Entropy stabilization and effect of A-site ionic size in bilayer nickelates

This study successfully stabilizes bilayer nickelates with smaller A-site ions through entropy engineering, revealing that the resulting chemical pressure enhances structural distortions and interlayer coupling, which projects a superconducting transition temperature exceeding 100 K.

The Gist

The Big Picture: Fixing a Wobbly Tower

Imagine a very special type of building block structure called a "bilayer nickelate." Scientists have recently discovered that one specific version of this structure, made mostly of Lanthanum (La), can become a superconductor (a material that conducts electricity with zero resistance) when you squeeze it incredibly hard with high pressure. This is a big deal because it could lead to super-fast electronics and powerful magnets.

However, there's a problem: this Lanthanum structure is like a wobbly tower of Jenga blocks. It is inherently unstable. If you try to build it, it often collapses or develops "stacking faults" (cracks where the layers don't line up perfectly). These cracks ruin the superconductivity, making it hard to study or use.

The Solution: The "High-Entropy" Recipe

To fix this wobbly tower, the researchers decided to try a new recipe. Instead of using just one type of block (Lanthanum), they decided to mix many different types of rare-earth blocks together at the same spot in the structure.

Think of it like baking a cake.

• The Old Way: You use only flour. If the flour is slightly bad, the whole cake fails.
• The New Way (High-Entropy): You mix flour, sugar, cornstarch, and oats all together in the same bowl. Even if one ingredient is a bit "off," the mixture of many different ingredients creates a chaotic but incredibly stable structure. In science, this chaos is called "entropy." The more mixed up the ingredients are, the harder it is for the structure to fall apart.

The team created two new "cakes":

1. ME-327: A "Medium-Entropy" mix with four different rare-earth elements.
2. HE-327: A "High-Entropy" mix with six different rare-earth elements.

What Happened? (The Results)

1. The Structure Became Stronger and Tighter
When they mixed these different elements in, something cool happened. The different-sized atoms acted like a chemical squeezer. Because some of the new atoms were smaller than the original Lanthanum, they pulled the whole crystal structure tighter together.

• The Analogy: Imagine a group of people holding hands in a circle. If you replace the tall people with shorter people, the circle shrinks and becomes tighter.
• The Result: The new High-Entropy (HE-327) sample was squeezed so tightly that it felt like it was under 4.3 billion Pascals of pressure (about 43,000 times atmospheric pressure), even though they didn't use a machine to squeeze it. They achieved this "chemical pressure" just by changing the ingredients.

2. The Layers Got Closer
Inside this nickelate structure, there are two layers of "active" material stacked on top of each other. For superconductivity to happen, these two layers need to talk to each other.

• The Analogy: Think of two people trying to whisper secrets to each other across a room. If they stand far apart, they can't hear. If they step closer, the whisper becomes clear.
• The Result: The new High-Entropy mix pulled these two layers significantly closer together. The scientists believe this "closer whisper" is the key to making the material superconduct better.

3. The "Traffic Jam" Effect
While the structure became more stable and tighter, the electricity didn't flow as easily at normal room pressure.

• The Analogy: Imagine a highway. The old Lanthanum road was smooth, but the new High-Entropy road is full of different types of speed bumps and potholes (caused by the mix of different atoms). Cars (electrons) get stuck and move slowly, acting like a semiconductor rather than a super-conductor.
• The Result: At normal pressure, the new material is a poor conductor. However, the scientists found that the "traffic jam" actually helped organize the magnetic spins in the material, raising a specific transition temperature (where the material changes its magnetic state) from 144 K to 168 K.

The Big Prediction: Superconductivity Over 100 K

The most exciting part of the paper is what the scientists predict will happen when they finally squeeze these new samples with a machine (physical pressure).

Because the High-Entropy mix already pulled the layers so close together (simulating high pressure), the scientists believe that when they apply actual high pressure, the superconducting temperature will skyrocket.

• The Prediction: They estimate that the High-Entropy sample could become a superconductor at temperatures above 100 Kelvin (which is about -173°C).
• Why it matters: This is much hotter than the original Lanthanum sample. In the world of superconductors, "hotter" means it's easier to cool down and use in real-world applications.

Summary

The researchers successfully built a new, stable version of a superconducting material by mixing six different elements together (High-Entropy). This mix naturally squeezed the material's internal structure tighter than ever before. While the material acts like a traffic jam at normal pressure, the scientists are confident that when they apply real pressure, it will become a superconductor at record-high temperatures, potentially exceeding 100 K. This proves that mixing many elements together is a powerful new tool for designing better superconductors.

Technical Summary

Technical Summary: Entropy Stabilization and A-site Ionic Size Effects in Bilayer Nickelates

Problem Statement
The discovery of high-temperature superconductivity in the bilayer Ruddlesden-Popper nickelate La$_3$Ni$_2$O$_{7-\delta}$ (La-327) under high pressure, and in thin films at ambient pressure, has opened new avenues in superconductivity research. However, the bulk La-327 phase possesses a narrow stability range, leading to inherent instability and the formation of stacking faults that can destroy superconductivity. While chemical substitutions (e.g., rare-earth doping at the A-site) have been used to improve phase purity and reduce stacking faults, the compositional space of stable bilayer nickelates remains limited. Furthermore, reducing the average A-site ionic radius ($\bar{r}_A$) is known to induce lattice contraction and enhance orthorhombic distortion, effects that mimic physical pressure and are theoretically predicted to enhance superconductivity. The challenge lies in stabilizing bilayer nickelates with significantly reduced $\bar{r}_A$ values (approaching those of Pr$^{3+}$ and Nd$^{3+}$) without compromising structural integrity.

