Emergence of low-energy spin waves in superconducting electron-doped cuprates

Using neutron spectroscopy on electron-doped $\mathrm{Nd}_{1.85}\mathrm{Ce}_{0.15}\mathrm{CuO}_{4-\delta}$, the study reveals that defects in as-grown crystals suppress both superconductivity and low-energy spin waves by creating a large spin pseudogap, which is significantly reduced upon annealing to remove these defects.

The Gist

The Big Picture: The "Superconducting" Mystery

Imagine you have a material that can conduct electricity with zero resistance (superconductivity). This is the "holy grail" of energy technology because it means no energy is lost as heat. Scientists have known about these materials (cuprates) for decades, but they don't fully understand how they work.

One big clue is that these materials are deeply connected to magnetism. It's like a dance between electricity and magnetism. To understand the dance, the scientists in this paper decided to study a specific partner: a material called NCCO.

The Setup: The "Before and After" Experiment

The NCCO material has a weird quirk. When you first grow the crystal in a lab, it is not a superconductor; it's just a magnetic insulator. To make it superconduct, you have to put it through a special "reductive annealing" process (basically, heating it up in a specific gas to remove some oxygen atoms).

The scientists took one single crystal and cut it in half:

1. Half A (The "As-Grown"): Left alone. It's messy, has defects, and isn't superconducting.
2. Half B (The "Annealed"): Put through the heat treatment. It's cleaner, has fewer defects, and is a superconductor.

By comparing these two halves, they could see exactly what the "cleaning process" did to the material's internal behavior.

The Discovery: The "Spin Waves" and the "Traffic Jam"

Inside these materials, electrons have a property called "spin," which acts like a tiny magnet. When these spins wiggle together, they create waves called spin waves. Think of these like ripples in a pond.

The scientists used a giant machine (neutron spectroscopy) to watch these ripples. Here is what they found:

1. The "As-Grown" Sample (The Messy Room)
In the untreated sample, the "ripples" (spin waves) were weird. The low-energy, long, smooth ripples were missing.

• The Analogy: Imagine a highway where a massive construction zone has blocked off all the long lanes. Cars (the spin waves) can only drive in short, jerky bursts. They can't get up to speed.
• The Result: This created a "Spin Pseudogap." In physics terms, this means there was a "forbidden zone" where low-energy waves couldn't exist. The material was essentially "clogged" with defects that stopped the long waves from forming.

2. The "Annealed" Sample (The Cleaned Room)
When they treated the sample to make it superconducting, they removed the defects (the construction zone).

• The Analogy: The road is cleared! Now, the cars can drive in long, smooth, low-energy waves again. The "traffic jam" of the spin waves disappears.
• The Result: The "Spin Pseudogap" shrank significantly. The material could now support those long, smooth waves.

The Big Surprise: It's Not Just About Superconductivity

Usually, scientists thought that the "Spin Pseudogap" was a special feature created by superconductivity (like a badge of honor for the superconducting state).

But this paper says: "Wait a minute!"
They found that the non-superconducting sample actually had a bigger gap than the superconducting one.

• The Lesson: The big gap wasn't caused by superconductivity; it was caused by the defects (the mess). The superconducting state didn't create the gap; the process of cleaning the material to enable superconductivity simply removed the gap.

The Conclusion: Healing the Crystal

The paper argues that the "reductive annealing" process works like a healing treatment for the crystal.

• Before: The crystal is full of tiny holes and broken spots (defects). These act like fences, chopping the magnetic waves into tiny, high-energy pieces.
• After: The heat treatment "heals" the crystal, removing the fences. Now, the magnetic waves can stretch out long and smooth.

Why does this matter?
The scientists believe that these long, smooth, low-energy magnetic waves are actually the "glue" that holds the superconducting electrons together. By cleaning the crystal, they allowed these waves to form, which in turn allowed the material to become a superconductor.

Summary in One Sentence

The researchers discovered that the "magic" of superconductivity in this material isn't a mysterious new force, but simply the result of cleaning up the material's defects, which allows long, smooth magnetic waves to flow freely and carry electricity without resistance.

Technical Summary

1. Problem Statement

The mechanism of high-temperature superconductivity in cuprates remains one of the most significant unsolved problems in condensed matter physics. A central debate concerns the relationship between superconductivity and antiferromagnetism. While hole-doped (p-type) cuprates are well-studied, electron-doped (n-type) cuprates, such as Nd$_{2-x}$Ce$_x$CuO$_{4-\delta}$ (NCCO), exhibit distinct behaviors:

• Synthesis Complexity: Unlike p-type cuprates, n-type NCCO is antiferromagnetic (AFM) immediately after synthesis and only becomes superconducting after a reductive annealing process to remove oxygen.
• The Spin Pseudogap: Previous studies on annealed (superconducting) NCCO revealed a "spin pseudogap" (a suppression of low-energy magnetic fluctuations) opening below the critical temperature ($T_c$). However, the origin of this gap was unclear: is it a direct consequence of the superconducting state, or is it influenced by the structural defects inherent to the synthesis and annealing process?
• The Gap: There was a lack of direct comparison between the magnetic excitation spectra of the as-grown (non-superconducting, defect-rich) and annealed (superconducting, defect-reduced) states using the same crystal to eliminate sample variability.

