Nature of theFe42center inKTaO3: A density functional theory study

Abstract

This work is aimed at clearing out the nature of the axial $\text{Fe}\frac{4}{2}$ center detected by electron-paramagnetic resonance in iron-doped ${\text{KTaO}}_{3}$ for which two different models have been put forward. While some authors ascribe such a center to a ${\text{Fe}}^{+}$ impurity at a ${\text{K}}^{+}$ site, although suffering an off-center motion along $⟨001⟩$ directions, other groups propose that the $\text{Fe}\frac{4}{2}$ center involves a ${\text{Fe}}^{5+}$ ion at a ${\text{Ta}}^{5+}$ site, which later also undergoes an off-center shift along a principal direction of the ${\text{KTaO}}_{3}$ lattice. Seeking to clarify this puzzling situation, the possible off-center shift of both ${\text{Fe}}^{5+}$ and ${\text{Fe}}^{+}$ impurities in ${\text{KTaO}}_{3}$ is explored in this work by means of density functional calculations. As a salient feature it is shown that there is a huge barrier that prevents the motion of ${\text{Fe}}^{5+}$ against one of the closest ${\text{O}}^{2\ensuremath{-}}$ anions. The case of ${\text{Fe}}^{+}$ at a ${\text{K}}^{+}$ site is more complex as the energy difference (10Dq) between the lower-lying ${e}_{g}$ ($\ensuremath{\sim}{x}^{2}\text{\ensuremath{-}}{y}^{2}$,$3{z}^{2}\text{\ensuremath{-}}{r}^{2}$) and ${t}_{2g}$ ($\ensuremath{\sim}xy$,$xz$,$yz$) ${\text{O}}_{h}$ levels is found to be equal to only $\ensuremath{-}0.038\text{ }\text{eV}$, and thus several states as a function of the displacement coordinate ${Z}_{\text{Fe}}$ have to be explored in order to determine what is the actual ground state and the associated equilibrium coordinate ${Z}_{\text{Fe}}^{0}$. The ground state is found to correspond to the ${b}_{1}{({x}^{2}\text{\ensuremath{-}}{y}^{2})}^{1}$ ${a}_{1}{(3{z}^{2}\text{\ensuremath{-}}{r}^{2})}^{2}$ ${b}_{2}{(xy)}^{2}$ $e{(xz,yz)}^{2}$ ${C}_{4v}$ configuration with spin $S=3/2$ and ${Z}_{\text{Fe}}^{0}=90\text{ }\text{pm}$, thus involving a significant off-center motion from the ${\text{K}}^{+}$ site, which is found to be accompanied by a small ligand relaxation. As a salient feature this ground state is different from that derived constraining ${\text{Fe}}^{+}$ at the ${\text{K}}^{+}$ site. The present calculations also reproduce the experimental feature ${g}_{\ensuremath{\perp}}\ensuremath{-}{g}_{0}g{g}_{\ensuremath{\parallel}}\ensuremath{-}{g}_{0}$ observed for the $\text{Fe}\frac{4}{2}$ center. An analysis of first-excited states at equilibrium allows one to understand this fingerprint in a simple way.