Field re-entrant superconductivity in Eu-doped infinite-layer nickelates

The study demonstrates that Eu-doped infinite-layer nickelates exhibit a magnetic-field-induced re-entrant superconducting phase in the over-doped regime, providing a new platform for exploring the interplay between magnetism and high-temperature superconductivity.

The Gist

The "Magic Magnet" Superconductor: A Simple Explanation

Imagine you are trying to push a heavy shopping cart through a thick, muddy field. The more you push, the harder it gets, and eventually, you get stuck. This is how most materials behave when you apply a strong magnetic field: the magnetism acts like "mud," creating resistance and eventually destroying the material's ability to conduct electricity perfectly.

In the world of physics, there is a special state called superconductivity. When a material is a superconductor, it’s like the shopping cart is suddenly gliding on a perfectly smooth, frictionless ice rink. Electricity flows through it with zero effort. However, strong magnetic fields are usually the "enemy" of this ice rink—they act like a sudden heatwave that melts the ice, turning it back into messy mud (resistance).

This paper describes a scientific discovery where, instead of the ice melting, the magnetic field actually re-freezes the ice!

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The Discovery: The "Double-Dip" Superconductor

The researchers studied a new family of materials called nickelates (specifically, ones doped with an element called Europium). They discovered something bizarre:

1. The First Glide: At low magnetic fields, the material is a superconductor (the ice rink is smooth).
2. The Muddy Middle: As they crank up the magnetic field, the "ice" melts. The material becomes a normal, resistive metal (the shopping cart is stuck in the mud).
3. The Re-entrant Glide: But here is the magic part—if they keep increasing the magnetic field to extreme levels, the material suddenly becomes a superconductor again! It’s as if the magnetic field, which was supposed to melt the ice, suddenly turned into a super-freezer and created a brand-new, even tougher ice rink.

This phenomenon is called "re-entrant superconductivity."

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How does it work? (The "Counter-Wind" Analogy)

How can a magnetic field—something that usually destroys superconductivity—actually help it?

The scientists believe it’s due to a "tug-of-war" happening inside the material.

• The External Field: This is like a massive, howling wind blowing against your shopping cart, trying to knock it over.
• The Internal Field: The Europium atoms inside the material act like a group of people standing behind the cart, blowing a wind in the exact opposite direction.

At a certain strength, the "internal wind" and the "external wind" cancel each other out. For a brief moment, the air becomes perfectly still, the "mud" disappears, and the material can glide effortlessly as a superconductor again.

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Why is this a big deal?

1. It’s Unusually Tough: In other materials where this has happened, the "re-frozen ice" is very fragile and only works at specific angles. In these nickelates, the effect is incredibly robust—it works even if you tilt the magnetic field significantly.
2. A New Playground: This discovery tells scientists that nickelates are a "fertile platform." It’s like finding a new type of soil where we can grow exotic quantum plants that we couldn't grow anywhere else.
3. The Mystery of the "Extra Boost": The researchers noticed that at very high doping levels, the effect is even stronger than their math predicted. This suggests there might be an even deeper, more mysterious "engine" driving this superconductivity—perhaps a type of "spin-triplet" pairing, which is a holy grail in quantum physics.

Summary in one sentence:

Scientists found a material that, when hit with an intense magnetic field that should destroy its efficiency, actually "reboots" itself into a state of perfect electrical flow.

Technical Summary

Technical Summary: Field Re-entrant Superconductivity in Eu-doped Infinite-Layer Nickelates

1. Problem and Motivation

The interplay between magnetism and superconductivity is a central theme in condensed matter physics. While magnetic fields typically destroy superconductivity via orbital and paramagnetic effects, certain "exotic" quantum phases allow for the coexistence or mutual enhancement of these orders. Phenomena such as field-induced and re-entrant superconductivity (where superconductivity disappears at low fields but reappears at much higher fields) have been documented in heavy-fermion systems (e.g., $UTe_2$, $URhGe$) and organic conductors.

However, such magnetism-enhanced superconductivity has remained elusive in high-temperature superconductors like cuprates. The infinite-layer nickelates represent a new class of unconventional superconductors that resemble cuprates but possess unique rare-earth magnetic properties. The researchers sought to investigate how the introduction of magnetic $Eu^{2+}$ ions (carrying large $S = 7/2$ moments) into the nickelate structure affects the superconducting state, specifically looking for evidence of magnetically driven high-field superconductivity.

