Re-entrant unconventional superconductivity induced by rare-earth substitution in Nd1-xEuxNiO2 thin films

This study demonstrates that substituting Eu in Nd1-xEuxNiO2 thin films induces re-entrant unconventional superconductivity characterized by a significantly enhanced superconducting gap and magnetic-field-enhanced behavior, indicating a transition to a strong-coupling pairing regime driven by interactions between magnetic Eu ions and the Ni dx2-y2 orbitals.

The Gist

The Big Picture: Finding a New Way to Make Superconductors "Stronger"

Imagine you are trying to build a superhighway where cars (electrons) can drive without any friction or traffic jams. This is what superconductivity is: electricity flowing with zero resistance. Usually, this only happens at extremely cold temperatures.

Scientists have been trying to make these "super-highways" work at higher temperatures (closer to room temperature) because that would revolutionize technology (like lossless power grids or super-fast computers).

For a long time, the best super-highways were made of Copper (called Cuprates). Recently, scientists found a new family of materials made of Nickel (called Nickelates) that also do this. However, the Nickel ones seemed "weak" compared to the Copper ones. They didn't have the strong "glue" needed to hold the electron pairs together tightly.

This paper is about a breakthrough: The researchers found a way to "supercharge" the Nickel superconductors by swapping out some of the atoms, making them behave like the strong Copper ones.

---

The Analogy: The "Magnetic Shield" (The Jaccarino-Peter Effect)

To understand the main discovery, imagine a superconductor is a delicate dance floor where couples (electron pairs) are dancing.

1. The Problem (Magnetic Fields): Usually, if you bring a giant magnet near the dance floor, the magnetic force pulls the dancers apart, stopping the dance. This is called the "Pauli Limit." It's a hard ceiling on how strong a magnetic field a normal superconductor can survive.
2. The Twist in this Paper: The researchers added a special ingredient: Europium (Eu) atoms. These atoms act like tiny, local magnets.
3. The Magic Trick: When a big external magnet tries to break up the dance, these tiny Europium magnets inside the material actually push back against the external magnet.
   • Think of it like this: Imagine you are trying to push a door open (the external magnet). But inside the room, there are people (the Europium atoms) pushing the door closed from the other side. If they push hard enough, they cancel out your force.
   • Because of this "canceling out," the dancers (electrons) feel like there is no magnet at all, so they keep dancing even when the external magnet is incredibly strong.

This is called the Jaccarino-Peter effect. It's rare to see this happen in a thin film, and it allowed these materials to survive magnetic fields far stronger than physics usually allows.

---

The "Re-entrant" Surprise: Getting Stronger as You Push Harder

Usually, if you turn up the magnetic field, the superconductivity gets weaker and dies. But in these new films, something weird happened:

• The "Re-entrant" Behavior: As they turned up the magnetic field, the superconductivity didn't just fade away. It actually got stronger for a while before fading.
• The Analogy: Imagine a rubber band. Usually, if you pull it too hard, it snaps. But imagine a rubber band that, when you pull it, gets tighter and stronger for a moment before it finally snaps. That is what happened here. The magnetic field actually helped stabilize the superconducting state for a specific range.

---

The "Glue" is Stronger Than We Thought

Scientists measure how "strong" a superconductor is by looking at the Gap.

• The Analogy: Think of the "Gap" as the strength of the glue holding the electron couples together.
  • Weak Glue (Old Nickelates): The glue was weak. If you shook the system (with heat or magnetism), the couples fell apart easily.
  • Strong Glue (New Nickelates with Europium): The researchers found that by swapping in Europium, the glue became twice as strong.
  • The ratio of the "Glue Strength" to the "Temperature" is now similar to the famous Copper superconductors. This proves that these Nickel materials are no longer "weak" superconductors; they are strong-coupling superconductors.

Why Did They Do This? (The Recipe Change)

The researchers took a standard Nickel superconductor (made of Neodymium, Nickel, and Oxygen) and swapped some of the Neodymium atoms for Europium atoms.

• Why Europium? Europium is a "magnetic" atom. Neodymium is not very magnetic in this context.
• The Result: By adding the magnetic Europium, they didn't just add charge; they added a magnetic interaction that:
  1. Created the "shield" against external magnets.
  2. Tightened the glue between electrons.
  3. Changed the physical structure slightly (making the layers closer together), which also helped the glue.

The Takeaway

This paper is a big deal because it shows that we can engineer better superconductors by playing with the magnetic properties of the atoms we use.

Instead of just hoping to find a material that works, scientists can now say: "If we want a stronger superconductor, let's add some magnetic atoms to create a shield and strengthen the glue." This opens a new door to designing materials that could one day carry electricity without any loss, even at higher temperatures.

In short: They found a way to make a Nickel-based superconductor so tough that it can withstand massive magnetic fields and has a very strong internal "glue," all by adding a little bit of magnetic Europium to the mix.

Technical Summary

1. Problem Statement

While infinite-layer nickelates (RENiO$_2$) have emerged as a new family of high-temperature superconductors, their pairing mechanism remains debated. Unlike cuprates, which are widely accepted as strong-coupling superconductors, existing nickelate data (specifically Sr-doped NdNiO$_2$) suggests weak-coupling behavior with small superconducting gaps ($2\Delta/k_B T_c \approx 3-3.4$). Furthermore, the role of the rare-earth (RE) spacer layer in modifying electronic structure and magnetic interactions is not fully understood. The authors aim to investigate whether substituting the RE layer with magnetic ions (Europium) can induce strong-coupling superconductivity and alter the upper critical magnetic field ($H_{c2}$) behavior, potentially revealing new mechanisms for high-$T_c$ superconductivity.

