The ³He Project – topics
The central aim of our project is the characterisation of magnetic and crystallographic properties of solid ³He on a microscopic scale. This can only be achieved using neutron diffraction techniques. The potential of neutron methods in magnetism and their application to nuclear magnetism is well known. They were very successful in the recent investigation of spontaneous nuclear order in copper and silver. The high neutron absorption cross section makes the application of neutron diffraction in solid ³He very difficult - but a careful feasibility study of diffraction experiments shows that new results of fundamental importance in the field of magnetism may be gained.
In addition, the course of the proposed experiments requires technical developments which will open a passage to many other experiments on the physics of ³He in the condensed state. One example is the careful study of the growth of ³He single crystals prior to the investigations of magnetism. The dependence of crystal properties on temperature, density and geometrical restrictions is a subject with an interest on its own. Improved heat exchangers with large surface and high thermal conductivity will be constructed. They will be used for new types of experiments: A direct determination of the relevant interaction in ³He using critical magnetic neutron scattering might be possible, though extremely difficult. The field of low temperature physics of course also benefits from the expected substantial improvement of cooling techniques.
The ³He Project – magnetism
The nucleus of the ³He isotope is a fermion with spin I = ½. Dependent on pressure and temperature a wealth of physical phenomena is observed in condensed ³He. A complex phase diagram of liquid and solid results from co-operative phenomena. They comprise the superfluid states of the liquid phases as well as the observation of magnetic order both in the 2d and the bulk solid.
The unique crystalline as well as magnetic properties of ³He can mainly be attributed to the low mass of the ³He particles. Quantum effects lead to large zero point fluctuations. Consequently, only under pressure the liquid solidifies. At low pressure the crystals have the body centered cubic (bcc) structure. Further increase of pressure then leads into the hexagonal close packed (hcp) phase. The high delocalisation of the ³He particles is related with the exchange of particles between neighbouring sites. These processes are the dominant magnetic interaction and involve the exchange of 2,3 and more ³He-atoms.
The multiple exchange interaction is the most unique feature of magnetism in ³He. It is the only case known in nature where a direct exchange of particles at different sites leads to magnetic order. An odd numbered ring exchange yields a ferromagnetic interaction and an even numbered ring exchange is antiferromagnetic. This competition makes it very difficult to access the interaction directly by experimental means.
The magnetic properties of the solid may be summarised as follows: At temperatures below 1 mK the exchange interaction leads to magnetic ordering [1,2]. The magnetic phase diagram and structures are the direct consequence of the exchange interaction and vice-versa the key to their understanding. The phase diagram is well known from several experimental studies. In contrast, investigations on the magnetic structure are scarce [3,4] and there are still major uncertainties left.
The phase diagram of the 3d-solid shows three different magnetic phases: In the bcc phase at temperatures below 1 mK two of them are found, dependent on the applied external field. In low field a doubled unit cell with spin arrangement up-up-down-down (U2D2) is expected. At fields above 0.4 T an antiferromagnetic structure without cell doubling, but with a moment canted into the field direction (CNAF) is suggested [11].
The present knowledge on the magnetic phase diagram has mostly been obtained using specific heat data and density or pressure measurements [1,2, 12l]. Almost any experiments on ³He requires the presence of a sinter material to ensure sufficient heat transfer. This made investigations using direct magnetic techniques like Squid experiments very difficult. Nevertheless, the NMR data by Osheroff et.al. [5] to date probably give the best characterisation of the low field phase in terms of its symmetry properties. Based on these NMR data the U2D2 or similar structures were suggested.
The relation between theory and experiment in the field of nuclear magnetism has proven to be very inspiring in the past and ³He is one good example: Experimental results have given the first hints to the relevance of ring exchange interactions. On the other hand, theory can predict the ferromagnetic order in the hcp phase and the CNAF structure, but both predictions are still awaiting direct experimental verification.
From the theoretical side the ring exchange model can be approached starting from the Schrödinger equation. This provides the unique possibility of a quantitative comparison between the result of first principle methods and the experiment. The theoretical interpretation of Roger et al. [13,14] is compared to the structure of the experimental phase diagram. They suggest that three and four particle exchange interactions should be dominant compared to both the Heisenberg nearest neighbour and higher order exchanges.
The structures proposed for the high and low field phase can be distinguished uniquely using neutron diffraction. For the U2D2 structure a (½00) reflection is characteristic, for the CNAF structure the (100) reflection would be expected. Consequently, in the early 80’s, neutron diffraction was attempted by two groups located at the CENG, Grenoble and the Argonne National Laboratory. The experiment of Benoit et al. [3] resulted in the observation of neutron intensity at the (½00) reflection, but with very low intensity. Unfortunately, up to now this is the only direct neutron diffraction result on nuclear order in solid ³He and it was never reproduced.
The CENG experiment was performed at a reactor source and the group there was using Ag sinter as heat exchanger. The group at Argonne used a somewhat different approach to the experiment. First, they chose ultra-fine Pt powder as sinter material and where able to demonstrate the cooling of solid ³He from 10 mK to below 1mK within a few hours [4]. Second, the neutron source there was a spallation source. One would have expected that the white beam emerging from such a source would have rendered the sample orientation and further experiments easier. In contrast, this group had severe difficulties with the determination of the sample orientation. With the present knowledge this must be attributed to the strong g-pulse. After the observation of Benoit et al. the work at Argonne discontinued.
