Perspective: Strongly correlated and topological states in [111] grown transition metal oxide thin films and heterostructures

Abstract: We highlight recent advances in the theory, materials fabrication, and experimental characterization of strongly correlated and topological states in [111] oriented transition metal oxide thin films and heterostructures, which are notoriously difficult to realize compared to their [001] oriented counterparts. We focus on two classes of complex oxides, with the chemical formula ABO3 and A2B2O7, where the B sites are occupied by an open-shell transition metal ion with a local moment, and the A sites are typically a rare earth. The [111] oriented quasi-two-dimensional lattices derived from these parent compound lattices can exhibit peculiar geometries and symmetries, namely, a buckled honeycomb lattice, as well as kagome and triangular lattices. These lattice motifs form the basis for emergent strongly correlated and topological states expressed in exotic magnetism, various forms of orbital ordering, topological insulators, topological semimetals, quantum anomalous Hall insulators, and quantum spin liquids. For transition metal ions with high atomic number, spin-orbit coupling plays a significant role and may give rise to additional topological features in the electronic band structure and in the spectrum of magnetic excitations. We conclude the Perspective by articulating open challenges and opportunities in this actively developing field.

• The paper presents engineered oxide heterostructures revealing novel quantum phases driven by strong correlations and spin–orbit coupling.
• It employs tight-binding and DFT analyses to characterize buckled honeycomb and kagome lattices with small insulating gaps.
• The study discusses synthesis challenges and experimental strategies crucial for realizing topologically nontrivial, correlation-driven states.

Strongly Correlated and Topological Phases in [111] Grown Transition Metal Oxide Thin Films and Heterostructures

Introduction

This essay synthesizes the perspectives and findings presented in "Perspective: Strongly correlated and topological states in [111] grown transition metal oxide thin films and heterostructures" (2003.12211), providing an expert-level analysis of the central themes, results, and implications for the oxide quantum materials community. Transition metal oxides (TMOs) grown along unconventional crystal orientations, notably the [111] direction, have recently emerged as a salient field for exploring new quantum phases arising from strong correlation, spin-orbit coupling (SOC), and geometric frustration. This essay reviews their theoretical predictions, fabrication challenges, experimental progress, and potential avenues for future research in correlated and topological oxide heterostructures.

Structural Motifs and Their Electronic Consequences

Oriented growth of ABO$_3$ and A$_2$B$_2$O$_7$ oxides along [111] uniquely generates quasi-two-dimensional geometric architectures, specifically buckled honeycomb, kagome, and triangular lattices. For perovskite ABO$_3$ bilayers, the resulting buckled honeycomb geometry steers the $d$ orbital manifold away from configurations encountered in standard [001] growth. The geometric modification induces quadratic band crossing points (QBC) at the $\Gamma$-point for specific fillings (notably $e_g$ electron quarter-filling), with six-fold rotational symmetry protecting the QBC against splitting into Dirac points. Notably, in the [111] perovskite heterostructures, complex orbital orderings compete and coexist with correlation-driven symmetry breaking, topologically nontrivial gapped states, and spontaneous magnetism, as supported by a wide array of tight-binding and DFT studies.

In [111] grown A$_2$B$_2$O$_7$-type pyrochlores, the architecture consists of alternating planes of kagome and triangular lattices, introducing a high degree of geometric frustration. For iridates (A$_2$Ir$_2$O$_7$), the active B-site Ir$^{4+}$ ions (5$d^5$) with strong SOC realize effective pseudospin $J_{\rm eff}=1/2$ moments on frustrated networks, amplifying the tendency toward unconventional ground states such as quantum spin liquids, Weyl semimetals, and axionic insulators.

Theoretical Landscape and Numerical Insights

The theoretical proposals for [111] oriented nickelate and cobaltate bilayers predict extensive phase diagrams hosting Dirac half-metal phases, QAHE states, spin nematics, and interaction-driven topological insulators even in the absence of large intrinsic SOC [Xiao et al., Nat. Commun. 2, 596 (2011); Ruegg & Fiete, Phys. Rev. B 84, 201103 (2011)]. Model Hamiltonian analysis combined with first principles calculations clarify that the competing energy scales—on-site Coulomb interaction $U$, Hund's coupling $J_H$, bandwidth control via quantum confinement, and epitaxial strain—regulate the windows for topological phase stability. Importantly, the gap sizes for topologically nontrivial states are small (tens to hundreds of meV), making them susceptible to disorder and competing orders.

