Spin resolved electron density study of YTiO3 in its ferromagnetic phase: signature of orbital ordering

Abstract

The present work reports on the charge and spin density modelling of YTiO₃ in its ferromagnetic state (T _C = 27 K). Accurate polarized neutron diffraction and high-resolution X-ray diffraction (XRD) experiments were carried out on a single crystal at the ORPHÉE reactor (LLB) and SPRING8 synchrotron source. The experimental data are modelled by the spin resolved pseudo-atomic multipolar model (Deutsch et al., 2012 ▸). The refinement strategy is discussed and the result of this electron density modelling is compared with that from XRD measured at 100 K and with density functional theory calculations. The results show that the spin and charge densities around the Ti atom have lobes directed away from the O atoms, confirming the filling of the t _2g orbitals of the Ti atom. The d _xy orbital is less populated than d _xz and d _yz , which is a sign of a partial lift of degeneracy of the t _2g orbitals. This study confirms the orbital ordering at low temperature (20 K), which is already present in the paramagnetic state above the ferromagnetic transition (100 K).

Keywords: X-ray diffraction; YTiO3; charge density; computational modelling; inorganic materials; magnetic order; materials modelling; multipolar refinement; orbital ordering; perovskites; polarized neutron diffraction; properties of solids; spin density.

Figure 1

(Left) Crystal structure of YTiO₃: O atoms in red and Ti in blue. (Right) Ti octahedron and local axes.

Figure 2

Residual density at high resolution (N _ref = 2549, sin (θ)/λ >1.25 Å⁻¹) in the (001) plane containing Y and Ti atoms: (a) and (c) harmonic, and (b) and (d) anharmonic models. Contour: 0.2 e Å⁻³.

Figure 3

Residual density around (a) Ti and (b) Y atoms after the joint refinement. Contour: 0.1 e Å⁻³ sin (θ)/λ < 1.2 Å⁻¹.

Figure 4

Electron density gradient map (black lines) defining the Ti and O atomic basins superimposed onto the spin density (positive in blue and negative in red using logarithmic contours), highlighting the spin density expansion towards the oxygen atomic basins.

Figure 5

Static deformation densities (top) and spin (bottom) densities in the xy (left), xz (middle) and yz (right) planes containing the Ti atom. Contour: 0.05 e Å⁻³ for charge and 0.03 e Å⁻³ for spin densities.

Figure 6

Isosurface spin density in the unit cell. Contour: 0.03 e Å⁻³.

Figure 7

Static deformation density (at 100 K) in the xy, xz and yz planes (left to right). Contour: 0.05 e Å⁻³.

Figure 8

Static deformation density around the Y atom in the (a) mirror plane passing through O1,Y O1′, (b) the plane of Y, O1 and O2 short contacts, and (c) the plane of O1, Y and TI. Contour: 0.05 e Å⁻³.

Figure 9

DFT charge deformation densities in xy, xz and yz planes (left to right). Contour: 0.05 e Å⁻³.

Figure 10

DFT spin densities in the xy, xz and yz planes (left to right). Contour: logarithmic 0.01 × 2ⁿ (n = 1 to 12).

Figure 11

Valence density in the xy, xz and yz planes for spin-up (a, b, c) and spin-down (a′, b′, c′) electrons. Contour: 0.1 e Å⁻³.