Charge localization in the Verwey structure of magnetite

Abstract

The thermal evolution of electronic order in the complex Verwey ground state of magnetite $(\mathrm{F}{\mathrm{e}}_{3}{\mathrm{O}}_{4})$ has been determined through 22 high-accuracy synchrotron x-ray structure refinements using three $10--40\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{m}$ grains of stoichiometric magnetite. A robust fitting function is introduced to extract values of order parameterlike quantities at zero temperature and at the upper limit of the Verwey phase ${T}_{\mathrm{u}}=123.4\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The low-temperature structural distortion is found to be almost frozen below the Verwey transition but small changes in lattice and local mode amplitudes and Fe-Fe distances reveal an increase in electron localization on cooling. These distortions confirm that electron localization within trimerons is the driving force behind the Verwey transition. Electron localization is also revealed by anomalous decreases in the largest principal thermal displacement factors of Fe cations as electron-phonon decoupling occurs on cooling.