Lanthanide exchange fields and intermultiplet transitions in permanent-magnet materials

Intermultiplet (spin-orbit) transitions in lanthanides, observed by means of high-energy inelastic neutron scattering are well-suited for the determination of exchange field Hex in permanent-magnet materials. The situation is particularly favorable in Nd-based magnets, where Hexis given by mu BHex=(143)/(296)(Einter-Delta(so)),E-inter being the observed transition energy and Delta sothespin-orbit splitting between the bary centers of the two lowest-lying multiplets. The latter can be regarded as a known atomic constant,Delta(so)=232 +/- 1 meV. A more accurate value of Delta sois obtainable by way of relativistic density-functional calculations, however, it proves material-dependent. Thus,Delta(so)=231.4meVforNd(2)Fe(14)B. Two obstacles in the way of the direct determination ofHexareJ-mixing and crystal electric field. In order to allow for theJ-mixing, approximate formulas are proposed that enable a definitivesolution of the problem. By contrast, crystal-field corrections have to be treated on a case-by-case basis