  Electrical control of structural and physical properties is a long-sought,
but elusive goal of contemporary science and technology. We demonstrate that a
combination of strong spin-orbit interactions (SOI) and a canted
antiferromagnetic (AFM) Mott state is sufficient to attain that goal. The AFM
insulator Sr2IrO4 provides a model system in which strong SOI lock canted Ir
magnetic moments to IrO6-octahedra, causing them to rigidly rotate together. A
novel coupling between an applied electrical current and the canting angle
reduces the N\'eel temperature and drives a large, non-linear lattice expansion
that closely tracks the magnetization, increases the electron mobility, and
precipitates a unique resistive switching effect. Our observations open new
avenues for understanding fundamental physics driven by strong SOI in condensed
matter, and provide a new paradigm for functional materials and devices.
