  Atomic physics experiments commonly use millitesla-scale magnetic fields to
provide a quantization axis. As atomic transition frequencies depend on the
amplitude of this field, many experiments require a stable absolute field. Most
setups use electromagnets, which require a power supply stability not usually
met by commercially available units. We demonstrate stabilization of a field of
14.6 mT to 4.3 nT rms noise (0.29 ppm), compared to noise of $\gtrsim$ 100 nT
without any stabilization. The rms noise is measured using a field-dependent
hyperfine transition in a single $^{43}$Ca$^+$ ion held in a Paul trap at the
centre of the magnetic field coils. For the $^{43}$Ca$^+$ "atomic clock" qubit
transition at 14.6 mT, which depends on the field only in second order, this
would yield a projected coherence time of many hours. Our system consists of a
feedback loop and a feedforward circuit that control the current through the
field coils and could easily be adapted to other field amplitudes, making it
suitable for other applications such as neutral atom traps.
