Finite temperature fluctuation-induced order and responses in magnetic topological insulators

We derive an effective field theory model for magnetic topological insulators and predict that a magnetic electronic gap persists on the surface for temperatures above the ordering temperature of the bulk. Our analysis also applies to interfaces of heterostructures consisting of a ferromagnetic and a topological insulator. In order to make quantitative predictions for MnBi_{2}Te_{4} and for EuS-Bi_{2}Se_{3} heterostructures, we combine the effective field theory method with density functional theory and Monte Carlo simulations. For MnBi_{2}Te_{4} we predict an upwards Néel temperature shift at the surface up to 15%, while the EuS-Bi_{2}Se_{3} interface exhibits a smaller relative shift. The effective theory also predicts induced Dzyaloshinskii-Moriya interactions and a topological magnetoelectric effect, both of which feature a finite temperature and chemical potential dependence.