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 MnBi2Te4, and for EuS-Bi2Se3 heterostructures, we combine the effective field theory method with density functional theory and Monte Carlo simulations. For MnBi2Te4 we predict an upwards N\'eel temperature shift at the surface up to 15%, while the EuS-Bi2Se3 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.
@article{arxiv.2101.08645,
title = {Finite temperature fluctuation-induced order and responses in magnetic topological insulators},
author = {Marius Scholten and Jorge I. Facio and Rajyavardhan Ray and Ilya M. Eremin and Jeroen van den Brink and Flavio S. Nogueira},
journal= {arXiv preprint arXiv:2101.08645},
year = {2021}
}