2. Methodology

• Material Synthesis: The team synthesized epitaxial thin films of $Sm_{0.95-x}Ca_{0.05}Eu_xNiO_2$ (SCEx) on LSAT substrates using Pulsed Laser Deposition (PLD). A small amount of Ca doping was used to facilitate the topotactic reduction from the perovskite phase to the infinite-layer phase.
• Doping Range: They explored a wide range of Eu concentrations ($x \approx 0$ to $0.80$).
• Characterization:
  • Structural: X-ray diffraction (XRD) and X-ray reflectivity (XRR) were used to confirm crystallinity and film thickness.
  • Electronic/Magnetic: X-ray absorption spectroscopy (XAS) was employed to determine the oxidation state of Eu ($Eu^{2+}/Eu^{3+}$ ratio).
• Transport Measurements:
  • Low-to-Mid Field: Standard four-probe resistivity ($\rho(T)$) and Hall effect ($\rho_{yx}(H)$) measurements were conducted down to 2 K and up to 14 T.
  • Ultra-High Field: Magnetoresistance (MR) was measured in extreme magnetic fields (up to 60 T) using pulsed magnets and high-field facilities (CHMFL and WHMFC).
  • Angular Dependence: Measurements were taken at varying angles ($\theta$) between the magnetic field and the $c$-axis to probe the anisotropy of the superconducting state.
  • Diamagnetism: Two-coil mutual inductance experiments were used to confirm the superconducting nature of the high-field phase via diamagnetic screening.
• Theoretical Modeling: The upper critical field $H_{c2}(T)$ was modeled using the Fisher extension of the Werthamer-Helfand-Hohenberg (WHH) theory, incorporating orbital/Pauli pair-breaking, spin-orbit scattering, and the Jaccarino-Peter (J-P) compensation effect.

3. Key Results

• Superconducting Dome: The study identified a robust superconducting "dome" in the doping range $0.08 < x < 0.45$, with a maximum $T_c$ of $\sim 32$ K.
• Discovery of Re-entrant Superconductivity: In the over-doped regime ($x \approx 0.32$ to $0.40$), the researchers observed a "superconducting-normal-superconducting" transition. As the field increases, the initial superconductivity is suppressed, but a new superconducting phase emerges at high fields (e.g., appearing at $\mu_0H \geq 6.23$ T for $x=0.34$).
• Unprecedented Robustness:
  • Angular Robustness: Unlike organic conductors or heavy-fermion systems where re-entrance is highly sensitive to field orientation, this phase persists across an exceptionally broad angular range (up to $70^\circ$–$90^\circ$).
  • Field Robustness: The re-entrant state remains stable up to very high fields (exceeding 30 T).
• Mechanistic Insights:
  • Jaccarino-Peter (J-P) Effect: For intermediate doping ($x \approx 0.33$–$0.38$), the re-entrance is qualitatively explained by the J-P mechanism, where the internal exchange field ($H_J$) from $Eu^{2+}$ moments partially cancels the external applied field ($H_{ext}$), reducing the effective field acting on Cooper pairs.
  • Beyond J-P Effect: At the highest doping levels ($x = 0.40$), the data deviates significantly from the J-P model, suggesting that the high-field phase might be driven by magnetically mediated superconducting pairing (potentially spin-triplet pairing), similar to heavy-fermion superconductors.
• Anomalous Transport: The over-doped regime exhibited nonlinear Hall transport and hysteretic magnetoresistance, signaling strong magnetic correlations or time-reversal-symmetry breaking.

4. Significance

This work is significant for several reasons:

1. New Materials Platform: It establishes infinite-layer nickelates as a unique platform that bridges the physics of high-$T_c$ cuprates and heavy-fermion superconductors.
2. Engineering Quantum Phases: It demonstrates that rare-earth magnetism can be used as a "tuning knob" to engineer exotic, high-field superconducting states in strongly correlated oxides.
3. Fundamental Physics: The discovery of a re-entrant state that is both high-temperature and angularly robust challenges existing models of field-induced superconductivity and provides a new playground for studying spin-triplet pairing and magnetically mediated superconductivity.