Non-Fermi liquid behavior in La$_3$Ni$_2$O$_7$ thin films under hydrostatic pressure

This study demonstrates that epitaxially grown La$_3$Ni$_2$O$_7$ thin films can be tuned from Fermi liquid-like to non-Fermi liquid behavior under modest hydrostatic pressures, suggesting a strong proximity to a fluctuating ordered state that requires significantly less pressure than in bulk single crystals.

The Gist

The Big Picture: Finding the "Sweet Spot" for Superconductivity

Imagine you are trying to bake the perfect cake (superconductivity, where electricity flows with zero resistance). For a long time, scientists knew that a specific type of cake ingredient called "nickelates" could make a great cake, but only if you squeezed the batter incredibly hard (using high pressure) and baked it just right.

Recently, scientists discovered a new "super-cake" recipe called La₃Ni₂O₇. In big chunks of this material (crystals), it only becomes a super-cake if you squeeze it with the force of a mountain (about 14 gigapascals of pressure). That's like trying to bake a cake inside a hydraulic press—it's hard to do and hard to study.

This paper is about a team of scientists who tried to make this cake in thin films (like a very thin layer of frosting) instead of big chunks. They wanted to see if they could get the cake to work without needing a mountain of pressure.

The Experiment: Stretching and Squeezing the Material

The scientists grew these thin films on two different types of "plates" (substrates):

1. LAO (LaAlO₃): A plate that fits the film almost perfectly, but slightly squeezes it (compressive strain).
2. SLAO (SrLaAlO₄): A plate that squeezes the film even harder.

They also tried different "seasonings" (oxygen treatments). Some films were just baked, while others were treated with ozone (a super-charged version of oxygen) to fill in any missing holes in the recipe.

The Discovery:

• The Ozone Mystery: They found that just adding regular oxygen wasn't enough to make the film super-conductive. It was like trying to fill a leaky bucket with a teaspoon; you needed a firehose. Ozone acted like the firehose, quickly filling the holes and making the material behave differently.
• The "Strange" Behavior: Even though they didn't get the film to become a super-conductor (zero resistance) in this specific experiment, they found something even more interesting: the material started acting like a mystery metal.

The Main Surprise: The "Non-Fermi Liquid"

To understand the main finding, let's use an analogy of a crowded dance floor.

• Normal Metal (Fermi Liquid): Imagine a dance floor where people (electrons) bump into each other politely. If you turn up the music (lower the temperature), they move in a predictable, orderly way. In physics, we call this "Fermi liquid" behavior. The resistance (how hard it is to move) changes in a predictable square pattern ($T^2$).
• The "Non-Fermi Liquid": Now, imagine the music changes, and suddenly the dancers start moving in a chaotic, wild, unpredictable way. They aren't bumping politely; they are swarming. This is called Non-Fermi liquid behavior. It usually happens right before a material undergoes a major phase change (like becoming a magnet or a super-conductor).

The Magic of the Thin Film:
Usually, to get a material to act like this "wild dancer," you need to squeeze it with a massive amount of pressure (like a Diamond Anvil Cell).

• The Old Way: Squeeze a big crystal until it breaks (14 GPa).
• The New Way (This Paper): The scientists took their thin film and applied a tiny amount of pressure (only 1.4 GPa).

The Result:
With just a tiny nudge (about 6–8% of the pressure needed for big crystals), the thin film suddenly switched from being a "polite dancer" to a "wild dancer." Its electrical resistance started behaving in a strange, non-linear way ($T^{1.4}$).

Why This Matters

Think of the thin film as a tightly wound spring.

• Because the film is so thin and stretched by the substrate, it is already "primed" and ready to snap. It is sitting right on the edge of a cliff (a Quantum Critical Point).
• When they applied a tiny bit of extra pressure, it was just enough to push the spring over the edge, causing it to snap into this new, strange state.
• In big crystals, the spring is loose, so you have to squeeze it with a hydraulic press to get it to snap.

