  Solid-state magnetic field sensors are important to both modern electronics
and fundamental materials science. Many types of these sensors maintain high
sensitivity only in a limited range of temperature and background magnetic
field, but Hall-effect sensors are in principle able to operate over a broad
range of these conditions. Here, we fabricate and characterize micrometer-scale
graphene Hall sensors demonstrating high magnetic field sensitivity from
liquid-helium to room temperature and in background magnetic field up to
several Tesla. By tuning the charge carrier density with an electrostatic gate,
we optimize the magnetic field sensitivity for different working conditions.
From measurements of the Hall coefficient and the Hall voltage noise at 1 kHz,
we estimate an optimum magnetic field sensitivity of 80 nT Hz$^{-1/2}$ at 4.2
K, 700 nT Hz$^{-1/2}$ at room temperature, and 3 $\mu$T Hz$^{-1/2}$ in 3 T
background magnetic field at 4.2 K. Our devices perform competitively with the
best existing Hall sensor technologies at room temperature, outperform any Hall
sensors reported in the literature at 4.2 K, and demonstrate high sensitivity
for the first time in a few Tesla applied magnetic field.
