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We propose an experiment for measuring the effective Casimir pressure betweentwo parallel SiC plates with aligned nuclear spins. The prospective constraintson an axion-neutron coupling constant for both hadronic and GUT axions arecalculated using the process of one-axion exchange. For this purpose, a generalexpression for the additional pressure arising between two polarized plates dueto the exchange of one axion between their constituent fermions is derived. Wedemonstrate that only the polarization component perpendicular to the platescontribute to the pressure. The obtained pressure can be both repulsive andattractive depending on whether the polarizations of both plates areunidirectional or directed in opposite directions. It is shown that althoughthe constraints on an axion-electron coupling obtained in the case ofmagnetized plates are not competitive, the constraints on an axion-neutroncoupling found for plates with polarized nuclear spins are of the same order ofmagnitude of those obtained previously for the GUT axions alone using theprocess of two-axion exchange. The proposed experiment allows also tostrengthen the presently known constraints on the axion-neutron couplingconstants of GUT axions by using both processes of one- and two-axion exchange.

Constraining axion coupling constants from measuring the Casimir interaction between polarized test bodies