First-Principles Calculations of Crystal Field Parameters of Nd Ions Near Surfaces and Interfaces in Nd-Fe-B Magnets

Abstract

We study the local magnetic anisotropy due to Nd ions located around surfaces of Nd <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">14</sub> B within the crystal field theory based on first-principles calculations. The Nd ions on the (001) surface exhibit A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sup> <; 0, that is, the in-plane anisotropy, as reported previously, but those on the (100) surface exhibit A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sup> > 0, which is consistent with the bulk c-axis uniaxial anisotropy. The physical origin of these conflicting local anisotropies can be understood from the 6p and 5d valence charge distributions realized in the Nd <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> Fe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">14</sub> B structure.