Magnetars can accelerate cosmic rays to high energies through the unipolar effect, and are also copious soft photon emitters. We show that young, fast-rotating magnetars whose spin and magnetic moment point in opposite directions emit high energy neutrinos from their polar caps through photomeson interactions. We identify a neutrino cut-off band in the magnetar period-magnetic field strength phase diagram, corresponding to the photomeson interaction threshold. Within uncertainties, we point out four possible neutrino emission candidates among the currently known magnetars, the brightest of which may be detectable for a chance on-beam alignment. Young magnetars in the universe would also contribute to a weak diffuse neutrino background, whose detectability is marginal, depending on the typical neutrino energy.
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