Two-dimensional ferromagnetism in few-layer van der Waals crystals: Renormalized spin-wave theory and calculations

Dimensionality shapes the behavior of magnetism. Recent experiments on quasi two-dimensional ( 2D) van der Waals crystals have demonstrated unusual ferromagnetic orders and phase transitions distinct from their bulk counterparts. In this work, we present a method using renormalized spin-wave theory to study the ferromagnetic behavior in Heisenberg-type 2D ferromagnets, and apply our method to few-layer Cr2Ge2Te63 crystals. We present the details of the method, which includes a self-consistent updating scheme of the spin-wave spectra at the Hartree-Fock level. The theoretical results obtained quantitatively explain the experimental measurements, showing strong dimensionality effects and sensitive external magnetic-field dependence which leads to easily tunable magnetism in this class of 2D materials. This method can be generalized to study various magnetic phenomena in other systems. (C) 2018 Elsevier B.V. All rights reserved.