Pis'ma v ZhETF, vol.86, iss.9, pp.681-686
© 2007 November 10
Transverse and longitudinal nuclear magnetic resonance in superfluid 3He in anisotropic aerogel
V. V. DmitrievD. A. Krasnikhin, N. Mulders*, V. V. Zavjalov, D. E. Zmeev P. L. Kapitza Institute for Physical Problems RAS, 119334 Moscow, Russia * Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
Submitted 20 September 2007
It was found that properties of nuclear magnetic resonance of both superfluid phases of 3He in anisotropic aerogel can be described in terms of the bulk superfluid order parameters with the orbital order parameter vector fixed by anisotropy of the aerogel sample. It was also shown that by a proper squeezing it is possible to get the sample with isotropic NMR properties.
PACS: 67.57.—/
Introduction. The system "liquid 3He + high porosity silica aerogel" allows to investigate the influence of disorder on p-wave superfluidity. The disorder is introduced by the aerogel strands. The diameter of the strands (~30 A) is much less than the correlation length of the bulk superfluid 3He and a characteristic distance between them is large enough, so the superfluidity of 3He is not fully suppressed [1, 2]. In a weak magnetic field there exist two superfluid phases of 3He in aerogel called A-like and B-like [3]. The A-like phase appears on cooling from the normal phase at pressures above « 20 bar and exists in rather large temperature range in a metastable (supercooled) state.
It is established [3, 4] that the B-like phase is analogous to the B phase of "usual" bulk 3He, i.e. it is described by the same Balian-Werthamer (BW) order parameter as the bulk B phase. It is also known [3] that the A-like phase belongs to the family of Equal Spin Pairing (ESP) phases, but the exact structure of its order parameter is still unclear. G.E. Volovik suggested that the A-like phase in aerogel is described by the Larkin-Imry-Ma (LIM) model with spatially random orientation of Anderson-Brinkman-Morel (ABM) order parameter [5, 6]. In the bulk A phase the order parameter is also described by the ABM model, but it is spatially homogeneous. I.A. Fomin has proposed the so called "robust" ESP phase - the phase in which the orientation of the order parameter is not influenced by the presence of aerogel - as a possible candidate for the Alike phase [7, 8].
In previous experiments in aerogel with porosity of about 98% [3,9-11] (and with aerogels of 97.5% and 99.3% porosity [12-14]) it was found that of nuclear
e-mail: dmitriev0kapitza.ras.ru
magnetic resonance (NMR), properties of the A-like phase are different from the properties of the A phase of bulk 3He. The observed NMR properties also do not correspond well to both LIM and "robust" phase models [11]. Recent experiments with 98% aerogel [15] have clarified the problem: it was found that in squeezed by 1-2 % aerogel sample the A-like phase behaves as the A phase of the bulk 3He with vector I fixed along the axis of deformation (i.e. along the axis of anisotropy). This observation agrees with recent theoretical studies, where it was shown that even for small anisotropy (~1 %) spatially homogeneous A phase order parameter is more favorable than LIM or "robust" state [16, 17]. Consequently, if the sample is inside a glass tube as probably was in [3, 14] (or there is no large enough gap between the sample and epoxy walls of the cell or spacers fixing the sample as it was in [9-11]) then a difference in thermal contraction coefficients of aerogel and the walls could result in uncontrolled deformation and complicate interpretation of the results.
Here we present and compare the results of our recent NMR studies of the A-like and the B-like phases in 3 aerogel samples. As it is shown below two of them were anisotropic, while the third one had isotropic NMR properties.
Experimental details. Experiments were done at pressures of 26.0 bar and 28.6 bar in the magnetic fields range of 40-467 Oe (corresponding to NMR frequencies from 132 to 1517kHz). We used 98.2% porosity aerogel in which silica strands occupy only about 1.8% of the whole volume. Three experimental cells (similar to that described in [4, 10]) with three different aerogel samples were used. The samples had a cylindrical form (sample 1: diameter=4mm, height=3.5mm; samples 2 and 3: diameter=5mm, height=1.5mm) with the axis ori-
ented along z. Samples 1 and 2 were laying freely inside the epoxy cells, so that there were large enough gaps («0.15mm) between the sample and the side and top walls. Correspondingly we believe that no additional deformation could appear during cooldown from room temperature due to thermal shrinkage of the cell, which is expected to be about 1 %. Sample 3 was fixed in the cell by 4 paper spacers (0.15mm thick, width=0.5mm and the length along z-axis is 1.5 mm). The spacers were glued to the side walls and the aerogel sample was presumably squeezed by them in the x-y plane after cooldown from room temperature.
