Crucial role of Fe in determining the hard magnetic properties of Nd$_2$Fe$_{14}$B

TL;DR

This study uses first-principles calculations to reveal how Fe atoms influence the magnetic order and anisotropy in Nd$_2$Fe$_{14}$B, highlighting their crucial role in maintaining high-temperature magnetic properties.

Contribution

It identifies the specific Fe sublattices that couple strongly with Nd spins and explains their role in the temperature dependence of magnetic anisotropy.

Findings

Fe sublattices 8$j_1$ and 8$j_2$ strongly couple with Nd spins.

Fe 8$j_1$ sublattice causes nonmonotonic temperature dependence of anisotropy.

Fe atoms maintain magnetic order and anisotropy at high temperatures.

Abstract

Nd$_2$Fe$_{14}$B's unsurpassed, hard magnetic properties for a wide range of temperatures result from a combination of a large volume magnetization from Fe and a strong single-ion anisotropy from Nd. Here, using finite temperature first-principles calculations, we focus on the other crucial roles played by the Fe atoms in maintaining the magnetic order on the Nd sublattices, and hence the large magnetic anisotropy, and directly generating significant uniaxial anisotropy at high temperatures. We identify effective spins for atomistic modelling from the material's interacting electrons and {quantify pairwise and higher order, non-pairwise magnetic interactions among them. We find the Nd spins couple most strongly to spins on sites belonging to two specific Fe sublattices, 8$j_1$, 8$j_2$. Moreover the Fe 8$j_1$ sublattice also provides the electronic origin of the unusual, nonmonotonic temperature dependence of the anisotropy of Y$_2$Fe$_{14}$B.} Our work provides atomic-level resolution of the properties of this fascinating magnetic material.