We investigate electric polarizations that emerge perpendicular to an applied thermal gradient in insulating systems. The thermally induced electric polarization, known as thermopolarization, has been studied conventionally in the case where an electric polarization appears along the thermal gradient. Here, we focus on the antisymmetric component of the thermopolarization tensor, and we reveal that it becomes nonzero due to the ferrotype order for electric-toroidal dipole moments. To describe local electric polarizations originating from the disproportionation of localized electronic clouds, we introduce a two-dimensional three-orbital model with localized $s$ and two $p$ orbitals, where the electric polarization at each site interacts with the neighboring one as dipole-dipole interactions. We find that a vortex-type configuration of local electric polarizations appears as a mean-field ground state, corresponding to a ferrotype electric-toroidal dipole order. By taking account of collective modes from this ordered state, we calculate the coefficient of the thermopolarization based on the linear-response theory. The antisymmetric component is nonzero in the presence of the electric-toroidal dipole order. We clarify that fluctuations in the $p$ orbitals are crucial in enhancing the antisymmetric thermopolarization. We discuss the appearance conditions based on the symmetry argument and the relevance to real materials.

• Received 12 December 2021
• Revised 17 February 2022
• Accepted 6 June 2022

DOI:https://doi.org/10.1103/PhysRevB.105.245125