The intracluster exchange interactions within the ``butterfly'' $[{\mathrm{Fe}}_{3}\mathrm{Ln}({\ensuremath{\mu}}_{3}\ensuremath{-}\mathrm{O}{)}_{2}({\mathrm{CCl}}_{3}\mathrm{COO}{)}_{8}({\mathrm{H}}_{2}\mathrm{O})(\mathrm{THF}{)}_{3}]$ molecules, where Ln(III) represents a lanthanide cation, have been determined by a combination of x-ray magnetic circular dichroism (XMCD) and vibrating sample magnetometry (VSM) along with an interaction model. We have studied the compounds with $\mathrm{Ln}=\mathrm{Tb}$ and Ho, both non-Kramers lanthanides and with high uniaxial anisotropy, and $\mathrm{Ln}=\mathrm{Lu}$(III) and Y(III) as pseudolanthanides, which supply nonmagnetic Ln reference cases. At low temperature, the three Fe atoms can be considered as a self-unit with total spin ${S}_{{\mathrm{Fe}}_{3}}=5/2$. Using the element selectivity of the XMCD magnetometry, measured at the Ln ${L}_{2,3}$ edges, together with the VSM measurements, the local magnetization of the Ln ion and the ${\mathrm{Fe}}_{3}$ subcluster, as a function of the field and low temperature ($T\ensuremath{\approx}2.5\phantom{\rule{0.28em}{0ex}}\mathrm{K}$), has been determined separately. These results are described quantitatively in the framework of a theoretical model based on an effective spin Hamiltonian, which considers the competing effects of intracluster interactions and the external applied magnetic field. The $\mathrm{Ln}\ensuremath{-}{\mathrm{Fe}}_{3}$ exchange interaction within the ${{\mathrm{Fe}}_{3}{\mathrm{LnO}}_{2}}$ cluster has been determined to be antiferromagnetic, in both Tb and Ho compounds, with ${\mathcal{J}}_{\mathrm{FeTb}}/{\mathrm{k}}_{\mathrm{B}}=\ensuremath{-}0.13(1)\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ and ${\mathcal{J}}_{\mathrm{FeHo}}/{\mathrm{k}}_{\mathrm{B}}=\ensuremath{-}0.18(1)\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, respectively. In both cases, a field-induced reorientation of the ${\mathrm{Fe}}_{3}$ and Ln spins from antiparallel to parallel orientation takes place at a threshold field ${\ensuremath{\mu}}_{0}H=1.1$ and 2 T, for the ${{\mathrm{Fe}}_{3}{\mathrm{TbO}}_{2}}$ and ${{\mathrm{Fe}}_{3}{\mathrm{HoO}}_{2}}$ compounds, respectively. By comparison with other compounds of the series with uniaxial anisotropy, it is concluded that the polarizability of the ${\mathrm{Fe}}_{3}$ subcluster magnetic moment decreases in the trend ${{\mathrm{Fe}}_{3}{\mathrm{YO}}_{2}}\phantom{\rule{0.28em}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{0.28em}{0ex}}{{\mathrm{Fe}}_{3}{\mathrm{TbO}}_{2}}\phantom{\rule{0.28em}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{0.28em}{0ex}}{{\mathrm{Fe}}_{3}{\mathrm{HoO}}_{2}}\phantom{\rule{0.28em}{0ex}}\ensuremath{\rightarrow}\phantom{\rule{0.28em}{0ex}}{{\mathrm{Fe}}_{3}{\mathrm{DyO}}_{2}}$, because of the increasing opposition of the exchange antiferromagnetic field caused by the Ln ion. In the $\mathrm{Ln}=\mathrm{Tb}$, Ho, and Dy, the magnetization of the whole molecule is dominated by the anisotropy of the Ln ion. The intracluster ${\mathrm{Fe}}_{3}\ensuremath{-}\mathrm{Ln}$ exchange interactions are very weak compared to the Ln ligand field and Fe-Fe exchange interactions.
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