Lattice strain effects on the finite-temperature magnetism of two-dimensional single-layer CrI3

The magnetic properties of two-dimensional single-layer ${\mathrm{CrI}}_{3}$ at finite temperatures are self-consistently calculated within the nonlinear spin wave formalism, where the Heisenberg exchange interaction and the single-ion magnetic anisotropy energy are calculated from first principles. The lattice strain modulates the exchange interactions and determines the magnetic ground state of the single-layer ${\mathrm{CrI}}_{3}$ as the ferromagnetic or antiferromagnetic configuration. In both cases, the magnon-magnon interaction at finite temperature softens the magnon spectra. The Curie temperature for the ferromagnetic state varies nonmonotonically with decreasing lattice constant, and the maximum value appears at the compressive strain of $\ensuremath{-}2.1%$. The N\'eel temperature for the antiferromagnetic order linearly increases with increasing compressive strain. The exchange interactions between the next-nearest and third-nearest-neighbor spins are found to play an important role in magnetism. Neglecting these exchange interactions results in a significant deviation in estimating the critical temperature.