  Ferroelectric-like metals are a relatively rare class of materials that have
ferroelectric-like distortion and metallic conductivity. LiOsO$_3$ is the first
demonstrated and the most investigated ferroelectric-like metal. The presence
of free carriers makes them difficult to be studied by traditional
ferroelectric techniques. In this paper, using the symmetry analysis and
first-principles calculations, we demonstrate that the ferroelectric-like
transition of LiOsO$_3$ can be probed by a kind of electrical transport method
based on nonlinear Hall effect. The Berry curvature dipole exists in the
ferroelectric-like phase, and it can lead to a measurable nonlinear Hall
conductance with a conventional experimental setup. However, the symmetry of
the paraelectric-like phase LiOsO$_3$ vanishes the Berry curvature dipole. The
Berry curvature dipole shows a strong dependence on the polar displacement,
which might be helpful for the detection of polar order. The nonlinear Hall
effect provides an effective method for the detection of phase transition in
the study of the ferroelectric-like metals and promotes them to be applied in
the ferroelectric-like electronic devices.

Materials Science