General spacetime nonmetricity coupled to neutrons is studied. In this context, it is shown that certain nonmetricity components can generate a rotation of the neutron's spin. Available data on this effect obtained from slow-neutron propagation in liquid helium are used to constrain isotropic nonmetricity components at the level of GeV. These results represent the first limit on the nonmetricity parameter as well as the first measurement of nonmetricity inside matter.
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