The Takeaway

1. Thin films are special: By growing these materials as thin layers, scientists can "tune" them to be much more sensitive to pressure than big chunks of the same material.
2. Ozone is key: To get the right chemical structure, you need ozone, not just regular oxygen.
3. We are close to the finish line: The fact that the material turns "wild" (Non-Fermi liquid) with such little pressure suggests that superconductivity (the zero-resistance state) is likely just one step away. If they tweak the pressure or the oxygen just a little more, they might finally get the film to conduct electricity with zero loss, all without needing a mountain of pressure.

In short: The scientists found a way to make a material that acts like a super-conductor's "cousin" using a tiny squeeze instead of a giant one. This proves that thin films are a powerful new tool for unlocking the secrets of high-temperature superconductivity.

Technical Summary

1. Problem Statement

The discovery of high-temperature superconductivity ($T_c \approx 80$ K) in bilayer nickelate $La_3Ni_2O_7$ (LNO) under high pressure (14 GPa) has sparked intense research into its relationship with cuprate superconductors. However, significant challenges remain:

• Pressure Requirement: Achieving superconductivity in bulk LNO crystals traditionally requires extreme pressures (14 GPa), limiting experimental accessibility and the study of underlying mechanisms.
• Phase Purity: Structural polymorphs and inter-growth phases often impede the formation of the desired bilayer Ruddlesden-Popper (RP) structure necessary for superconductivity.
• Oxygen Stoichiometry: The role of oxygen content and the specific efficacy of ozone vs. molecular oxygen annealing in inducing superconductivity in thin films is not fully understood.
• Normal State Behavior: The nature of the normal state (Fermi liquid vs. non-Fermi liquid) and its evolution under pressure in thin films, particularly regarding proximity to quantum critical points (QCP), requires further elucidation.

2. Methodology

The authors employed Pulsed Laser Deposition (PLD) to fabricate high-quality epitaxial $La_3Ni_2O_7$ thin films on various substrates to control strain and oxygen content.

• Film Growth:
  • Substrates: $LaAlO_3$ (LAO), $SrLaAlO_4$ (SLAO), and $YAlO_3$ (YAO) were used to induce varying levels of compressive strain (lattice mismatches ranging from -1.1% to -3.6%).
  • Capping Layer: A single-unit-cell $SrTiO_3$ (STO) layer was deposited to protect the LNO film from degradation.
  • Parameters: Growth occurred at 750°C (LNO) and 650°C (STO) with specific oxygen partial pressures (100 mtorr for LNO).
• Post-Growth Treatments:
  • Annealing: Films were annealed in-situ (PLD chamber) and ex-situ in a high-pressure furnace (15 bar $O_2$) at 650°C for 18 hours.
  • Reduction: Some samples underwent topotactic reduction using $CaH_2$ to simulate oxygen deficiency.
  • Ozone vs. Oxygen: The study compared the effects of high-pressure molecular oxygen annealing against previous findings regarding ozone annealing.
• Characterization:
  • Structural: X-ray diffraction (XRD) and Reflection High-Energy Electron Diffraction (RHEED) confirmed epitaxial growth and phase purity.
  • Transport: Four-probe resistance measurements and Hall effect measurements were performed from 2 K to 300 K.
  • High Pressure: Hydrostatic pressure was applied up to 1.41 GPa using a piston-cylinder cell (PCC) with Daphne 7575 oil as the pressure-transmitting medium.

3. Key Contributions

• Strain Engineering: Demonstrated that the electronic ground state of LNO thin films is highly tunable via substrate-induced strain. Films on LAO (low mismatch) behave differently than those on YAO (high mismatch).
• Oxygen Annealing Efficacy: Showed that high-pressure molecular oxygen annealing alone is insufficient to induce superconductivity or fully restore metallic behavior in LNO films, contrasting with ozone-annealed films which become superconducting. This highlights the unique role of ozone in rapidly filling oxygen vacancies.
• Discovery of Non-Fermi Liquid (NFL) Behavior: Identified a transition from Fermi liquid to non-Fermi liquid behavior in LNO films under modest hydrostatic pressure (1.41 GPa), a finding previously only observed in bulk crystals at much higher pressures.
• Quantum Criticality: Provided evidence that epitaxial strain combined with oxygen tuning places the LNO thin film close to a Spin Density Wave (SDW) quantum critical point, requiring minimal external pressure to access NFL regimes.