The cells were surrounded by transverse NMR coils with their axes oriented along the x direction. Standard NMR setup was used, i.e. radiofrequency (RF) excitation was applied to the NMR circuit; the voltage across the coil was amplified by a preamplifier and then detected by lock-in amplifier (in case of continuous wave, CW, NMR) or by digital oscilloscope (in case of pulsed NMR). Cell with sample 1 also had a superconducting longitudinal NMR coil for the longitudinal resonance experiments. The corresponding NMR circuit was cold and had the fixed frequency (9095 Hz) with the quality factor of 1860. External steady magnetic field H could be rotated in the z-y plane: most of the experiments were done for H||z (longitudinal field) and for H±z (transverse field).
The temperature was obtained by copper nuclear demagnetization refrigerator and was measured with a vibrating wire viscometer and a quartz tuning fork situated in a large volume connected to the experimental cell by a short (« 5 mm) and narrow (diameter of 1 mm) channel. In order to avoid signal from paramagnetic solid 3He on the surface of aerogel strands, all our aerogel samples were preplated with ~2.5 atomic layers of 4He. Consequently no Curie-Weiss behavior of spin susceptibility was observed in our experiments.
CW NMR experiments in samples 1 and 2. For H||z it was found that in samples 1 and 2 CW NMR line in the A-like phase had large negative frequency shift from the Larmor value. The value of the shift was of the same order as in [15]. We also observed that the negative shift converts to positive as the direction of the external magnetic field is changed to H±z. It is known that in the ABM phase the frequency shift from the Larmor value (Aw) depends on the angle £ between H and the orbital vector 1:
AU,= ^cos(2£), (1)
where w is the NMR frequency and is the Leggett frequency. Accordingly our observations can be explained
if we suggest that the A-like phase in samples 1 and 2 corresponds to the ABM model and both these samples are intrinsically anisotropic with the main axis of anisotropy directed along z. It was also found that the anisotropy of sample 1 was not homogeneous: for H±z at low enough temperature CW NMR line was rather broad and had 3 distinct maxima (line c in Fig.l). The
Frequency shift (Hz)
Fig.l. CW NMR lines in sample 1 in transverse field (H_Lz) obtained by cooling from the normal phase down to onset of the A-like^B-like transition and subsequent warming (for clarity the lines are shifted in y-direction). Temperatures in units T/Tca are shown near each NMR line, where Tca is the superfluid transition temperature of 3He in aerogel. P = 26.0 bar, H = 58.3 Oe, Tca = 0.80 Tc, where Tc is the superfluid transition temperature of bulk 3He
observed maxima can be attributed to 3 parts of the sample where £ is approximately equal to 90° (i.e. 1 ||z), 70° and 45° correspondingly (Аш is maximal at £=90° and equals zero at £=45°). The temperature width of the transition from the A-like to B-like phase in sample 1 was rather wide 0.02 Tca) and it was found that at first the transition occurred for the less shifted part of the A-like phase NMR line (see lines c,d,e in Fig.l). This allowed us to cool the sample down to the A-like^ B-like transition region and then warm up so that the A-
like phase survived only in part of the sample (lines e-j in Fig.l) and the other part was in the B-phase (the B-like phase signal has much larger frequency shift and in Fig.l it can be seen only near Tca as shown by arrows near lines i and j). The obtained in such a way NMR lines in the A-like phase were rather narrow and we used them for the quantitative measurements assuming that they correspond to the part of sample 1 where 1 ||z and £=90° (or £=0° in the case of longitudinal orientation of H). In particular, when we rotated H at a fixed temperature from transverse to longitudinal orientation (H||z) the shift of the A-like phase line changed the sign, but the absolute value of the shift remained the same as it is expected from (1). The obtained dependencies of the frequency shift in the A-like phase on temperature may be recalculated to 0^ (open symbols in Fig.2).
0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.0
TIT
ca
Fig.2. Leggett frequencies ft в and Пдш sample 1 calculated from transverse NMR frequency shift assuming 1 \\z. • - the B-like phase; А,О - the A-like phase, calculated from positive and negative frequency shift data correspondingly. Note that data for fl2A are multiplied by a factor of 6. Tca = 0.80Tc, P = 26.0 bar
In sample 1 we also carried out longitudinal NMR experiments. In these experiments we were sweeping the temperature while recording the signal from the longitudinal NMR coil. To simplify the interpretation we describe below the results where the A-like phase was left only in the region of the sample where 1 ||z. For the ABM order parameter the frequency of longitudinal NMR On should depend on
On =
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