Constraining spacetime nonmetricity with neutron spin rotation in liquid 4He

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 10−22 GeV. These results represent the first limit on the nonmetricity ζ(6)2S000 parameter as well as the first measurement of nonmetricity inside matter.