Magnetisation studies in the fractional quantum Hall and electron solid regimes

Brief report of EPSRC grant GR/H99202
Investigators: Dr M. Elliott, Dr W.G. Herrenden-Harker (Cardiff University); Dr Alan Usher (University of Exeter).

This was a 2-year collaborative pilot programme to demonstrate the feasibility of performing torque magnetometry measurements in a dilution refrigerator. The motivation for doing this is to study the phase diagram of the exotic new states of matter which occur when a 2- dimensional electron system (2DES) is subjected to high magnetic fields and low temperatures.

Magnetometry has two distinct advantages for such studies: (1) the equilibrium magnetisation of a 2DES is a thermodynamic state variable and therefore provides direct information about the equilibrium Free Energy of the system; this information is very difficult to obtain using more conventional techniques. (2) non-equilibrium magnetisation, originating from induced eddy currents, can be used to study the integer and fractional quantum Hall effects, and the contactless geometry of such a measurement means that the results obtained are unequivocally associated with the 2DES rather than its contacts. The principal achievements of this programme have been:

1. the use of induced eddy currents to determine the energy gap associated with the fractional quantum Hall effect [1]
2. observation of the high-current breakdown of the integer quantum Hall effect [2]
3. measurement of quantum oscillations in the equilibrium magnetisation (de Haas - van Alphen effect) in 2DES [3]
4. measurement of the exceedingly small resistivities associated with the quantum Hall effect (~10^-14 ohms per square) [4]

This research programme has resulted in four publications in international research journals, three conference publications and eight invited talks. It has contributed to the training of three PhD students at Exeter University and two at Cardiff University. The research continues with funding from the Leverhulme Trust and from HEFCE and Oxford Instruments plc through the Joint Research Equipment Initiative.

References
[1] JP Watts, A Usher, AJ Matthews, M Elliott, WG Herrenden-Harker, MY Simmons and DA Ritchie, Phys Rev Lett (1998) 81, 4220
[2] CL Jones, A Usher, M Elliott, WG Herrenden-Harker, A Potts, RA Shepherd, TS Cheng, CT Foxon, Solid State Comm (1996) 97 763
[3] A Potts, RA Shepherd, M Elliott, WG Herrenden-Harker, CL Jones, A Usher, GAC Jones, DA Ritchie, EH Linfield, M Grimshaw, J Phys: Condensed Matter (1996) 8 5189
[4] CL Jones, A Usher, M Elliott, WG Herrenden-Harker, A Potts, RA Shepherd, TS Cheng, CT Foxon, Solid State Comm (1995) 95 409

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