Effect of small in-plane anisotropy in the large-D phase systems based on Ni2+ (S=1) ions in Heisenberg antiferromagnetic chains

Heisenberg antiferromagnetic chains based on Ni2+ ions with integer spin S=1 exhibit intriguing behavior, e.g. the Haldane gap phase and the large-D phase. The predicted transitions between the two phases and the Neel phase has generated search for real candidate systems. Crucial to this search is the interplay between the 'in-plane anisotropy', i.e. the rhombic zero-field splitting (ZFS) E-term, and the 'planar anisotropy', i.e. the axial ZFS D-term. This paper clarifies intricate properties of orthorhombic ZFS Hamiltonians (HZFS) and inconsistencies revealed by critical survey of pertinent studies. Reporting the non-standard (D, E) sets with λ=E/D out of the standard range (0, 1/3) alongside the standard sets with λ∝(0, 1/3) indicates that these properties are not recognized. We show that direct comparisons of the non-standard and standard sets are meaningless and lead to incorrect conclusions on the strength of the 'in-plane anisotropy' (E) as compared with the 'planar anisotropy' (D). To remedy such problems, the ZFSP sets reported for the large-D phase candidate systems are reanalyzed using orthorhombic standardization. The six physically equivalent ZFSP sets are determined in the conventional (D, E) and Stevens (b20, b22) notation. These considerations help understanding intricacies inherent in orthorhombic HZFS and provide consistent data for future modeling of ZFS parameters in the large-D phase and Haldane gap systems.