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Our magnetic, electrical, and thermal measurements on single crystals of the J eff =1/ 2 Mott insulator, Sr 2 IrO 4 , reveal a giant magnetoelectric effect ͑GME͒ arising from a frustrated magnetic/ferroelectric state whose signatures are: ͑1͒ a strongly enhanced electric permittivity that peaks near an observed magnetic anomaly at 100 K, and ͑2͒ a large ͑ϳ100%͒ magnetodielectric 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.

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