3He-4He Mixture Films
Helium Mixture Films
Most recent update: fall 2010
We are engaged in a long-term systematic study of the NMR and third sound
properties of 3He-4He mixture films. Initial studies confirmed the Fermi gas
character of such films at low temperatues for low 3He coverages , and
observed the step-like structure of the magnetization as a function of 3He
coverage . More detailed measurements of the relaxation times and magnetization
a determination of the energetics of the 3He in the 4He film environment [3,4], and
the energies of the ground state and first excited state for the 3He are in good
agreement with current theoretical calculations. Recent work has focused on the
diffusion of the 3He in the 4He film, and has resulted in the observation of a
dramatic change in the difusion coefficient as a function of 4He coverage over a
narrow range of 4He coverage for
0.1 layers of 3He on the 4He film . This mobility edge is apparently analogous
to a metal-insulator transition in the case of a conducting system. Recent work
documented this mobility edge  and compared the observations to
theoretical work on localized Fermi particles. This recent work also uncovered an
unexpected maximum in the diffusion coefficient as a function of 3He coverage.
Figure 1: The energy of the ground state and the first excited state for 3He in the
environment of a 4He film as a function of bulk-density equivalent 4He layers. The smooth
curves are theoretical predictions from density functional calculations (dashed) due to
Treiner and his colleagues, and from variational calculations due to Krotscheck
and his colleagues.
In parallel experiments we are investigating the velocity and damping of third
sound in the mixture film system with a third sound resonator which is located in
the same experimental cell as is the NMR resonator. Early results  from this work
show interesting structure in the third sound velocity as a function of temperature
which is not explained by current theory. An interesting transition of some sort
is present in the film system near a temperature of 200 mK, with changes apparent in
the velocity, the damping and the phase of the resonance. Presumably these changes
are related to the configuration of the 3He in the film, although no theory which adequately explains
the observations has been advanced. There is a gentle peak in the resonance frequency near
150 mK at the higher converages (which is not shown well in this figure)
which has not been explained.
Figure 2: The third sound frequency, (a), and phase between the third sound
driver and capacitive detector, (b), as a function of temperature. The frequency is
shown for various thickness of 3He (0.099 [top] to 0.721 [bottom] monolayers) on a 5.0 (bulk equivalent)
layer thickness 4He film. The
phase is shown for several drive powers for the case of a 3He film of coverage 0.68
monolayers. From .
More recently we have initiated a study of the specific heat of the 3He on thin 4He films. This work
is valuable in its own right, but especially so when viewed in the context of our previous
NMR work on these films. Early results from the specific heat experiment confirm the presence
of a step in the specific heat in analogy with that seen in the magnetization. When this work
is completed, we will be in a good position to determine the two most important Fermi liquid
parameters for the two-dimensional 3He system .
Our most recent work involves a study of very thin helium 3He-4He mixture films on a hydrogen substrate. There we have
observed a very unusual second decoupling of mass from the substrate, but only in the presence of 3He. This requires further study.
 J.M. Valles, Jr., R.H. Higley, B.R. Johnson, and R.B. Hallock, Phys. Rev.
Lett. 60, 428 (1988).
 R.H. Higley, D.T. Sprague and R.B. Hallock, Phys. Rev. Lett. 63, 2570 (1989).
 N. Alicacem, D.T. Sprague, and R.B. Hallock, Phys. Rev. Lett. 67, 2501 (1991).
 D.T. Sprague, N. Alikacem, P.A. Sheldon and R.B. Hallock, Phys. Rev. Lett. 72,
 D.T. Sprague, N. Alikacem, and R.B. Hallock, Phys. Rev. Lett. 74, 4479 (1995).
 P.A. Sheldon and R.B. Hallock, Phys. Rev. B, 50, 16082 (1994).
 P.A. Sheldon and R.B. Hallock, Phys. Rev. Lett. 77, 2973 (1996).
 P.A. Sheldon and R.B. Hallock, Phys. Rev. Lett. 85, 1468 (2000).
 P-C. Ho and R.B. Hallock, J. Low Temp. Phys. (QFS 2000, in press).
 R.B. Hallock, Physics Today 51, 30 (1998).
 P.T. Finley, P.S. Ebey and R.B. Hallock, "Unexpected Mass Decoupling for 3He - 4He Films on a Solid Hydrogen Substrate",
Phys. Rev. Lett. 98, 265301 (2007).