Spin density in YTiO_3: I. Joint refinement of polarized neutron diffraction and magnetic x-ray diffraction data leading to insights into orbital ordering

摘要

Orbital ordering below 30 K was previously observed in the ferromagnetic YTiO_3 compound both by polarized neutron diffraction (PND) and x-ray magnetic diffraction (XMD). In this paper we report a procedure for the joint refinement of a unique spin-density model based on both PND and XMD data. The distribution of the unpaired 3d electron of titanium is clearly seen on the magnetization density reconstructed by the maximum entropy method from the PND data collection at 5 K. The Ti~(3+) 3d orbital populations obtained by joint model refinement are discussed in terms of the orbital ordering scheme. Small but significant magnetic moments on apical oxygen O_1 and yttrium atoms are found. The agreement between experimental and theoretical spin densities obtained using density functional theory is discussed.