Giant Magneto-electric Effect in the J$_{eff}$ = $\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} $ Mott Insulator Sr$_{2}$IrO$_{4}$*

Our magnetic, electrical, and thermal measurements on single-crystals of the J$_{eff}$ = 1/2 Mott insulator, Sr$_{2}$IrO$_{4}$, reveal a novel giant magneto-electric effect (GME) arising from a frustrated magnetic/ferroelectric state [1] whose signatures are: (1) a strongly enhanced electric permittivity that peaks near a newly observed magnetic anomaly at 100 K, and (2) a large ($\sim $100{\%}) magneto-dielectric shift that occurs near a metamagnetic transition. The GME hinges on a spin-orbit gapping of 5d-bands, rather than the magnitude and spatial dependence of magnetization, as traditionally accepted. \\[4pt] [1] S. Chikara, et al, Phys. Rev. B 80, 140407 (R) (2009)