Data assimilation method for experimental and first-principles data: Finite-temperature magnetization of (Nd,Pr,La,Ce)2(Fe,Co

We propose a data assimilation method for evaluating the finite-temperature magnetization of a permanent magnet over a high-dimensional composition space. Based on a general framework for constructing a predictor from two data sets including missing values, a practical scheme for magnetic materials is formulated in which a small number of experimental data in limited composition space are integrated with a larger number of first-principles calculation data. We apply the scheme to ${({\mathrm{Nd}}_{1\ensuremath{-}\ensuremath{\alpha}\ensuremath{-}\ensuremath{\beta}\ensuremath{-}\ensuremath{\gamma}}{\mathrm{Pr}}_{\ensuremath{\alpha}}{\mathrm{La}}_{\ensuremath{\beta}}{\mathrm{Ce}}_{\ensuremath{\gamma}})}_{2}{({\mathrm{Fe}}_{1\ensuremath{-}\ensuremath{\delta}\ensuremath{-}\ensuremath{\zeta}}{\mathrm{Co}}_{\ensuremath{\delta}}{\mathrm{Ni}}_{\ensuremath{\zeta}})}_{14}\mathrm{B}$. The magnetization in the whole $(\ensuremath{\alpha},\ensuremath{\beta},\ensuremath{\gamma},\ensuremath{\delta},\ensuremath{\zeta})$ space at arbitrary temperature is obtained. It is shown that the Co doping does not enhance the magnetization at low temperatures, whereas the magnetization increases with increasing $\ensuremath{\delta}$ above 320 K.