Topological Nodal Planes in Magnetic Space Groups

Topological semimetals and metals may contain nodal points or lines, i.e., zero- or one-dimensional crossings in the energy bands. In the present work we discuss an extension to two-dimensional nodal features. These nodal planes are enforced in systems described by certain nonsymmorphic space groups. We give criteria to predict nodal planes and consider in the process paramagnetic as well as magnetic space groups. Based on an analysis of symmetry eigenvalues we identify space groups with a necessarily non-zero Chern number associated to the nodal planes. The arguments are supported by minimal models and explicit calculation of the topological invariants. We have identified a number of materials with topological nodal planes, among them MnSi in its ferromagnetic phase.