  Emergent electromagnetism in magnets originates from the strong coupling
between conduction electron spins and those of noncollinear ordered moments and
the consequent Berry phase. This offers possibilities to develop new functions
of quantum transport and optical responses. The emergent inductance in spiral
magnets is an example recently proposed and experimentally demonstrated, used
the emergent electric field induced by alternating currents. However, the
microscopic theory of this phenomenon is missing, which should reveal the
factors to determine the magnitude, sign, frequency dependence, and
nonlinearity of the inductance L. Here we theoretically study electromagnetic
responses of spiral magnets taking into account their collective modes. In
sharp contrast to the collinear spin-density wave, the system remains metallic
even in one-dimension, and the canonical conjugate relation of uniform
magnetization and phason coordinate plays an essential role, determining the
properties of L. This result opens a way to design the emergent inductance of
desired properties.
