Spin density in YTiO3 : 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 Y T iO3 compound both by polarized neutron diffraction (PND) and X-ray magnetic diffraction (XMD). In this paper we report a new 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 of Entropy Method from the PND data collection at 5 K. The T i 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 O1 and yttrium atoms are found. The agreement between experimental and theoretical spin densities obtained using density functional theory is discussed.

Spin resolved electron density study of YTiO3in its ferromagnetic phase: signature of orbital ordering

“…This observation confirms that the unpaired electron occupies an orbital which is a linear combination of the d yz and d xz orbitals. This is consistent with our previous results obtained using PND only (Kibalin et al, 2017), theoretical calculations and magnetic Compton measurements (Yan et al, 2017), and the X-ray magnetic diffraction of Itoh (Itoh et al, 1999), in accordance with the distortion of Ti octahedron and crystal field effects (Varignon et al, 2017;Okatov et al, 2005).…”

“…In the last two decades, YTiO 3 has been the subject of many studies using a variety of experimental methods and theoretical models (Suzuki et al, 2007;Knafo et al, 2009;Ulrich et al, 2009;Ichikawa et al, 2000;Akimitsu et al, 2001;Itoh et al, 1999;Nakao et al, 2002;Varignon et al, 2017). Akimitsu's (Akimitsu et al, 2001) and Itoh's (Itoh et al, 1999) results using the joint refinement of polarized neutron diffraction (PND) and X-ray magnetic diffraction (XMD) data, showing that the Ti 3+ 3d 1 wavefunction can be described by a linear combination of d xz and d yz orbitals (Kibalin et al, 2017). The reconstructed spin density in momentum space, using either theoretical calculations or the experimental Compton profiles, is in very good agreement with the description in direct space (Yan et al, 2017).…”

“…The X-ray statistical agreement factors are excellent [R(F) = 1.11% and R w (F) = 1.36%, GooF = 1.34 for 4244 reflections; 0.79 and 1.0% for 1000 reflections with sin / < 1 Å À1 and I > 3(I)], attesting to the high quality of the data and model. The statistical agreement factors for PND are very good: R w (|1 À R|) = 11.6% and GooF = 9.7; all statistical indices are slightly larger than values obtained when the refinement is carried out on PND or X-ray data only (Kibalin et al, 2017), which is to be expected as the model must be in agreement with both sets of data. The atomic fractional coordinates and anisotropic displacement parameters at the end of the multipolar joint refinement are given in Table S4.…”

“…. For more details, see the work of Kibalin et al (2017). Table 1 summarizes the experimental and crystallographic data.…”

Development of a joint refinement model for the spin-resolved one-electron reduced density matrix using different data sets

“…The one-electron reduced density matrix (1-RDM) (Lö wdin, 1955;Coleman, 1963;McWeeny, 1960;Davidson, 1976) is widely accepted as playing a central role in the description of electronic properties (Gillet & Becker, 2004). In addition, considerable work is in progress on the properties of the density matrix of N-particle systems (Lathiotakis & Marques, 2008;Luken, 1982;Hansen & Coppens, 1978;Jayatilaka & Grimwood, 2001;Barnett & Shull, 1967;Krusius et al, 1979;Gillet et al, 1999Gillet et al, , 2001Gillet, 2007;Kibalin et al, 2017;Yan et al, 2017). The refinement of the 1-RDM relative to the pseudo-experimental data has yielded many useful and very interesting results, providing excellent information about chemical bonding, electrostatic potential and orbital occupations (Gillet & Becker, 2004;Deutsch et al, 2012Deutsch et al, , 2014.…”