  We develop a technique for predicting the Curie temperature of magnetic
materials using density functional theory calculations suitable to include in
high-throughput frameworks. We apply four different models, including
physically relevant observables and assess numerical constants by studying 32
ferro- and ferrimagnets. With the best-performing model, the Curie temperature
can be predicted with a mean absolute error of approximately 126 K. As
predictive factors, the models consider either the energy differences between
the magnetic ground state and a magnetically disordered paramagnetic state, or
the average constraining fields acting on magnetic moments in a disordered
local moments calculation. Additionally, the energy differences are refined by
incorporating the magnetic entropy of the paramagnetic state and the number of
nearest magnetic neighbors of the magnetic atoms. The most advanced model is
found to extend well into Fe$_{1-x}$Co$_x$ alloys, indicating the potential
efficacy of utilizing our model in designing materials with tailored Curie
temperatures by altering alloy compositions. This examination can illuminate
the factors influencing magnetic transition temperatures in magnetic materials
and provide insights into how they can be employed to make quantitative
predictions of Curie temperatures. Our approach is not restricted to specific
crystal structures or chemical compositions. It offers a more cost-effective
alternative, in terms of human time and need for hands-on oversight, to other
density functional theory methods for predicting the Curie temperature. As a
result, it provides a practical strategy for conducting high-throughput
screening for new technologically applicable magnetic materials. Alternatively,
it can complement ML-based screening of magnetic materials by integrating
physical principles into such approaches, thereby enhancing their prediction
accuracy.
