We present a novel experimental scheme enabling investigation of transient exotic spin couplings. The scheme is based on synchronous measurements of optical-magnetometer signals of several devices operating in magnetically shielded environments in distant locations (> 100 km). Although signatures of such exotic couplings may be present in a signal of the single magnetometer, it would be challenging to extract them from noise. With correlation measurements of signals from the magnetometers, not only the effects can be identified but their nature may also be investigated. The ability of the network to investigate physics beyond the Standard Model is discussed by considering the spin coupling to stable topological defects (e.g. domain walls) of axion-like fields. It is shown that the network consisting of sensitive optical magnetometers is capable to probe an axion-like-field parameter space unconstrained by other experiments.