Spin density in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>YTiO</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math>: I. Joint refinement of polarized neutron diffraction and magnetic x-ray diffraction data leading to insights into orbital ordering

Abstract

Orbital ordering below 30 K was previously observed in the ferromagnetic ${\text{YTiO}}_{3}$ 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 ${\text{Ti}}^{3+}$ $3d$ orbital populations obtained by joint model refinement are discussed in terms of the orbital ordering scheme. Small but significant magnetic moments on apical oxygen ${\text{O}}_{1}$ and yttrium atoms are found. The agreement between experimental and theoretical spin densities obtained using density functional theory is discussed.