  In solid state physics, any phase transition is commonly observed as a change
in the microscopic distribution of charge, spin, or current. Here we report the
nature of an exotic order parameter inherent in the localized electron orbitals
that cannot be primarily captured by these three fundamental quantities. This
order parameter is described as the electric toroidal multipoles connecting
different total angular momenta under the spin-orbit coupling. The
corresponding microscopic physical quantity is the spin current tensor on an
atomic scale, which induces spin-derived electric polarization and the
chirality of the Dirac equation. We stress that the chirality intrinsic to the
elementary particle is the essence of electric toroidal multipoles. These
findings link microscopic spin currents and chirality in the Dirac theory to
the concept of multipoles and provide a new perspective for quantum states of
matter.
