Design of a bespoke 3-axis cryogenic Hall probe and application to measuring the flux density produced by bulk superconductors with a triangular cross-section

Mapping simultaneously the three components of the magnetic flux density B at 77 K and above the mT range is of particular significance in several applications involving high-temperature superconductors. However, finding Hall probes operating in these conditions is nowadays almost impossible. Hence, we recently designed our own device able to perform such measurements [1]. The device uses a commercial, room-temperature 3-axis Hall sensor located in a cylindrical insert whose temperature is carefully controlled to be 25°C, while the outer temperature is 77 K. The active area of the Hall sensor is placed at 2.2 ± 0.25 mm from the bottom of the insert. The sensor shows a linear and temperature-independent response over ±217.5 mT for the axial direction and ±159 mT for the transverse directions. We give details of the experimental set-up and show that the measurement uncertainty is typically around a few hundred µT.
We then demonstrate the successful operation of this 3-axis cryogenic Hall probe by measuring the spatial distribution of B generated by a permanently magnetized bulk with a shape differing from the usual parallelepipeds or cylinders. We investigate large grain YBa2Cu3O7 superconducting cube (13 mm side) cut at 45° with respect to the c-axis. The resulting sample has a square cross-section parallel to the ab-planes and a triangular cross-section parallel to the c-axis. Mapping B along a line parallel to the c-axis, at ~3.5 mm of the largest face, shows that the component parallel to the c-axis is strongly asymmetric while |B| appears almost constant over ~5 mm. We also investigate how the three components of B evolve along a line z perpendicular to the c-axis and parallel to the triangular cross-section. The results point out a strongly off-centred and asymmetric |B| distribution, with |d|B|/dz| differing by a factor ~1.4 on both sides of the maximum. Interestingly, the main features of the |B| distribution can be understood by analytical calculations assuming a homogeneously magnetized sample with uniform critical current density.

References:
[1] N. Rotheudt, J.-F. Fagnard, P. Harmeling, P. Vanderbemden “Adapting a commercial integrated circuit 3-axis Hall sensor for measurements at low temperatures: Mapping the three components of B in superconducting applications” Cryogenics 133 (2023) 103693