  The discovery of intrinsic magnetic topological order in $\rm MnBi_2Te_4$ has
invigorated the search for materials with coexisting magnetic and topological
phases. These multi-order quantum materials are expected to exhibit new
topological phases that can be tuned with magnetic fields, but the search for
such materials is stymied by difficulties in predicting magnetic structure and
stability. Here, we compute over 27,000 unique magnetic orderings for over
3,000 transition metal oxides in the Materials Project database to determine
their magnetic ground states and estimate their effective exchange parameters
and critical temperatures. We perform a high-throughput band topology analysis
of centrosymmetric magnetic materials, calculate topological invariants, and
identify 18 new candidate ferromagnetic topological semimetals, axion
insulators, and antiferromagnetic topological insulators. To accelerate future
efforts, machine learning classifiers are trained to predict both magnetic
ground states and magnetic topological order without requiring first-principles
calculations.
