Experimental exploration of ErB$_2$ and SHAP analysis on a machine-learned model of magnetocaloric materials for materials design

Abstract: Stimulated by a recent report of a giant magnetocaloric effect in HoB$_2$ found via machine-learning predictions, we have explored the magnetocaloric properties of a related compound ErB$_2$, that has remained the last ferromagnetic material among the rare-earth diboride (REB$_2$) family with unreported magnetic entropy change |{\Delta}SM|. The evaluated $|\Delta S_M|$ at field change of 5 T in ErB$_2$ turned out to be as high as 26.1 (J kg$^{-1}$ K$^{-1}$) around the ferromagnetic transition (${T_C}$) of 14 K. In this series, HoB$_2$ is found to be the material with the largest $|\Delta S_M|$ as the model predicted, while the predicted values showed a deviation with a systematic error compared to the experimental values. Through a coalition analysis using SHAP, we explore how this rare-earth dependence and the deviation in the prediction are deduced in the model. We further discuss how SHAP analysis can be useful in clarifying favorable combinations of constituent atoms through the machine-learned model with compositional descriptors. This analysis helps us to perform materials design with aid of machine learning of materials data.