Magnetic excitations in the spin-trimer compoundsCa3Cu3−xNix(PO4)4(x=0,1,2)

Abstract

Inelastic neutron scattering experiments were performed for the spin-trimer compounds ${\mathrm{Ca}}_{3}{\mathrm{Cu}}_{3\ensuremath{-}x}{\mathrm{Ni}}_{x}{(\mathrm{P}{\mathrm{O}}_{4})}_{4}$ $(x=0,1,2)$ in order to study their dynamic magnetic properties. The observed excitations can be associated with transitions between the low-lying electronic states of linear Cu-Cu-Cu, Cu-Cu-Ni, and Ni-Cu-Ni trimers, which are the basic constituents of the title compounds. The exchange interactions within the trimers are well described by the Heisenberg model with dominant antiferromagnetic nearest-neighbor interactions $J$. For $x=0$, we find ${J}_{\mathrm{Cu}\text{\ensuremath{-}}\mathrm{Cu}}=\ensuremath{-}4.74\ifmmode\pm\else\textpm\fi{}0.02\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$, which is enhanced for $x=1$ to ${J}_{\mathrm{Cu}\text{\ensuremath{-}}\mathrm{Cu}}=\ensuremath{-}4.92\ifmmode\pm\else\textpm\fi{}0.06\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. For $x=1$ and $x=2$, we find ${J}_{\mathrm{Cu}\text{\ensuremath{-}}\mathrm{Ni}}=\ensuremath{-}0.85\ifmmode\pm\else\textpm\fi{}0.10\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ and an axial single-ion anisotropy parameter ${D}_{\mathrm{Ni}}=\ensuremath{-}0.7\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$. While the $x=0$ and $x=1$ compounds do not exhibit long-range magnetic ordering down to $1\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the $x=2$ compound shows antiferromagnetic ordering below ${T}_{N}=20\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, which is compatible with the molecular-field parameter $\ensuremath{\lambda}=0.63\ifmmode\pm\else\textpm\fi{}0.12\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ derived by neutron spectroscopy.