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The excess increase of the local field distribution width $\DeltaH\equiv\sigma/\gamma_{\mu}$ (with $\gamma_{\mu}=135.5\,$MHz/T being thegyromagnetic ratio of $\mu^{+}$), and/or the spontaneous magnetic field $H_{\rmspon}$, have been reported in the superconducting state of a series ofcompounds more than 10 by $\mu$SR (muon spin rotation or relaxation)experiment. Sizes of these quantities are of the order of 1G on the whole. Wepropose that the increase of the local field distribution $\Delta H$ in thosecompounds, including ions with strong spin-orbit interaction of 5d electrons,such as La in LaNiGa$_2$ or Re in Re$_6$Zr, is possible through the cooperationof the spin-orbit coupling between the quasiparticles and ionic vibrations(phonons) and the conventional quasiparticles-phonon coupling, inducing thespin-triplet p-wave pairing with helical symmetry breaking superconductingstate with chiral super spin current around stopped $\mu^{+}$ site. The size of$\Delta H$ is estimated as of the order of 1G, in consistent with experimentalobservations.

Spin-orbit-phonon interaction as an origin of helical-symmetry breaking spin-triplet superconducting state