Well controlled and highly stable magnetic fields are desired for a widerange of applications in physical research, including quantum metrology,sensing, information processing, and simulation. Here we introduce a low-costhybrid assembly of rare-earth magnets and magnetic field coils to generate afield strength of $\simeq\,10.9\,$mT with a spatial variation of less than10$^{-6}$ within a diameter of spherical volume of $150\,$um. We characteriseits tuneability and stability performance using a single Mg$^{+}$ atom confinedin a radio-frequency surface-electrode trap under ultra-high vacuum conditions.The strength of the field can be tuned with a relative precision of $\leq2\,\times\,10^{-5}$ and we find a passive temporal stability of our setup ofbetter than $1.0\,\times\,10^{-4}$ over the course of one hour. Slow drifts ontime scales of a few minutes are actively stabilised by adjusting electriccurrents in the magnetic field coils. In this way, we observe coherence timesof electronic superposition states of greater than six seconds using afirst-order field insensitive (clock) transition. In a first application, wedemonstrate sensing of magnetic fields with amplitudes of $\geq0.2\,$uToscillating at $\simeq 2\pi\,\times\,60\,$MHz. Our approach can be implementedin compact and robust applications with strict power and load requirements.
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