Paramagnetically driven superconducting re-entrance in Eu-doped infinite layer nickelates

This study demonstrates that field-induced re-entrant superconductivity in Eu-doped NdNiO2 arises from a delicate balance between competing Eu2+ and Nd3+ magnetic ions, whose influence on magneto-transport is activated only upon magnetic polarization.

The Gist

Imagine a material that acts like a superhighway for electricity, allowing current to flow with zero resistance. This is superconductivity. Scientists have been hunting for new materials that can do this, especially ones that work at higher temperatures, for decades. Recently, they found a promising new family of materials called nickelates (made of nickel, oxygen, and rare earth metals).

This paper is about a specific, strange discovery made in a nickelate film doped with two types of rare earth metals: Europium (Eu) and Neodymium (Nd).

Here is the story of what they found, explained simply:

1. The "Goldilocks" Problem

Usually, if you put a magnet near a superconductor, it kills the superconductivity. It's like trying to run a marathon while someone is constantly tripping you; the more the magnet pushes, the harder it is for the electricity to flow smoothly.

However, in this specific film, the scientists found something weird:

• No Magnet: The electricity flows perfectly (Superconducting).
• Weak Magnet: The magnet trips the runners, and the flow stops (Normal, resistive state).
• Strong Magnet: Suddenly, the runners get back on their feet, and the electricity flows perfectly again! (Superconducting returns).

This is called "re-entrant superconductivity." It's like a movie where the hero gets knocked down, but when the villain pushes even harder, the hero suddenly stands up stronger than before.

2. The Cast of Characters: Two Rival Teams

Why does this happen? The paper explains that the film contains two different "teams" of magnetic ions (tiny magnets inside the atoms):

• Team Eu (Europium): They are like a group of rowdy fans who get excited by a magnetic field and start pushing against the superconducting flow.
• Team Nd (Neodymium): They are a different group of fans who also react to the magnetic field, but they push in the opposite direction.

The Analogy:
Imagine a tug-of-war game happening inside the wire.

• At low magnetic fields, the "Eu team" starts pulling hard, disrupting the flow and stopping the superconductivity.
• As you increase the magnetic field, the "Nd team" wakes up and starts pulling back just as hard.
• At a medium-to-high field, the two teams pull with equal force. They cancel each other out! Because the internal "tug-of-war" is balanced, the external magnetic field stops bothering the electricity, and the superconductivity returns.

The scientists call this a "Jaccarino-Peter effect," but with a twist. Usually, this effect involves just one type of magnetic ion canceling out an external field. Here, it's a delicate balance between two different types of ions working together to neutralize the chaos.

3. How They Proved It

The researchers didn't just guess this; they measured it carefully:

• The "Hall Effect" Test: They measured how the electrons moved sideways when a magnetic field was applied. This is like watching how a crowd of people sways when a strong wind blows. They found that the swaying behavior perfectly matched a mathematical model where the Eu and Nd ions were pulling in opposite directions and eventually canceling each other out.
• The "Critical Field" Map: They mapped out exactly how much magnetic field was needed to kill the superconductivity and how much was needed to bring it back. Their computer models, which accounted for the "tug-of-war" between the two ions, matched their experimental data perfectly.

4. The Catch

This magic trick only works under specific conditions:

• The Temperature: It has to be very cold. If it's too warm, the magnetic ions are too jittery to line up and cancel each other out properly.
• The Material: They found that films grown on one type of crystal (LSAT) showed this superconductivity, while films grown on a different crystal (NdGaO3) did not become superconducting at all. However, the non-superconducting films were actually very useful because they allowed the scientists to study the magnetic ions without the "noise" of superconductivity getting in the way.

Summary

In short, this paper describes a material where two different magnetic elements act like a self-correcting system. When a magnetic field is applied, one element tries to stop the superconductivity, but a second element kicks in to neutralize that stoppage. This creates a "sweet spot" where the superconductivity comes back to life, defying the usual rule that magnets always destroy superconductors.

The authors emphasize that this is a fundamental discovery about how magnetism and superconductivity can dance together in these new nickelate materials, rather than a technology ready for immediate use.

Technical Summary

Technical Summary: Paramagnetically Driven Superconducting Re-entrance in Eu-doped Infinite Layer Nickelates

Problem and Context
Since the 2019 discovery of superconductivity in Sr-doped infinite-layer nickelates (NdNiO$_2$), research has focused on identifying the pairing mechanism, electronic structure, and similarities to high-$T_c$ cuprates. While significant efforts have aimed at increasing the critical temperature ($T_c$) and characterizing charge ordering, the specific role of magnetic rare-earth ions within the superconducting state remains a critical open question. Previous reports have suggested that magnetic moments can modulate superconductivity, notably through the Jaccarino-Peter effect, where a negative exchange interaction between rare-earth moments and conduction electrons can, under specific conditions, compensate for an external magnetic field and induce superconductivity. However, the interplay between multiple magnetic species (specifically Eu$^{2+}$ and Nd$^{3+}$) in infinite-layer nickelates had not been fully explored. This study investigates the magnetotransport properties of Eu-doped NdNiO$_2$ to understand how these competing magnetic ions influence the superconducting phase.