Almost in parallel to the neutron experiments on ³He a group of scientists from the Low Temperature Laboratory in Helsinki, the Helmholtz-Zentrum Berlin and the Risø National Laboratory in Denmark started a neutron diffraction investigation on nuclear order in Cu. These experiments, which had similar demands as the ³He experiment, were very successful: It was possible to determine the field dependent phase diagram of nuclear order in copper, including a quite unexpected type of antiferromagnetic order in the fcc-crystal system [13]. Later, the experiments were transferred from Risø to the HZB. There they were continued in a similar co-operation on nuclear spin ordering in Ag which occurs at extremely low temperatures (T < 560 pK).
The experiments on Ag have shown the large potential of neutron scattering: The nuclear spin system in metals is de-coupled from the lattice with time constants up to several hours and consequently the nuclear spin temperature can differ from the electron temperature by several orders of magnitude. Still it was possible to determine the order parameter, the field dependence and the entropy-field phase diagram using neutron methods [9].
To summarise, multiple particle exchange processes in the quantum solid ³He are by far the dominant and responsible for the "high" transition temperature of about 1mK. The proposal suggests neutron diffraction techniques for the direct investigation of the nuclear magnetic structure and interaction mechanism. This includes the construction of an optimised diffractometer and other instrumental developments on the field of ultra-low temperature physics.
The ³He Project – scientific and technical aims
Scientific objectives: The scientific objective of this proposal is the study of magnetically ordered solid ³He using neutron scattering and transmission.
1. Characterisation of ³He crystals
The characterisation of crystal growth and crystalline properties is essential for the planned neutron experiments on magnetic order in ³He. The crystal quality as a function of growing condition like pressure, density and temperature will be characterised. A search for preferred directions of crystal growth will be conducted. The influence of geometry restrictions and different types of sinter on the crystal quality growth will be characterised.
2. Magnetic ordering in the bcc-phase
The experiments will provide information crucial for a full understanding of exchange processes in this fundamental magnetic system. The low-pressure, bcc - phase of solid ³He orders antiferromagnetically with two different magnetic phases at T = 1mK. This unusual behaviour can be interpreted using a multiple-exchange model with two-, three-, four-, and higher order exchanges.
Previously, the low field phase (LFP) which occurs at B<0.4T, has been investigated by both nuclear magnetic resonance [5] and neutron scattering [3] and was shown to have an up-up-down-down magnetic structure (U2D2). From the NMR data, however, an U3D3 or similar structures cannot be excluded. The high-field phase (HFP) that occurs above 0.4 T has not been studied by neutron scattering. Based on other results [c.f. 1] it is thought to have a canted normal antiferromagnetic (CNAF) structure.
The objective of this work will be the determination of the structures of both antiferromagnetic phases. Simultaneously with the measurement of the order parameter by means of neutron diffraction the pressure and density of the sample will be determined. This connects the neutron experiment to data sets obtained by other workers in the field. With proper calibration this will allow the determination of the sample temperature parallel to the neutron experiment.
3. Magnetic ordering in the hcp-phase
For pressures above 10 MPa the crystal has the hcp structure. Within the hcp lattice, exchanges of three particles are expected to predominate over even numbers of exchange. This exchange of an odd number of particles should lead to ferromagnetic ordering but at a transition temperature as low as T = 20 mK.
To date, essentially no experiments have been performed on this ordered phase and the only indication of ferromagnetism is based on the behaviour of the pressure in a cascade demagnetisation, with the clearest evidence having been provided by the Florida workers [6]. The objective will be to use neutron scattering to study and characterise this phase.
4. Critical magnetic scattering study
Finally, a critical scattering study shall be attempted on the bcc-solid at temperatures well above TN. The critical scattering and its temperature dependence yields the most direct information on the relevant exchange processes that can experimentally be obtained [7].
5. Neutron diffractometer and cryostat
At the Helmholtz-Zentrum Berlin an ultra low-temperature refrigerator for temperatures below 1 mK, including a magnet system and the necessary thermometry standards, will be constructed. A neutron diffractometer dedicated for the use in the ³He project will be build. It will be optimised for the special requirements set by the planned experiments. Major improvements compared to previous experiments on ³He will be the use multi-counter systems combined with effective means of background reduction, e.g. using radial collimator systems.
6. Development and optimisation of complementary techniques
The environment of a reactor is very noisy. The operation of ultra-low temperature instruments in such a surrounding requires special precautions to avoid electrical interference problems and excessive heating due to mechanical vibrations. This technically very demanding task shall be solved analogous to the previous neutron diffraction experiments on nuclear ordering in Cu and Ag [8,9].
The neutron techniques will be combined with Squid - and NMR methods to measure static magnetisation and temperature parallel to the neutron experiment. NMR methods may also be developed for the orientation of ³He crystals and the verification of the magnetic domain orientation. Effective noise reduction techniques are necessary and will be developed for this experiment.
7. Sample cell
A new type of heat exchanger, using a sinter of ultrafine Pt / Ag powder will be developed and tested. It is expected that this type of heat exchanger is superior to the commonly used Ag-sinter heat exchanger with regard to the specific surface area and its transverse thermal conductivity. The construction of this high efficiency heat exchanger is expected to be of interest for a large community of scientists working in the field of low temperature physics.
The experiments on ³He require a determination of the pressure inside the sample cell. A modified Straty-Adams [10] pressure gauge shall be developed which can be used in conjunction with the neutron experiment. This objective also has a connection to objective 6 through the necessary construction of the electronic read out circuitry. It is expected that this high precision technique is of commercial interest as a gauge for strain and pressure or any other physical quantity which can technically be converted to a strain measurement.
