A Predictive 4D Electrostatic Framework for Rare-Earth-Free Permanent Magnet Screening: Curie Temperature, Magnetic Hardness, and Coercivity from a Classical Phase-Locking Model

Rare-earth permanent magnets underpin every electric motor, wind turbine, andMRI scanner built today, yet their supply chains are geographically concentratedand strategically fragile. Substituting them requires quantitative guidance onwhich candidate materials are worth synthesising---before expensive fabricationattempts are made. We present a three-stage predictive framework, grounded inthe 4D Electrostatic Model, that calculates from crystal structure alone:(i)~the Curie temperature TC, (ii)~the dimensionless magnetic hardnessparameter $\kappa$, and (iii)~the ideal coercive field and domain-wallenergy---the three quantities that together determine whether a magnet isuseful. The central predictive quantity is a magnetic phase-locking potential, calibrated againsthelium ionisation energetics and verified against eight well-characterised3d ferromagnets. Predicted Curie temperatures fall within 10--17\% ofexperiment for Fe16N2, tau-MnAl, MnBi, and FeCo; the hardnessclassification (soft, semi-hard, hard) is correct for every material tested.We further apply the framework to a novel class of graphene-intercalated ironfilms, predicting that N-doped graphene spacers can raise the magneticanisotropy of FeCo thin films into the semi-hard regime (kappa ~= 0.5)while retaining M_s > 1.3~MA/m---a combination absent in any knownrare-earth-free bulk material. All predictions are made by a MIT licenseopen-source Python library.