correspond to the transition from the normal phase into a "high temperature" superfluid phase. This phase belongs to a family of Equal Spin Pairing (ESP) phases because its spin susceptibility is the same as in the normal phase and does not depend on T. Below we call this phase as the ESP1 phase. The triangles correspond to a beginning of the lst-order phase transition from the ESP1 phase into a "low temperature" super-fluid phase (LTP), where the susceptibility is less than in the normal phase. A region of coexistence of the LTP and the ESP1 phase is marked by a two-tone area fill. Such a coexistence may be due to a pinning of the interphase boundary on local inhomogeneities of the aerogel. The squares correspond to the end of the transition into the LTP. On subsequent warming the reverse lst-order transition (from the LTP into the ESP phase) is clearly visible only at P > 12 bar and begins at higher temperatures 0.85 T/Tc). More detailed description of the transitions and the superfluid phases is given below.
We have found that NMR-properties at high pressures (P > 12 bar) and at low pressures (P < 6.5 bar) are qualitatively different. The high pressure behavior is illustrated by Fig. 5 where we present the temperature dependence of the effective NMR-frequency shift (2wAw, where w is the NMR-frequency) in continuous wave (CW) NMR-experiments at P = 29.3 bar and with H || z. On cooling from the normal phase we observed the transition into the ESP1 phase with positive Aw (open circles in Fig. 5). At T ~ 0.7Tc the lst-order transition into the LTP starts. The frequency shift in this phase is larger than in the ESP1 phase and on fur-
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Fig. 5. The effective NMR-frequency shift versus temperature (P = 29.3 bar, ¡i = 0, Tca = 0.979 Tc and H = = 346 0e): 1 - the ESP1 phase; 2 - the LTP; 3 - the ESP2 phase on cooling; 4 - the ESP2 phase on warming. Solid and dashed lines (see Section 5 for the explanation). Insert: CW NMR-absorption lines in the ESP1 (dashed) and in the ESP2 phases (solid) at the same temperature (T = 0.79 Tc)
ther cooling in some temperature range we observe two NMR-lines (from the LTP and from the ESP1 phase) with different values of Aw. After the complete transition, we observe on warming only the line from the LTP (filled circles in Fig
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