2. Methodology

The study employs a multi-faceted experimental and theoretical approach:

• Sample Synthesis: Nd$_{1-x}$Eu$_x$NiO$_2$ (NENO) thin films with Eu concentrations $x = 0.20, 0.22, 0.35$ were grown via Molecular Beam Epitaxy (MBE) on LSAT substrates with an Al$_2$O$_3$ capping layer.
• High-Field Transport Measurements: Magnetoresistance (MR) was measured up to 41 T (DC fields) and 60 T (pulsed fields) at the National High Magnetic Field Laboratory (NHMFL). Measurements were taken for magnetic fields oriented both parallel to the $c$-axis ($H \parallel c$) and parallel to the $ab$-plane ($H \parallel ab$).
• Optical Spectroscopy: Fourier Transform Infrared (FTIR) spectroscopy was used to measure reflectivity spectra in the far-infrared range (10–800 cm$^{-1}$) to determine the superconducting energy gap ($2\Delta$).
• Theoretical Modeling:
  • Density Functional Theory (DFT): Calculations using the SCAN meta-GGA functional were performed to estimate exchange coupling coefficients ($J_{ik}$) between Eu 4f moments and Ni orbitals.
  • Phenomenological Modeling: The temperature dependence of $H_{c2}(T)$ was modeled using Ginzburg-Landau (G-L) theory and the Fischer formula (based on Werthamer–Helfand–Hohenberg theory) to account for the Jaccarino-Peter effect.

3. Key Contributions

• Discovery of Re-entrant Superconductivity: The paper reports the first observation of re-entrant superconductivity (where superconductivity is suppressed at low fields but restored/enhanced at intermediate fields) in nickelates.
• Identification of the Jaccarino-Peter (J-P) Mechanism: The authors attribute the anomalous magnetic field behavior to the Jaccarino-Peter effect, where the antiferromagnetic exchange field from polarized Eu$^{2+}$ ions compensates the external magnetic field acting on the superconducting electrons.
• Evidence for Strong-Coupling Superconductivity: Through infrared spectroscopy, the study provides direct evidence of a large superconducting gap, establishing NENO as a strong-coupling system, contrasting sharply with the weak-coupling behavior of Sr-doped NdNiO$_2$.
• Orbital Selectivity: DFT calculations identify the Ni $3d_{x^2-y^2}$ orbital as the primary contributor to superconductivity, which is strongly coupled to Eu magnetic moments, while other orbitals ($3d_{z^2}$, $4p_z$) are less relevant or suppressed.

4. Key Results

• Magnetic-Field-Enhanced Superconductivity:
  • Resistance measurements show a non-monotonic behavior: resistance increases at low fields, reaches a maximum, and then drops to zero resistance at $\sim$20 T before rising again at higher fields.
  • This indicates a "re-entrant" phase where superconductivity is stabilized by the magnetic field.
  • The upper critical field $H_{c2}$ significantly violates the Pauli paramagnetic limit ($H_{c2}^P \approx 1.86 T_c$) for both field orientations, with $H_{c2}$ reaching up to 60 T.
• Jaccarino-Peter Effect Validation:
  • DFT calculations reveal a large antiferromagnetic exchange field ($H_J \approx 21.3$ T) induced by Eu 4f moments on the Ni $3d_{x^2-y^2}$ orbital.
  • This exchange field opposes the external field, effectively reducing the total field on the carriers ($H_T = H + H_J$), allowing superconductivity to persist at fields far exceeding the intrinsic Pauli limit.
  • The extracted exchange field from G-L fitting ($H_{J0} \approx 17-23$ T) matches the DFT prediction.
• Superconducting Gap and Coupling Strength:
  • FTIR spectroscopy reveals a superconducting gap of $2\Delta \approx 75$ cm$^{-1}$ (9.3 meV).
  • The gap-to-$T_c$ ratio is calculated as $2\Delta/k_B T_c \approx 5-6$, which is significantly higher than the BCS weak-coupling limit (3.52) and comparable to strongly coupled hole-doped cuprates.
  • The data fits a dirty-limit nodal $d$-wave pairing model, suggesting the presence of uncondensed quasiparticles.
• Doping Dependence: The enhancement of pairing strength and the violation of the Pauli limit are specific to Eu substitution; Nd and Sr dopants show negligible exchange fields on Ni orbitals.

5. Significance

• Paradigm Shift in Nickelates: This work challenges the prevailing view that nickelates are weak-coupling superconductors. It demonstrates that chemical substitution in the spacer layer can tune the system into a strong-coupling regime.
• Magnetic Control of Superconductivity: The study establishes a rare example of the Jaccarino-Peter effect in a thin-film superconductor, proving that local magnetic moments can be engineered to enhance superconductivity rather than suppress it.
• Pathway to Higher $T_c$: By linking the Eu magnetic moment, exchange coupling, and the reduction of the NiO$_2$ plane separation (due to smaller ionic radius), the authors propose a viable strategy to engineer higher critical temperatures in infinite-layer nickelates.
• Insight into Unconventional Mechanisms: The similarity in gap ratios and strong-coupling behavior between Eu-doped nickelates and cuprates suggests a potential commonality in the physics of high-$T_c$ layered oxides, driven by strong electron-electron interactions and magnetic fluctuations.