Due to a very low production rate of electron anti-neutrinos ($bar{ u}_e$) via nuclear fusion in the Sun, we expect to see $bar{ u}_e$ from other contribution. An appearance of $bar{ u}_e$ in solar neutrino flux opens a new window for the new physics beyond the standard model. In particular, a spin-flavor precession process is expected to convert an electron neutrino into an electron anti-neutrino (${ u_etobar{ u}_e}$) if neutrino has a finite magnetic moment. In this work, we have searched for solar $bar{ u}_e$ in the Super-Kamiokande experiment, using neutron tagging to identify their inverse beta decay signature. We identified 78 $bar{ u}_e$ candidates for neutrino energies of 9.3 to 17.3 MeV in 2970.1 live days with a fiducial volume of 22.5 kiloton water (183.0 kton$cdot$year exposure). The energy spectrum has been consistent with background predictions and we thus derived a 90% confidence level upper limit of ${3.6times10^{-4}}$ on the $ u_etobar{ u}_e$ conversion probability in the Sun. We used this result to evaluate the sensitivity of future experiments, notably the Super-Kamiokande Gadolinium (SK-Gd) upgrade.
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