Electronic Structure of Epitaxial Films of the Bilayer Strontium Ruthenate: Sr$_{3}$Ru$_2$O$_{7}$

Technical Summary: Electronic Structure of Epitaxial Films of the Bilayer Strontium Ruthenate: Sr3Ru2O7

Problem and Motivation
The bilayer strontium ruthenate, Sr$_3$Ru$_2$O$_7$, is a quasi-two-dimensional, strongly correlated material known for its complex ground states and field-induced metamagnetic transitions. These phenomena are theoretically linked to the detailed structure of its Fermi surface (FS), particularly saddle points and van Hove singularities near the Fermi level ($E_F$). While the bulk crystal structure is often described as tetragonal ($I4/mmm$), structural refinements suggest an in-plane rotation of RuO$_6$ octahedra that lowers the symmetry to orthorhombic. This structural nuance is critical, as it drives Brillouin zone reconstruction and band backfolding. However, understanding how epitaxial strain and substrate-induced lattice constraints modify the electronic band structure and FS topology in thin films remains an open challenge. Previous studies on single crystals have established a baseline, but thin films offer a unique platform to tune these properties via strain engineering, provided phase-pure, high-quality epitaxial growth can be achieved.

Methodology
The authors employed a combined experimental and theoretical approach to investigate the low-energy electronic band structure of epitaxial Sr$_3$Ru$_2$O$_7$ films.

• Sample Growth: Sr$_3$Ru$_2$O$_7$ thin films (6 nm thick, approx. 3 unit cells) were grown using Molecular Beam Epitaxy (MBE) on two single-crystal substrates: (LaAlO$_3$)$_{0.3}$(Sr$_2$TaAlO$_6$)$_{0.7}$ (LSAT) and SrTiO$_3$ (STO). The lattice mismatch between the film ($a \approx 3.890$ Å) and the substrates (LSAT: $3.868$ Å; STO: $3.905$ Å) was utilized to induce compressive strain (on LSAT) and tensile strain (on STO), respectively.
• Structural Characterization: Film quality and strain states were verified using Reflection High-Energy Electron Diffraction (RHEED) during growth, X-ray diffraction (XRD) $\theta$-$2\theta$ scans, and Reciprocal Space Maps (RSMs).
• Electronic Characterization: Angle-Resolved Photoemission Spectroscopy (ARPES) measurements were conducted at 7 K using a high-resolution Scienta DA-30L analyzer (5 meV energy resolution) to map the Fermi surfaces and band dispersions.
• Theoretical Modeling: Density Functional Theory (DFT) calculations were performed using pseudopotential, plane-wave implementations to simulate the electronic structure under the specific strain conditions of LSAT (modeled as orthorhombic) and STO (modeled as tetragonal).

Key Results

1. Strain-Dependent Symmetry and Fermi Surface Topology:

   • LSAT (Compressive Strain): The ARPES data for films grown on LSAT revealed a reconstructed Fermi surface consistent with an orthorhombic-like symmetry. The measured FS displayed hole-like pockets ($\alpha_1, \alpha_2$) and features near the X point, aligning qualitatively with DFT calculations for a lower-symmetry orthorhombic structure.
   • STO (Tensile Strain): Films grown on STO exhibited a Fermi surface topology characteristic of a tetragonal-like symmetry, lacking the band backfolding seen in the orthorhombic phase. The FS consisted of $\Gamma$-centered electron-like pockets and a broad feature at $\Gamma$, matching DFT predictions for a tetragonal phase where RuO$_6$ octahedral rotations are suppressed.

2. Suppression of Octahedral Rotations:
   The results indicate that the tensile strain imposed by the STO substrate suppresses the in-plane rotation of RuO$_6$ octahedra, preserving the high-symmetry tetragonal configuration. Conversely, the compressive strain on LSAT allows for or induces the structural distortions associated with orthorhombic symmetry.

3. Low-Energy Flat Bands:
   Both experimental datasets and DFT calculations identified weakly dispersive (flat) spectral features within $\sim$15 meV below the Fermi level.

   • In the LSAT (orthorhombic) film, flat bands were observed along the $\Gamma$-X direction.
   • In the STO (tetragonal) film, a flat band feature was observed centered at $\Gamma$.
     These features are attributed to specific orbital hybridizations and interlayer interactions, potentially enhancing the low-energy density of states.

4. Agreement between Experiment and Theory:
   Despite the challenges of resolving fine spectral features in thin films (due to disorder and finite thickness), the measured Fermi surface topologies and band dispersions showed qualitative agreement with the DFT calculations, validating the use of strain engineering to control the electronic structure.

Significance and Claims
The paper claims to provide the first combined experimental and theoretical investigation of the electronic band structure and Fermi surface topology of epitaxial Sr$_3$Ru$_2$O$_7$ thin films. The primary significance lies in demonstrating that the electronic structure of this bilayer ruthenate is highly sensitive to epitaxial strain. By selecting specific substrates, the authors successfully tuned the underlying crystal symmetry (between orthorhombic-like and tetragonal-like) and the resulting Fermi surface topology.

The authors assert that these findings establish a foundation for future efforts to tune correlated phases in bilayer ruthenates. Specifically, the ability to control the Fermi surface via strain-induced structural changes offers a pathway to manipulate the magnetic-field-controlled instabilities and potentially stabilize new quantum phases. The work highlights that thin-film constraints can effectively suppress or enhance structural distortions (such as octahedral rotations) that are present in bulk crystals, thereby providing a versatile platform for engineering electronic and magnetic interactions in correlated 4d electron systems.