Soft magnons in van der Waals multiferroic NiI2

The ferroelectric polarization in van der Waals multiferroic ${\mathrm{NiI}}_{2}$ is believed to be induced by the helimagnetic spin order. The formation of the helimagnetic ground spin configuration and the properties of its spin excitation are yet to be clarified. In the present work, we explore the proper magnetic ground states with well-defined magnon spectra in a single-layer ${\mathrm{NiI}}_{2}$, by analyzing the role of different interactions. While the spin frustration due to the ferromagnetic and antiferromagnetic exchange terms stabilizes a helimagnetic phase, the anisotropic Kitaev interaction introduces a canting of the spin rotation plane. We find the modulation vector of the helimagnetic structure can be continuously oriented within the atomic plane by the competition between the Kitaev interaction and the third-nearest-neighbor exchange. The calculation of magnon spectrum reveals anomalous features with soft magnons at finite wave vectors, which is found to be related with the vibration of the canting plane. From the finite-temperature calculation of the magnon spectra, we predict a magnetic phase transition driven by soft magnons, which cause a spatial modulation of the canting plane. Furthermore, a sign change is predicted in the temperature dependence of the transverse magnon thermal conductivity. Our results provide a comprehensive understanding of the spin ground state and the soft magnons in the van der Waals ${\mathrm{NiI}}_{2}$.