Methodology
To address these challenges, the authors employed a high-entropy (HE) strategy, incorporating multiple rare-earth elements into the A-site to stabilize the 327 phase through configurational entropy. Two specific compositions were synthesized as polycrystalline samples:

1. Medium-Entropy (ME-327): La$_{1.2}$Pr$_{0.6}$Nd$_{0.6}$Sm$_{0.6}$Ni$_2$O$_{7-\delta}$
2. High-Entropy (HE-327): La$_{0.67}$Pr$_{0.67}$Nd$_{0.67}$Sm$_{0.33}$Eu$_{0.33}$Gd$_{0.33}$Ni$_2$O$_{7-\delta}$

The A-site occupations were designed to maximize configurational entropy while achieving a small average ionic radius ($\bar{r}_A$). The structural properties were characterized using powder X-ray diffraction (XRD) with Rietveld refinement, high-resolution transmission electron microscopy (HRTEM), and scanning electron microscopy with energy-dispersive X-ray spectroscopy (SEM-EDX). Thermogravimetric analysis (TGA) under a reducing atmosphere was performed to determine oxygen stoichiometry. Physical properties were investigated via electrical resistivity measurements at ambient pressure and magnetic susceptibility measurements. Preliminary high-pressure resistivity measurements were also conducted on the HE-327 sample.

Key Results

• Phase Stability and Crystallinity: Both ME-327 and HE-327 samples were successfully synthesized as single-phase materials with high crystallinity. XRD patterns showed sharp reflections comparable to unalloyed La-327, and HRTEM images confirmed the absence of stacking faults. HAADF imaging and EDS mapping demonstrated a homogeneous distribution of rare-earth elements at the microscopic level.
• Structural Evolution: The introduction of smaller A-site cations resulted in a systematic reduction of the average ionic radius ($\bar{r}_A$ = 1.181 Å for ME-327 and 1.164 Å for HE-327). This led to significant lattice contractions: the $a$-axis decreased by 0.9% and 1.3%, and the $c$-axis by 1.6% and 2.4% for ME- and HE-327, respectively, compared to La-327. Notably, the HE-327 sample exhibited a lattice contraction exceeding that of previously reported La$_{0.6}$Nd$_{2.4}$Ni$_2$O$_{7-\delta}$.
• Orthorhombic Distortion: Unlike physical pressure, which tends to drive the system toward a tetragonal structure at high pressures, the chemical pressure in these samples progressively increased orthorhombic distortion. The interlayer Ni–Ni distance ($d_\perp$) was reduced by 2.2% in HE-327 (from 4.03 Å to 3.94 Å), suggesting enhanced coupling between interlayer Ni-$d_{z^2}$ orbitals.
• Electronic and Magnetic Properties:
  • Resistivity: Both ME- and HE-327 samples exhibited semiconducting-like behavior across the measured temperature range, attributed to carrier localization caused by lattice distortions and chemical disorder.
  • Density Wave (DW) Transition: The density-wave transition temperature ($T_{DW}$) increased significantly with decreasing $\bar{r}_A$. While unalloyed La-327 shows a transition at $\approx$144 K, ME-327 and HE-327 exhibited $T_{DW}$ values of 159 K and 168 K, respectively. Magnetic susceptibility data confirmed these transitions, showing a decrease in residual susceptibility consistent with the resistivity anomalies.
  • Superconductivity: Preliminary high-pressure measurements on HE-327 revealed an anomaly in resistivity at 103 K under 31 GPa, potentially signaling a superconducting transition.

Significance and Claims
The paper claims that the high-entropy strategy successfully stabilizes bilayer nickelates with significantly reduced average A-site ionic radii, a compositional space previously difficult to access. The work demonstrates a clear correlation between $\bar{r}_A$, orthorhombicity, and physical properties. Specifically, the chemical pressure exerted by the HE-327 composition is estimated to be equivalent to approximately 4.3 GPa of physical pressure.

The authors posit that the reduction in $\bar{r}_A$ enhances interlayer superexchange coupling via the shortening of the Ni–Ni distance, a mechanism theoretically predicted to be crucial for superconducting pairing. Consequently, the study suggests that the superconducting transition temperature ($T_c$) under high pressure increases with chemical pressure, with extrapolations for HE-327 suggesting a potential $T_c$ exceeding 100 K. The paper concludes that the high-entropy approach provides a viable new avenue for developing superconducting bilayer nickelates, offering a pathway to optimize superconductivity through ionic size engineering and entropy stabilization. Future work is suggested to focus on growing single-crystalline and thin-film forms of these materials to explore intrinsic anisotropic properties.