  Electric fields have played a key role in discovering and controlling exotic
electronic states of condensed matter. However, electric fields usually do not
work in metals as free carriers tend to screen electrostatic fields. While a
pseudo-electric field generated by inhomogeneous lattice strain, namely a
flexoelectric field, can in principle work in all classes of materials, it
remains experimentally unexplored in metals. Here, using heteroepitaxy and
atomic-scale imaging, we show that flexoelectric fields can polarize a metallic
oxide SrRuO3 with unexpectedly large Ru off-center displacements. We also
observe that the flexoelectrically induced polar state of SrRuO3 leads to
sizable lattice expansion, similar to the electrostrictive expansion caused by
ionic displacements in dielectrics under an external electric field. We further
suggest that flexoelectrically driven Ru off-centering promotes strong coupling
between lattice and electronic degrees of freedom, possibly enhancing the
ferromagnetism of SrRuO3. Beyond conventional electric fields, flexoelectric
fields may universally engender novel electronic states and their control via
pure atomic displacements in a nondestructive and fast manner.
