  With its potential for drastically reduced operation power of information
processing devices, electric field control of magnetism has generated huge
research interest. Recently, novel perspectives offered by the inherently large
spin-orbit coupling of 5d transition metals have emerged. Here, we demonstrate
non-volatile electrical control of the proximity induced magnetism in SrIrO3
based back-gated heterostructures. We report up to a 700 % variation of the
anomalous Hall conductivity {\sigma}_AHE and Hall angle {\theta}_AHE as
function of the applied gate voltage Vg. In contrast, the Curie temperature TC
= 100K and magnetic anisotropy of the system remain essentially unaffected by
Vg indicating a robust ferromagnetic state in SrIrO3 which strongly hints to
gating-induced changes of the anomalous Berry curvature. The electric-field
induced ferroelectric-like state of SrTiO3 enables non-volatile switching
behavior of {\sigma}_AHE and {\theta}_AHE below 60 K. The large tunability of
this system, opens new avenues towards efficient electric-field manipulation of
magnetism.
