Proposal for the search for exotic spin-spin interactions at the micrometer scale using functionalized cantilever force sensors

Spin-dependent exotic interactions can be generated by exchanging hypothetical bosons, which were introduced to solve some puzzles in physics. Many precision experiments have been performed to search for such interactions, but no confirmed observation has been made. Here, we propose new experiments to search for the exotic spin-spin interactions that can be mediated by axions or Z$^\prime$ bosons. A sensitive functionalized cantilever is utilized as a force sensor to measure the interactions between the spin-polarized electrons in a periodic magnetic source structure and a closed-loop magnetic structure integrated on the cantilever. The source is set to oscillate during data acquisition to modulate the exotic force signal to high harmonics of the oscillating frequency. This helps to suppress the spurious signals at the signal frequency. Different magnetic source structures are designed for different interaction detections. A magnetic stripe structure is designed for Z$^\prime$-mediated interaction, which is insensitive to the detection of axion-mediated interaction. This allows us to measure the coupling constant of both if we assume both exist. With the force sensitivity achievable at low temperature, the proposed experiments are expected to search for the parameter spaces with much smaller coupling constant than the current stringent constraints from micrometer to millimeter range. Specifically, the lower bound of the parameter space will be seven orders of magnitude lower than the stringent constraints for Z$^\prime$-mediated interaction, and an order of magnitude lower for axion-mediated interaction, at the interaction range of $10\, \mu$m.