  We investigate experimentally and theoretically the Faraday effect in an
atomic medium in the hyperfine Paschen-Back regime, where the Zeeman
interaction is larger than the hyperfine splitting. We use a small permanent
magnet and a micro-fabricated vapour cell, giving magnetic fields of the order
of a Tesla. We show that for low absorption and small rotation angles, the
refractive index is well approximated by the Faraday rotation signal, giving a
simple way to measure the atomic refractive index. Fitting to the atomic
spectra, we achieve magnetic field sensitivity at the $10^{-4}$ level. Finally
we note that the Faraday signal shows zero crossings which can be used as
temperature insensitive error signals for laser frequency stabilisation at
large detuning. The theoretical sensitivity for $^{87}$Rb is found to be $\sim
40$ kHz/$^\circ$C.
