First principles electric field gradients at A and B site cations across the NaRTiO4 Ruddlesden Popper series

Abstract

The $n = 1$ Ruddlesden-Popper titanates, NaRTiO$_{4}$ (R = rare-earth), exhibit a structural behaviour where non-centrosymmetry is driven by cooperative oxygen octahedral rotations (OORs) rather than conventional second-order Jahn-Teller distortions. In this work, we present an \textit{ab-initio} investigation of the structural, electronic and hyperfine properties of the entire NaRTiO$_{4}$ series across the two disputed ground states, $Pbcm$ and $P\bar{4}2_1m$, and the high temperature $P4/nmm$ symmetries. Our results reveal an ionic-radius-dependent evolution from a tilt-dominated regime for small rare-earth ions to a distortion-dominated regime for larger cations, leading to an asymptotic regime in which the high-temperature phase becomes increasingly competitive with the ground-state structures as the ionic radius increases. In parallel, the electronic band gap follows a systematic evolution across the series, reflecting the underlying structural changes and the increasing dominance of octahedral distortions at larger ionic radii. The Electric Field Gradient (EFG) tensor reveals that, in the large-radius limit, all symmetries tend locally towards a similar environment. Away from this limit, the EFG tensor for different symmetries progressively diverges, providing a sensitive probe for phase transitions and revealing symmetry-specific fingerprints, particularly for the rare-earth and Ti sites. By establishing these EFG signatures, this work provides a roadmap for experimental techniques, such as Nuclear Magnetic Resonance (NMR) and Perturbed Angular Correlation (PAC), to resolve the ground-state symmetry of these structures.

Figures (14)

• Figure 1: Representation of the unit cell of all three phases adopted: the orthorhombic $Pbcm$ (s.g. #57); acentric $P\bar{4}2_{1}m$ (s.g. # 113), and the tetragonal $P4/nmm$ (s.g. #129) In this illustration, the R-site in NaRTiO$_{4}$ is occupied by the ytrium atom. Figures plotted with the help of VESTA software momma2011vesta.
• Figure 2: Phase stability and structural evolution of the NaRTiO$_{4}$ family. (a) Relative DFT-calculated ground-state energies for the $P4/nmm$ and $Pbcm$ phases as a function of the rare-earth ionic radius, benchmarked against the acentric $P\bar{4}2_1m$ phase. Yttrium is shown with dashed lines in order to stand out further from the Lanthanide trend. (b) Experimental phase transition map determined via Second Harmonic Generation (SHG) measurements up to 1073 K.
• Figure 3: DFT-calculated cell parameters of the NaRTiO$_{4}$ (R = rare-earth) series, as a function of ionic radii ($r_{i}$). From top to bottom: Long-axis (c) ; Short-axis (a) and Tetragonal Ratio (c/a). All three symmetries are highlighted in distinct colors: P4/nmm (red); P$\bar{4}$2$_{1}$m (blue); Pbcm (green). Yttrium data points are represented by hollow markers.
• Figure 4: Evolution of the local TiO$_{6}$ environment in the NaRTiO$_{4}$ series, as a function of the ionic radius. (Top) Displacement of the Ti ion toward the apical oxygen, Ti--O$_{\text{top}}$, where O$_{\text{top}}$ is defined as the oxygen neighbor closest to the Na layer. (Middle) Total vertical height ($L_v$) of the TiO$_{6}$ octahedron. (Bottom) Octahedral deformation factor ($\sigma$). All three symmetries are highlighted in distinct colors: P4/nmm (red); P$\bar{4}$2$_{1}$m (blue); Pbcm (green). Yttrium data points are represented by hollow markers.
• Figure 5: Theoretical electric field gradient (EFG) parameters in NaRTiO$_{4}$ (R = rare-earth), as functions of ionic radius, $r_{i}$ for different atomic sites: (Left) Na, (Middle) Ti, and (Right) R. The upper panel shows the absolute principal component $|V_{zz}|$ (in $V \AA^{-2}$), while the lower panel displays the asymmetry parameter $\eta$, both calculated for the three symmetries in study: P$\bar{4}$2$_{1}$m (blue), Pbcm (green), P4/nmm (red). Yttrium data points are represented by hollow markers.