2. Methodology

The authors employed a rigorous comparative approach using inelastic neutron scattering (INS) to probe magnetic excitations.

• Sample Preparation: A single, optimally doped ($x=0.15$) NCCO crystal was grown using the traveling-solvent floating-zone method. It was cut into two pieces:

  1. As-Grown (AG) Sample: Kept in its as-synthesized state (non-superconducting, AFM ground state).
  2. Annealed (SC) Sample: Subjected to reductive annealing (removing oxygen) to induce superconductivity ($T_c \approx 23$ K).
  • Significance: Using halves of the same crystal ensures identical chemical composition and doping levels, isolating the effects of the annealing process (defect removal) from doping variations.

• Experimental Techniques:

  • Neutron Spectroscopy: Measurements were performed at the ILL (IN20) and ANSTO (TAIPAN) facilities using thermal triple-axis spectrometers.
  • Measurements: Constant-energy $q$-scans and 3-point scans were conducted around the antiferromagnetic wave vector $\mathbf{Q} = (0.5, 0.5, 0)$ (tetragonal notation) at various energy transfers ($\hbar\omega = 2$ to $13$ meV) and temperatures (2 K to 55 K).
  • Data Normalization: Intensities were normalized using acoustic phonon scans to allow quantitative comparison between the two samples.
  • Statistical Analysis: Wilks' theorem was used to rigorously determine the statistical significance of magnetic peaks versus background noise.

3. Key Contributions

• Direct Comparison: The study provides the first direct, side-by-side comparison of the low-energy spin dynamics in as-grown vs. annealed NCCO from the same crystal growth.
• Re-evaluation of the Spin Pseudogap: The authors challenge the conventional view that the spin pseudogap is solely a signature of superconductivity. They demonstrate that a larger pseudogap exists in the non-superconducting as-grown sample.
• Defect-Driven Fragmentation Model: The paper proposes a physical model linking structural defects (introduced during synthesis) to the suppression of long-wavelength spin waves, effectively "fragmenting" the magnetic lattice.

4. Key Results

A. Magnetic Response and the Spin Pseudogap

• Annealed (Superconducting) Sample:
  • Exhibits a small spin pseudogap of $2.0 \pm 0.6$ meV at 2 K.
  • The gap opens below $T_c$, consistent with previous literature suggesting a link to superconductivity.
  • Low-energy spectral weight is recovered compared to the as-grown state.
• As-Grown (Non-Superconducting) Sample:
  • Exhibits a significantly larger spin pseudogap, increasing from $2.8 \pm 0.1$ meV at 27 K to $10.0 \pm 0.5$ meV at 2 K.
  • The magnetic signal at low energies (below ~10 meV) is almost entirely suppressed at low temperatures, vanishing at 2 K.
  • Crucial Finding: The presence of a massive pseudogap in the non-superconducting state proves that the gap is not exclusively a superconducting phenomenon.

B. Spectral Weight Redistribution

• Upon annealing, there is a massive shift of spectral weight from high energies to low energies.
• The annealing process "heals" the crystal, allowing low-energy spin fluctuations to emerge.
• In the as-grown sample, the defects act as scattering centers that suppress long-wavelength spin waves, creating a high-energy cutoff (the large pseudogap).

C. Quantitative Modeling

• The authors model the system as a 2D analogue of a fragmented spin chain (similar to SrCuO$_2$ with impurities).
• Defect Scattering: Defects in the as-grown sample act as boundaries, limiting the maximum wavelength ($\lambda_{max}$) of allowed spin waves.
• Patch Size Calculation: Using linear spin wave theory, the authors estimate the effective size of the antiferromagnetic "patches":
  • As-Grown: Patch size $\approx$ 40 nm (corresponding to the 10 meV gap).
  • Annealed: Patch size $\approx$ 130 nm (corresponding to the 3 meV gap).
• This confirms that annealing removes defects, allowing larger magnetic domains to form and supporting lower-energy spin excitations.

5. Significance and Implications

• Decoupling Defects from Superconductivity: The study clarifies that the "large" spin pseudogap observed in as-grown samples is an artifact of structural disorder (defects), not a precursor to superconductivity.
• Role of Low-Energy Fluctuations: The emergence of superconductivity correlates with the recovery of low-energy spin fluctuations (the closing of the large defect-induced gap). This supports theories (e.g., by Scalapino) that spin fluctuations mediate the pairing mechanism in high-$T_c$ superconductors.
• Mechanism of Annealing: The results suggest that reductive annealing does not just change carrier density but fundamentally "repairs" the CuO$_2$ planes by removing oxygen/copper defects, thereby restoring long-range magnetic coherence necessary for superconductivity.
• Resolution of Contradictions: The findings reconcile previous conflicting data where annealed samples showed small gaps and as-grown samples showed large gaps, attributing the difference to sample quality rather than intrinsic electronic phase differences.

In conclusion, the paper establishes that low-energy spin waves are essential for superconductivity in electron-doped cuprates and that the suppression of these waves in as-grown samples is caused by structural defects, which are subsequently removed by reductive annealing.