Pyrochlore thin films, theoretically treated via both slab models and dynamical mean-field theory (DMFT), are predicted to display a dimensional crossover from 3D correlated metals, Mott insulators and Weyl semimetals to 2D quantum anomalous Hall and quantum spin liquid states as the film thickness is reduced [Hu et al., Phys. Rev. B 86, 235141 (2012)]. Nontrivial surface and domain-wall conduction phenomena are predicted, including robust chiral edge states associated with all-in-all-out (AIAO) domain structures, carrying direct implications for interface and edge engineering.

Materials Synthesis: Challenges and Strategic Advances

Realizing [111] films at the atomic scale is nontrivial due to a combination of factors: (i) lack of lattice-matched commercial substrates for [111] orientation, (ii) polar discontinuities yielding large electric fields and possible electronic or ionic reconstruction, (iii) enhanced surface and interface instability for polar terminations, and (iv) volatility and off-stoichiometry, especially for heavy transition metals like Ir.

Experimental advances have come from the judicious selection of substrate/film combinations, buffer layers to screen polar mismatch, and adoption of solid-phase epitaxy, where an amorphous precursor is ex-situ crystallized. Films of LaNiO$_3$, NdNiO$_3$, Eu$_2$Ir$_2$O$_7$, Tb$_2$Ir$_2$O$_7$, and Pr$_2$Ir$_2$O$_7$ have been grown with control on thickness, interface quality, and, increasingly, stoichiometry.

Experimental Signatures and the Search for Topological Phases

Despite robust theoretical predictions, direct experimental observation of nontrivial topological phases, such as QAHE or quantum spin liquids, in [111] perovskite or pyrochlore bilayers remains elusive. Notably, ARPES, STM, and other traditional probes are hindered by high surface sensitivity and the buried nature of the relevant layers. Instead, state-of-the-art techniques such as SX-ARPES and HAXPES with large probing depths have enabled direct observation of Fermi-level states and band topology in buried LaNiO$_3$ and NdNiO$_3$ [Arab et al., Nano Lett. 19, 8311 (2019)].

Bulk and interfacial transport experiments reveal strong correlation physics—antiferromagnetic and orbital ordering, emergence of AIAO-magnetism, and even domain-wall-localized conduction. For instance, in [111] Eu$_2$Ir$_2$O$_7$ films, observed odd-parity terms in magnetoresistance and a field-independent Hall effect below the MIT are indicative of single-variant AIAO domain selection and switching. In Pr$_2$Ir$_2$O$_7$, spontaneous anomalous Hall signals at unexpectedly high temperatures suggest possible Ir-derived spin chirality or strain-induced multipolar magnetism.

A strong result highlighted is the observation of small insulating gaps in [111] nickelates and pyrochlores, consistent with correlation-driven phases but no direct quantization of Hall conductance or signature of topological edge modes—underscoring the narrowness of the theoretical window for such phenomena, the effect of disorder, and the pertinence of Hund's coupling and orbital overlaps [Ruegg et al., Phys. Rev. B 88, 115146 (2013)].

Implications and Future Directions

The research delineates both the immense challenges and rich opportunities in the field of oxide heterostructures grown along high-index directions. Key implications include:

• Designer Quantum Phases: The ability to geometrically engineer atomic lattices unlocks classes of strongly correlated, topological, and potentially fractionalized states not accessible in naturally occurring crystals or conventional growth directions.
• Disorder and Competing Orders: The practical realization of topological phases is highly sensitive to stoichiometry, domain structure, disorder, and interface effects; significant advances in materials synthesis, in-situ growth monitoring, and interface engineering are required.
• Probing Collective Excitations: Beyond dc and Hall transport, resonant inelastic x-ray scattering (RIXS) and related probes are poised to provide momentum-resolved characterization of magnons and collective excitations in these ultra-thin, highly correlated systems.

Looking forward, the extension of geometrical lattice engineering to spinel and $f$-electron systems, leveraging the interplay of $d$-$f$ interactions and additional orbital degrees of freedom, is expected to yield new phenomena including multipolar orders and enhanced quantum entanglement. The scalable realization of designer lattices such as kagome, pyrochlore, or trifold structures in ultrathin limit remains a formidable yet high-value target.

Conclusion

The paper comprehensively articulates the state-of-the-art in the realization and study of strongly correlated and topologically nontrivial states in [111] grown transition metal oxide thin films and heterostructures (2003.12211). It establishes the theoretical foundations for novel quantum phases emergent from geometric lattice engineering, provides a critical appraisal of the barriers in synthesis and characterization, and identifies experimental strategies that have begun to bridge these challenges. The confluence of materials science, correlated electron physics, and symmetry-driven topology in this context presents a fertile territory for discovering and controlling new phases of matter, with the potential to expand the toolkit for quantum materials design and quantum information applications.