Aharonov-Casher-induced electric quadrupole of charge-neutral particles

For charged particles, their orbital angular momentum (OAM) in solid have a direct magnetic manifestation as an orbital magnetization. For charge-neutral particles, however, the physical manifestation of the OAM in solid remains unclear. Here, we show that a charge-neutral particle carrying a magnetic moment couples to electric-field gradient through the Aharonov-Casher (AC) effect, thereby exhibiting the electric quadrupole in crystalline solids. This AC-induced electric quadrupole (AC-EQ) contains the scalar, toroidal dipole, and reduced quadrupole components, which are conjugate to the divergence, circulation, and shear of the electric field, respectively. As representative examples, we calculate the AC-EQ of magnons in two magnetic systems. In ferromagnetic pyrochlore, Dzyaloshinskii-Moriya interaction (DMI) induces a sizable AC-EQ, whereas in helical Fe langasite the AC-EQ emerges from the helical spin configuration even in the absence of DMI. In both systems, the unit-cell-integrated AC-EQ components reach magnitudes comparable to typical nuclear electric quadrupole moments.