3He spin diffusion in thin4He films

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Physica B 194-196 (1994) 631-632 North-Holland

3 H e S p i n D i f f u s i o n in T h i n 4 H e F i l m s * D.T. Sprague, t N. Alikacem, P.A. Sheldon and R.B. Hallock Laboratory for Low Temperature Physics, Department of Physics and Astronomy, University of Massachusetts, Amherst, MA 01003. We report measurements of the transverse and longitudinal spin diffusion coefficients for 0.1 - 0.24 monolayers of SHe adsorbed on thin 3He films as a function of temperature and 4He coverage. A strong 4He coverage dependence is observed in the spin diffusion which suggests that the SHe quasiparticles in the film are strongly scattered by substrate inhomogeneities for 4He coverages below 0.5 ~ - ~ . Submonolayer coverages of 3He atoms in the surface state of a 4I-Ie film constitute a twodimensional Fermi gas [1]. Thermodynamic properties of the bound state are sensitive to the structure of the liquid-vapor interface of the film [2], and exhibit a dependence on the 4He areal coverage, n4 [1,3]. Transport properties are similarly affected by the local 4He density and Fermi interactions [4]. Here we report measurements of the spin diffusion coefficient, D, in the SHe quasi-two dimensional state together with measurements of the spin susceptibility, X, and the longitudinal and transverse relaxation rates, 1/T1 and 1/7"2, using pulsed NMtt techniques at 62.9 MHz. The susceptibility and relaxation measurements are made by use of Hahn spin echoes and the inversion recovery technique, while stimulated echoes and spin echoes in a static field gradient, 0 < g < 15gauss/cm, are used to measure the diffusion. A submonolayer coverage of SHe, n3 = 1.08pmoles/m 2 ( ~ 0.1 monolayers), is adsorbed to a thin 4He film of varying thickhesS, 5.2 > D4 > 2.1 layers, on Nuclepore, where n4 - 12.82 ~moles/m2/layer x D4. Stimulated echoes were used at low 4He coverages where relatively long values of Tx ( " 1 - 100 see) allowed measurements of low diffusion rates, Do~a, < 10 -4 eraS/see. The measured diffusion is related to the bare diffusion rate by a tortuosity factor D,-aea, = D/a, where c~ = 16 on Nuclepore [5]. For 4He coverages D4 > 2.66, degenerate susceptibility is observed with degeneracy tempera-

tures, T~', in the range 1 0 0 < T F < 3 0 0 mK. However, for 0 < D4 < 2.66 the magnetization contMns a Curie component to the lowest temperatures investigated; T > 2 4 m K (see Fig. 1). For coverages D4 "-~ 2 layers these 3Hie account for --- 10% of the total 3Hie coverage in the film.

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Figure 1. Temperature dependence of the spin susceptibility for D4 = 2.1 (circles), 2.2 (triangles) and 4.4 layers (squares). Coverages D4 < 2.66 display a Curie contribution to the magnetization for temperatures T < TF. The vanishing of the Curie component for D4 > 2.66 layers (see Fig. 2) may be interpretated as the absense of localized 3He in a solidified second layer of the 4He film. Below this coverage,

* Supported through NSF DMR 88-20517 and DMR 91-22348. t Current address: Physics Department, Northwestern University, Evanston, Illinois 0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved SSDI 0921-4526(93)E0896-O

60208.

632 spin diffusion D ~ 10 -6 cm2/sec is measured, and long (--~ 1 0 - 100 sec) T1 relaxation times are seen, both consistent with aHe participating in a solidified second layer. It is also apparent from the temperature dependence of the T1 data that there is a dramatic reduction in the spin correlation time as D4 is increased beyond 2.66 layers. '

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REFERENCES

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Figure 2. Spin diffusion isotherm at 30 mK using stimulated echoes (circles) and spin echoes (triangles). The predicted n4 dependence (solid curve) from Miyake and Mullin [6] is shown for 30 mK. A fraction, N o , of 3tie atoms exhibit Curie magnetization to low temperatures (squares). A marked increase in the aHe mobility for coverages D4>2.66 layers can be seen in the 30 mK isotherm of D shown in Fig. 2. The expected dependence [6] of D on the atte effective mass in the film and the Fermi liquid parameter F~ for a 2-D degenerate Fermi gas can be expressed in terms of the spin susceptibility,

D ,.~

yields the solid curve of Fig. 1. While the coverage dependence is similar (primarily due to the role of the hydrodynamic mass in both the susceptibility and the diffusion), the measured diffusion is at least an order of magnitude small than expected• Furthermore, the temperature dependence is much weaker than 1 / T ~. It is likely that scattering from substrate inhomogeneities contributes to the strong 4He coverage dependence and weak temperature dependence seen in the 3He mobility. Weak localization effects, similar to those seen in thin metallic films with quenched disorder, may be present. In 2D the spin susceptibility is expected to diverge and the spin diffusion is expected to vanish as T ---+ 0 [7]. This may be the proper interpretation of the apparent Curie component seen in X for D4 < 2.66 and what appears to be a mobility edge in the diffusion data. It is necessary to continue these measurements to much lower temperatures to distinguish between these possibilities.

~

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(1)

The use of X / X o measured at each 4He coverage, and calculated values of F~' [2,4] in eqn. (1)

1 B. K. Bhattacharyya, M.J. DiPirro, and F. M. Gaspirini, Phys. Rev. B 30, 5029 (1984); J.M. Valles, Jr., R.H. Higley, B.R. Johnson, and R.B. Hallock, Phys.Rev.Lett. 60, 428 (1988). 2 E. Krotscheck, M. Saarela, and J.L. Epstein, Phys.Rev.B 38,111 (1988); N. Pavloff and J. Treiner, J. Low Temp. Phys. 83,331 (1991). 3 R.H. Higley, D.T. Sprague, and R.B. Hallock, Phys.Rev.Lett.63, 2570 (1989); N• Alikacem, D. T. Sprague and R. B. Hallock, Phys. Rev. Lett. 67, 2501 (1991). 4 D. T. Sprague, N. Alikacem, P. A. Sheldon, and R. B. Hallock, J. Low Temp. Phys. 89, 605 (1992). 5 J.M. Valles, Jr., P h . D . Thesis, University of Massachusetts, 1988 (unpublished). 6 K. Miyake and W. J. Mullin, J. Low Temp. Phys. 56,499 (1984); 7 T. R. Kirkpatrick, private communication; D. Belitz and T. R. Kirkpatrick, Phys. Rev. Lett 63, 1296 (1989); R. N. Bhatt and D. S. Fisher, Phys. Rev. Lett. 68, 3072 (1992).