  We explore the complementarity of direct detection (DD) and spallation source
(SS) experiments for the study of sterile neutrino physics. We focus on the
sterile baryonic neutrino model: an extension of the Standard Model that
introduces a massive sterile neutrino with couplings to the quark sector via a
new gauge boson. In this scenario, the inelastic scattering of an active
neutrino with the target material in both DD and SS experiments gives rise to a
characteristic nuclear recoil energy spectrum that can allow for the
reconstruction of the neutrino mass in the event of a positive detection. We
first derive new bounds on this model based on the data from the COHERENT
collaboration on CsI and LAr targets, which we find do not yet probe new areas
of the parameter space. We then assess how well future SS experiments will be
able to measure the sterile neutrino mass and mixings, showing that masses in
the range 15-50 MeV can be reconstructed. We show that there is a degeneracy in
the measurement of the sterile neutrino mixing that substantially affects the
reconstruction of parameters for masses of the order of 40 MeV. Thanks to their
lower energy threshold and sensitivity to the solar tau neutrino flux, DD
experiments allow us to partially lift the degeneracy in the sterile neutrino
mixings and considerably improve its mass reconstruction down to 9 MeV. Our
results demonstrate the excellent complementarity between DD and SS experiments
in measuring the sterile neutrino mass and highlight the power of DD
experiments in searching for new physics in the neutrino sector.
