the smallest temperature coefficient is preferred. Similarly, radiations that can induce  demagnetization must be limited.   Magnet material The field intensity requirement imposes the use of rare earth magnets (meaning that one of the components is a lanthanide). The common compounds are NdFeB or SmCo. In general, NdFeB have a higher residual field (from 1 to 1.4 T instead of 0.8 to 1.1 T for SmCo) but this advantage is largely degraded by the other characteristics. First, SmCo has a smallest temperature coefficient (the reversible magnetism in SmCo decreases by 0.04 %/°C, which is about 10 times less than in NdFeB), higher Cure temperature and higher irreversible point (around 300°C for SmCo against 100°C for NdFeB), and therefore is less prone to irreversible loss of magnetism. As mentioned above, these effects are unwanted because a non-uniform demagnetization may lead to a change in the field orientation. Second, SmCo withstand radiation 2 to 40 times better than NdFeB. Finally, even though SmCo material is brittle and fragile, it is more resistant to corrosion and has a high resistance to oxidation. SmCo with the highest grade (corresponding to a higher coercively) are favorable to further improve the long-term stability. Among the highest grades, grade 28 is usually commercially available and is therefore a suitable material. The compound composition is Sm2Co17 and the blocks are fabricated by sintering. Its characteristics are listed in Table 1.   Table 1. Properties of SmCo28 

Single magnet configuration   For production and magnetization simplicity the magnet assembly must consist of simple basic blocks (parallelepiped, cylinders, etc), with the magnetic moment orients and aligned with one edge. For illustration, we show the performances obtained with a simple parallelepiped block (20 x 20 x 10 mm (x-y-z), magnetized along the x-axis). Figure 9 shows the field intensity and the HR as a function of the distance z from the magnet surface.  Figure 9. Field intensity (left) and homogeneity radius of a 20 x 20 x10 mm single block magnet 

At 2 mm from the above single magnet surface (reasonable position of the sensor), the field intensity is around 140 mT and the homogeneity radius is 0.5 mm. These values comply with the homogeneity and  intensity requirements. But the stray field distance is relatively large: 85 mm. Better performances in more  compact configuration can be achieved with more complex magnet configurations. 

Complex magnet configuration

The main idea is to constructively superpose the field from different magnet at the sensor location and  destructively superpose at the outside. An arrangement known to allow this is the “Halbach” array [7].  Cylindrical Halbach array produce an intense field in a limited region and have a small stray distance because the total magnetic moment is zero. For the desired high accuracy, one suitable configuration consists in a Halbach crown made of 8 cubes, as shown in Figure 10. With fewer blocks, some volume is lost and with more blocks, the elementary cube is too small and the field intensity decreases (it is roughly  proportional to the cube volume) [RD5]. A stack of two such crowns improves the field homogeneity and  gives some displacement freedom along the z-axis (rotation axis). A comparison between the field  178