  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.
