Diverse polymorphism in Ruddlesden-Popper chalcogenides

Abstract

Ruddlesden-Popper (RP) chalcogenides are stable, non-toxic candidates for optoelectronic or thermoelectric applications. The structural diversity of RP oxides is already exploited to tune properties or achieve more advanced functionalities like multiferroicity, however, little is known about the structural evolution of RP chalcogenides. In this work, we develop a high-accuracy machine-learned interatomic potential to run large-scale molecular dynamics simulations on $Ba_{n+1}Zr_nS_{3n+1}$ for $n=1$ to $n=6$. We predict new polymorphs for each $n$-value, calculate their corresponding phase transition temperatures, and validate our approach through comparison to published experimental results. We find that the $n=1$ phase exhibits negative thermal expansion, that $n=1$ and $n=3$ undergo unusual ascending symmetry breaking, and that phases with $n\geq4$ form layer-dependent tilt patterns previously unreported for inorganic RP materials. This unique behaviour results from competition between octahedral rotations and rumpling at the rocksalt interface, and suggests new strategies for accessing advanced functionalities.

Figures (5)

• Figure 1: a) Ba_n+1Zr_nS_3n+1 Ruddlesden-Popper (RP) crystal structures in the high-symmetry ${ {\lccode'~='- } {\lccode'\mkern1mu\overline{\mkern-1mu=\mkern-1mu}\mkern1mu'* } {\lccode'\frac{=}{m}'i } I4/mmm}$ phase. The primitive cell is formed from two unique perovskite slabs with a half-cell offset. Each slab contains $n$ layers of ZrS6 octahedra; the $n=\infty$ limit is equivalent to BaZrS3. Common distortions in RP materials: b) in-phase ($\psi$) and c) out-of-phase ($\phi$) octahedral tilting; d) out-of-plane rumpling distortion; e) in-plane cation displacement. The rumpling amplitude is defined as positive when A-site cations at the rocksalt layer move towards the BX6 octahedra. In-plane refers to displacements along the $x$- or $y$-axes.
• Figure 2: Neuroevolution potential heating simulations for Ba_n+1Zr_nS_3n+1: a) in-plane lattice parameters. Scatter points at 0K correspond to the lattice parameters from HSE06 relaxations. Note the perovskite lattice parameter is for a conventional cubic cell; b) heat capacities. A sharper peak in the heat capacity indicates a first-order (discontinuous) phase transition, whilst a broader peak indicates more second-order (continuous) character.
• Figure 3: Summary of space groups, tilt patterns, and phase transition temperatures for Ba_n+1Zr_nS_3n+1. Bars are colour-coded by tilt pattern; see Table S3 for Aleksandrov tilt notation. Space groups, labelled in text, depend on both the tilt pattern and the parity of $n$. Solid, dashed, and dotted lines mark first-order, second-order, and surface transitions, respectively. Gradient fade on $n=3$ indicates a possible low-temperature ${ {\lccode'~='- } {\lccode'\mkern1mu\overline{\mkern-1mu=\mkern-1mu}\mkern1mu'* } {\lccode'\frac{=}{m}'i } C2/c}$ phase.
• Figure 4: Snapshots of Euler angles ($\theta_x$, $\theta_y$, $\theta_z$) for Ba_n+1Zr_nS_3n+1 for a) $n=3$ and b) $n=4$. Octahedra are colour-coded by the magnitude of their Euler tilt angles. Solid lines separate structures by temperature, and dashed lines distinguish tilt axis. Structures are viewed along the $x$-axis for $\theta_x$ and $\theta_z$, and along the $y$-axis for $\theta_y$.
• Figure 5: Rumpling amplitudes ($\delta$) in Ba$_{n+1}$Zr$_n$S$_{3n+1}$ materials with a) $n=1$ to 3 and b) $n = 4$–6. Scatter points at 0K correspond to the rumpling amplitudes from HSE06 relaxations. Surface transition temperatures are indicated by dashed vertical lines. c) Normalised out-of-plane lattice parameters for $n = 4$–6. One-dimensional potential energy surfaces for out-of-plane, in-phase octahedral tilts ($Q_{\psi_z}$) in Ba4Zr3S10 ($n=3$) are shown as a function of d) rumpling and e) in-plane, out-of-phase tilt amplitudes ($Q_\phi$). Distortions are illustrated in \ref{['fig:crystal_structures_phonons']}.