Exchange interaction in theYbCrBr93−mixed dimer: The origin of a strongYb3+−Cr3+exchange anisotropy

Abstract

The superexchange interaction between ${\mathrm{Yb}}^{3+}$ and ${\mathrm{Cr}}^{3+}$ ions in the mixed ${\mathrm{YbCrBr}}_{9}^{3\ensuremath{-}}$ bioctahedral face-sharing dimer is quantitatively analyzed using a modified kinetic exchange theory, which is adapted to a realistic description of the electronic structure of lanthanide ions in solids. The general procedure of the calculation of the $4f\ensuremath{-}3d$ anisotropic exchange spin Hamiltonian is presented and applied to the ${\mathrm{YbCrBr}}_{9}^{3\ensuremath{-}}$ dimer. The spin-Hamiltonian of the ${\mathrm{Yb}}^{3+}\ensuremath{-}{\mathrm{Cr}}^{3+}$ exchange interaction is found to be extremely anisotropic, ${H=J}_{z}{S}_{\mathrm{Yb}}^{z}{S}_{\mathrm{Cr}}^{z}{+J}_{\ensuremath{\perp}}{(S}_{\mathrm{Yb}}^{x}{S}_{\mathrm{Cr}}^{x}{+S}_{\mathrm{Yb}}^{y}{S}_{\mathrm{Cr}}^{y}),$ with the antiferromagnetic ${J}_{z}$ and ferromagnetic ${J}_{\ensuremath{\perp}}$ parameters, where ${S}_{\mathrm{Yb}}^{\ensuremath{\mu}}$ and ${S}_{\mathrm{Cr}}^{\ensuremath{\mu}}$ $(\ensuremath{\mu}=x,y,z)$ are the components of the effective spin ${S}_{\mathrm{Yb}}=\frac{1}{2}$ of the ${\mathrm{Yb}}^{3+}$ ion (corresponding to the ground ${\ensuremath{\Gamma}}_{6}$ Kramers doublet) and the true spin ${S}_{\mathrm{Cr}}=\frac{3}{2}$ of the ${\mathrm{Cr}}^{3+}$ ion, respectively. The calculated exchange parameters are quite consistent with the experimental data ${(J}_{z}=\ensuremath{-}5.16{\mathrm{cm}}^{\ensuremath{-}1}$ and ${J}_{\ensuremath{\perp}}=+4.19{\mathrm{cm}}^{\ensuremath{-}1})$ at reasonable values of the $\mathrm{Yb}\ensuremath{\rightarrow}\mathrm{Cr}$ and $\mathrm{Yb}\ensuremath{\leftarrow}\mathrm{Cr}$ charge transfer energies. The contributions to the ${J}_{z}$ and ${J}_{\ensuremath{\perp}}$ exchange parameters from the individual states of the ${4f}^{12}{\ensuremath{-}3d}^{4}$ and ${4f}^{14}{\ensuremath{-}3d}^{2}$ charge transfer configurations are analyzed in detail and general regularities are established. Our results indicate that a very strong $4f\ensuremath{-}3d$ exchange anisotropy can appear even in the absence of the crystal-field anisotropy on the lanthanide ion.