Interacting spin-wave dispersion relations of ferrimagnetic Heisenberg chains with crystal-field anisotropy
Published in Solid State Communications, 2010
Ferrimagnetism is observed in quantum mixed-spin chains as a result of a ferromagnetic-antiferromagnetic crossover. The spin-wave theory has been a cornerstone for understanding this, as a theoretical probe for the low energy spectrum of these systems.
When I was crawling the literature, I found that when this theory (using the Holstein-Primakoff transformation) was applied to homogeneous spin chains with crystal-field anisotropy $D$, it completely failed for systems with easy-plane anisotropy ($D>0$) and sometimes failed for those with easy-axis anisotropy ($D<0$).
Given the importance of this anisotropy, as ubiquitously found in many real materials, and the fact that its incorporation in the spin-wave theory for mixed-spin chains had not been explored, it felt like water for the thirsty to me … so I took my pencil and did the required math: it indeed fails in the easy-plane regime but is surprisingly accurate in the easy-axis regime!