The Experimentalist's Guide to the Cycloid, or Noncollinear Antiferromagnetism in Epitaxial BiFeO₃

Abstract Bismuth ferrite (BiFeO₃) is one of the most widely studied multiferroics. The coexistence of ferroelectricity and antiferromagnetism in this compound has driven an intense search for electric‐field control of the magnetic order. Such efforts require a complete understanding of the various exchange interactions that underpin the magnetic behavior. An important characteristic of BiFeO₃ is its noncollinear magnetic order; namely, a long‐period incommensurate spin cycloid. Here, the progress in understanding this fascinating aspect of BiFeO₃ is reviewed, with a focus on epitaxial films. The advances made in developing the theory used to capture the complexities of the cycloid are first chronicled, followed by a description of the various experimental techniques employed to probe the magnetic order. To help the reader fully grasp the nuances associated with thin films, a detailed description of the spin cycloid in the bulk is provided. The effects of various perturbations on the cycloid are then described: magnetic and electric fields, doping, epitaxial strain, finite size effects, and temperature. To conclude, an outlook on possible device applications exploiting noncollinear magnetism in BiFeO₃ films is presented. It is hoped that this work will act as a comprehensive experimentalist's guide to the spin cycloid in BiFeO₃ thin films.