Methodology
The authors synthesized optimally doped Nd$_{1-x}$Eu$_x$NiO$_2$ thin films (with $x=0.3$) using off-axis RF magnetron sputtering on two distinct substrates: LSAT ((La$_{0.3}$Sr$_{0.7}$)(Al$_{0.65}$Ta$_{0.35}$)O$_3$) and NdGaO$_3$. The films were grown as perovskite Nd$_{0.7}$Eu$_{0.3}$NiO$_3$ and subsequently reduced to the infinite-layer phase via a topotactic reaction induced by a metallic aluminum capping layer. This reduction process was optimized by increasing the Al deposition rate and avoiding post-annealing.

• Structural Characterization: High-resolution X-ray diffraction (XRD) and scanning transmission electron microscopy (STEM) confirmed high crystalline quality and sharp interfaces, with an out-of-plane lattice constant of 3.329 Å.
• Transport Measurements: Resistivity was measured as a function of temperature (2–20 K) under magnetic fields ranging from 0 to 12 T (Geneva) and up to 30 T (LNCMI-EMFL, Grenoble) in both perpendicular and parallel configurations. Current-voltage ($I-V$) characteristics were also recorded.
• Hall Effect Measurements: To isolate the magnetic contributions of the rare-earth ions without the masking effect of superconductivity, Hall resistance ($R_{xy}$) was measured on non-superconducting films grown on NdGaO$_3$ and in the normal state of superconducting films on LSAT.
• Spectroscopy: X-ray magnetic circular dichroism (XMCD) and X-ray absorption spectroscopy (XAS) were performed at the ALBA Synchrotron to directly measure the spin polarization of Eu and Nd ions.
• Modeling: The authors developed a theoretical model based on Gorkov's pair-breaking theory and a modified BCS gap equation. This model incorporates the total effective magnetic field ($B_{tot}$), defined as the sum of the external field and the exchange fields generated by the polarized Eu$^{2+}$ and Nd$^{3+}$ moments. The Hall effect data was fitted using a two-component magnetic model based on Brillouin functions for the two ion species.

Key Results

1. Field-Induced Re-entrant Superconductivity: In optimally doped films on LSAT, the application of a magnetic field initially suppresses superconductivity, shifting the transition to lower temperatures. However, above a critical field of approximately 3.5 T, the superconducting transition sharpens and shifts back to higher temperatures. This "re-entrant" behavior persists up to at least 30 T, creating a phase diagram with two distinct superconducting regions separated by a dissipative state.
2. Role of Rare-Earth Ions: The re-entrant behavior is specific to samples containing both Eu$^{2+}$ and Nd$^{3+}$. Films grown on NdGaO$_3$ with the same composition did not exhibit superconductivity but showed strong non-linearities in the Hall effect, attributed to the magnetic moments.
3. Hall Effect and Spin Polarization: The extraordinary Hall effect data revealed pronounced non-linearities at low temperatures. A model treating the Hall response as a weighted sum of the projected spins of Eu$^{2+}$ and Nd$^{3+}$ successfully reproduced the experimental data. The analysis indicates that as the external field increases, the paramagnetic contributions of the two ion species partially cancel each other out.
4. Microscopic Mechanism: Theoretical modeling of the upper critical field ($B_{c2}$) demonstrates that the re-entrance arises from a delicate balance between the opposing influences of Eu$^{2+}$ and Nd$^{3+}$. At low fields, the moments are disordered. At intermediate fields (~3 T), Eu$^{2+}$ polarizes, creating an internal exchange field that breaks Cooper pairs (dissipative state). At higher fields, Nd$^{3+}$ spins align, compensating the Eu$^{2+}$ contribution and reducing the total effective field acting on the conduction electrons, thereby restoring superconductivity.
5. Critical Current: The critical current density ($J_c$) was found to be high ($1-2 \times 10^5$ A/cm$^2$) and recovered at high fields (12 T), consistent with the bulk-like nature of the re-entrant state.

Significance and Claims
The paper claims to identify a unique mechanism for field-induced superconductivity in infinite-layer nickelates driven by the interplay of two distinct magnetic rare-earth species. Unlike the original Jaccarino-Peter effect, which relies on the compensation between an external field and a single magnetic species, this study demonstrates a "Jaccarino-Peter-like" effect where the compensation arises from the opposing spin polarizations of Eu$^{2+}$ and Nd$^{3+}$.

The authors assert that this phenomenon is observable only in samples with relatively low $T_c$ (around 9.5 K), where the temperature is sufficiently low to allow for strong paramagnetic responses of the rare-earth moments. The work provides quantitative evidence linking the extraordinary Hall effect and the re-entrant superconducting phase to the specific magnetic compensation mechanism, highlighting the complex interplay between local magnetism and superconductivity in these materials. The findings suggest that the magnetic environment created by rare-earth doping is a critical factor in determining the stability and behavior of the superconducting state in nickelates.