Data assimilation method for experimental and first-principles data: Finite-temperature magnetization of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>Nd</mml:mi><mml:mo>,</mml:mo><mml:mi>Pr</mml:mi><mml:mo>,</mml:mo><mml:mi>La</mml:mi><mml:mo>,</mml:mo><mml:mi>Ce</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>Fe</mml:mi><mml:mo>,</mml:mo><mml:mi>Co</mml:mi><mml:mo>,</mml:mo><mml:mi>Ni</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mn>14</mml:mn></mml:msub><mml:mi mathvariant="normal">B</mml:mi></mml:mrow></mml:math>

Abstract

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.

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