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cond-mat.str-el2026
Thermodynamic Electric Toroidal Dipole and Intrinsic Longitudinal Spin Transport
Taisei Yamanaka, Takumi Sato, Satoru Hayami
Electric toroidal dipoles (ETDs) characterize ferroaxial order, yet their bulk definition in periodic crystals has remained elusive because conventional multipole operators involve…
cond-mat.str-el2026
Magnetic toroidal monopoles from relativistic polarization responses to magnetic field gradients
Taisei Yamanaka, Takumi Sato, Satoru Hayami
The magnetic toroidal monopole, a time-reversal-odd scalar, has attracted attention through its characteristic responses, such as electric-field-induced nonreciprocal directional d…