Recently it was discovered that, in contrast to expectations, the low-temperature dielectric properties of some multicomponent glasses depend strongly on magnetic fields. The low-temperature dielectric response of these materials is governed by atomic tunneling systems. We now have investigated the influence of magnetic fields on the coherent properties of atomic tunneling states in a crystalline host in two-pulse echo experiments. As in glasses, we observe a very strong magnetic field dependence of the echo amplitude. Moreover, for the first time we have direct evidence that the magnetic fields change the phase of coherent tunneling systems.