4. Results

Structural and Phase Purity

• Films grown on LAO and SLAO exhibited high-quality epitaxial growth with distinct (00l) diffraction peaks characteristic of the bilayer RP structure.
• The out-of-plane lattice constant was found to be 20.25 Å (LAO) and 20.35 Å (SLAO), consistent with fully strained films.
• Films grown at higher oxygen pressures (>100 mtorr) tended to form competing $LaNiO_3$ phases, while ~100 mtorr yielded pure bilayer LNO.

Transport Properties and Oxygen Effects

• LAO Substrates: As-grown films showed Fermi-liquid-like metallic behavior with a slight low-temperature upturn (Kondo-like). Annealing in high-pressure oxygen doubled the resistivity but did not induce superconductivity or significantly alter the metallic character.
• SLAO Substrates: Pristine films grown at low oxygen pressure were insulating. Annealing in high-pressure oxygen increased metallicity but did not fully convert the films to the superconducting state observed in ozone-annealed samples.
• Reduction: Topotactic reduction rendered films insulating, confirming the sensitivity of LNO to oxygen stoichiometry.

Hall Effect and Magnetic Ordering

• YAO Substrates: Films on YAO (high strain mismatch) exhibited a pronounced kink in resistance and Hall coefficient ($R_H$) around 117–120 K. This is attributed to a Spin Density Wave (SDW) transition, similar to bulk behavior.
• LAO Substrates: Films on LAO (low strain mismatch) showed no such transition in resistivity, suggesting the SDW state is suppressed or broadened by epitaxial strain.
• Carrier Concentration: $R_H$ remained positive but decreased with temperature, suggesting a multi-band electronic structure dominated by Ni $3d$ orbitals ($3d_{z^2}$ and $3d_{x^2-y^2}$).

Pressure-Induced Non-Fermi Liquid Behavior

• Low-Temperature Upturn: At ambient pressure, LAO films showed a resistance upturn at ~10 K, fitting a Kondo model ($R \propto -\ln T + T^\gamma$).
• Pressure Evolution:
  • At 0.53 GPa, the low-temperature resistance followed a $T^2$ dependence, characteristic of a Fermi Liquid (quasiparticle-quasiparticle scattering).
  • At 1.41 GPa, the power-law exponent evolved to $\alpha \approx 1.4$ ($R \propto T^{1.4}$) over a wide temperature range (1.8 K – 60 K).
• Significance of Pressure Scale: This transition to NFL behavior occurred at only 1.41 GPa, which is merely 6–8% of the pressure (14 GPa) required to induce similar effects in bulk LNO single crystals.

5. Significance

• Proximity to Quantum Critical Point (QCP): The dramatic shift from Fermi liquid ($\alpha=2$) to non-Fermi liquid ($\alpha=1.4$) under such low pressure suggests that the strained LNO thin film is already positioned very close to a QCP associated with SDW order. The applied pressure simply tunes the system across this critical point.
• Mechanism of Superconductivity: The observation of NFL behavior (often a precursor to unconventional superconductivity) in the normal state supports the hypothesis that spin fluctuations drive the superconducting pairing mechanism in nickelates, similar to cuprates and iron-based superconductors.
• Experimental Efficiency: The ability to access NFL and potentially superconducting states in thin films using modest pressures (achievable in standard piston-cylinder cells) rather than extreme Diamond Anvil Cell (DAC) pressures opens new avenues for investigating the phase diagram of nickelates.
• Material Tunability: The study underscores that thin-film engineering (strain + oxygen control) is a powerful tool to manipulate the electronic ground state of correlated oxides, potentially enabling the discovery of ambient-pressure superconductivity in future iterations of this material system.