The paper by I. A. Sergienko and E. Dagotto explores the role of the Dzyaloshinskii-Moriya interaction (DMI) in the coexistence and strong coupling between ferroelectricity and incommensurate magnetism in multiferroic perovskites, specifically focusing on $RMnO_3$ ($R = Gd, Tb, Dy$). Using Monte-Carlo simulations and zero-temperature exact calculations, they incorporate double-exchange, superexchange, Jahn-Teller, and DMI terms into a model to study the phase diagram. The results show a multiferroic phase between A and E antiferromagnetic phases, which aligns well with experimental findings. The DMI is found to be crucial in stabilizing helical magnetic structures and inducing ferroelectric lattice displacements, contributing to the magnetoelectric effect. The study also discusses the stabilization of the magnetic helix and the influence of finite size effects on the phase diagram. The authors conclude that the DMI provides a natural explanation for the coexistence and strong coupling between ferroelectricity and IC magnetism in perovskite manganites, with the empirically estimated value of $\gamma$ agreeing with previous experiments.The paper by I. A. Sergienko and E. Dagotto explores the role of the Dzyaloshinskii-Moriya interaction (DMI) in the coexistence and strong coupling between ferroelectricity and incommensurate magnetism in multiferroic perovskites, specifically focusing on $RMnO_3$ ($R = Gd, Tb, Dy$). Using Monte-Carlo simulations and zero-temperature exact calculations, they incorporate double-exchange, superexchange, Jahn-Teller, and DMI terms into a model to study the phase diagram. The results show a multiferroic phase between A and E antiferromagnetic phases, which aligns well with experimental findings. The DMI is found to be crucial in stabilizing helical magnetic structures and inducing ferroelectric lattice displacements, contributing to the magnetoelectric effect. The study also discusses the stabilization of the magnetic helix and the influence of finite size effects on the phase diagram. The authors conclude that the DMI provides a natural explanation for the coexistence and strong coupling between ferroelectricity and IC magnetism in perovskite manganites, with the empirically estimated value of $\gamma$ agreeing with previous experiments.