  We propose a supersymmetric scenario in which the small Yukawa couplings for
the Dirac neutrino mass term are generated by the spontaneous-breaking of
Pecci-Quinn symmetry. In this scenario, a right amount of dark matter relic
density can be obtained by either right-handed sneutrino or axino LSP, and a
sizable amount of axion dark radiation can be obtained. Interestingly, the
decay of right-handed sneutrino NLSP to axino LSP is delayed to around the
present epoch, and can leave an observable cosmological background of neutrinos
at the energy scale of $\mathcal{O}(10-100) {\rm GeV}$.
