Octahedral rotation instability in Ba$_2$IrO$_4$

TL;DR

This study confronts the assumption that Ba$_2$IrO$_4$ adopts a static, undistorted $I4/mmm$ structure by testing its dynamical stability with spin-orbit coupling included. Using first-principles phonon dispersions and group-theoretical analysis, the author identifies a nearly flat unstable branch along $XP$ that corresponds to in-plane IrO$_6$ rotations and enumerates twelve symmetry-allowed distortions at $X$ and $P$, finding five that can be stabilized. The stabilized structures show energy gains up to $-5.8$ meV/atom and reveal that the total energy scales with the number of rotated layers, while electronic structure calculations indicate a narrow, half-filled $J_{ extrm{eff}} = 1/2$ manifold when rotations occur in all layers. These results imply that octahedral rotations must be considered to accurately model Ba$_2$IrO$_4$’s correlated electronic and magnetic properties and motivate a reinvestigation of its crystal structure and stacking order, complemented by experimental probes sensitive to stacking correlations.

Abstract

Ba$_2$IrO$_4$ has been refined in the tetragonal $I4/mmm$ phase without octahedral rotations, and its physical properties have been interpreted in this high-symmetry structure. However, the dynamical stability of this undistorted phase has not previously been questioned. It is important to establish whether other lower-symmetry structures are energetically more favorable because octahedral rotations control electronic bandwidths and constrain which magnetic interactions are allowed by symmetry. Here I compute first-principles phonon dispersions of $I4/mmm$ Ba$_2$IrO$_4$ including spin-orbit interaction. I find a nearly-flat nondegenerate unstable branch along the Brillouin-zone boundary segment $XP$ associated with inplane rotations of the IrO$_6$ octahedra. Using group-theoretical analysis, I enumerate the symmetry-allowed distortions associated with the $X_2^+$ and $P_4$ instabilities and fully relax the resulting structures. Only five of the twelve possible distortions can be stabilized, and the energy gain scales with the number of layers that exhibit octahedral rotations: phases with rotations in every IrO$_6$ layer are lower by $-5.8$ meV/atom and are nearly degenerate with respect to the stacking phase. Electronic structure calculations show that these rotated phases host a narrow and well-separated half-filled $J_{\textrm{eff}} = 1/2$ manifold, whereas structures with rotations only in alternate layers have broader and more entangled bands. This motivates a reinvestigation of the crystal structure of Ba$_2$IrO$_4$ and indicates that octahedral rotations should be considered in modeling its correlated electronic and magnetic properties.

Figures (6)

• Figure 1: Calculated non-spin-polarized phonon dispersions of fully-relaxed Ba$_2$IrO$_4$ in the $I4/mmm$ phase obtained using the PBE functional and including the spin-orbit interaction. The high-symmetry points are $\Gamma$$(0,0,0)$, $X$$(1/2,1/2,0)$, $P$$(1/4,1/4,1/4)$, $N$$(0,1/2,0)$, and $M$$(1/2,1/2,1/2)$ in terms of the primitive body-centered tetragonal reciprocal basis vectors proportional to $(0,1,1)$, $(1,0,1)$, and $(1,1,0)$. Imaginary frequencies are indicated by negative values.
• Figure 2: a) Octahedral layer in the parent $I4/mmm$ phase. b) Octahedral rotation due to the unstable phonon branch along $XP$. Only the basal oxygen ions move due to the instabilities. The octahedral rotation patterns at $X$ and $P$ are identical within the plane; they differ only in the phase of the rotation along the out-of-plane direction. The oxygen ions are denoted by red spheres. The iridium ions reside inside the octahedra.
• Figure 3: Isotropy subgroups and the corresponding order parameters of the $X_2^+$ and $P_4$ irreps of the $I4/mmm$ space group. The space group numbers are given in parentheses.
• Figure 4: Rotation patterns of the IrO$_6$ octahedral layers in the structures that could be stabilized after structural relaxation calculations. The relative patterns of the rotations between different layers are denoted by $+$ and $-$. The layers without octahedral rotation are denoted by $0$. Note that the $z = \{0, \frac{1}{2}\}$ and $z=\{\frac{1}{4},\frac{3}{4}\}$ layers are shifted with respect to each other by an inplane wavevector of $(\frac{1}{2},0)$.
• Figure 5: Calculated band structures of Ba$_2$IrO$_4$ in the (top) $I4/mmm$, (middle) $I4_1/acd$, and (bottom) $P4_2/mbc$ phases obtained using the PBE functional and including the spin-orbit interaction. The two low-symmetry structures involve octahedral rotations in all layers, and their $J_{\textrm{eff}} = 1/2$ manifold is narrow, well separated, and half filled.