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We study spin transport in a Hubbard chain with strong, random, on--sitepotential and with spin--dependent hopping integrals, $t_{\sigma}$. For the theSU(2) symmetric case, $t_{\uparrow} =t_{\downarrow}$, such model exhibits onlypartial many-body localization with localized charge and (delocalized)subdiffusive spin excitations. Here, we demonstrate that breaking the SU(2)symmetry by even weak spin--asymmetry, $t_{\uparrow} \ne t_{\downarrow}$,localizes spins and restores full many-body localization. To this end we derivean effective spin model, where the spin subdiffusion is shown to be destroyedby arbitrarily weak $t_{\uparrow} \ne t_{\downarrow}$. Instability of the spinsubdiffusion originates from an interplay between random effective fields andsingularly distributed random exchange interactions.

Instability of subdiffusive spin dynamics in strongly disordered Hubbard chain