${H}$-linear magnetoresistance in the ${T^2}$ resistivity regime of overdoped infinite-layer nickelate La$_{1-x}$Sr$_{x}$NiO$_2$

This study reveals that overdoped infinite-layer nickelate La$_{1-x}$Sr$_{x}$NiO$_2$ thin films exhibit a coexistence of $H$-linear magnetoresistance and $T^2$ resistivity in the normal state, challenging conventional transport models and offering new insights into the ground state of these unconventional superconductors.

The Gist

The Big Picture: A Traffic Jam in a Strange City

Imagine electricity flowing through a metal wire like cars driving through a city.

• Normal Metals (Fermi Liquids): In a normal city, traffic flows smoothly. If it rains (heat), cars slow down a bit. If there's a police car with sirens (magnetic field), they have to take a wider turn, slowing down even more. The rules of this traffic are predictable and follow standard laws (like "Kohler's Rule").
• Strange Metals: In some exotic materials, the traffic behaves weirdly. The cars seem to ignore the usual rules. They might slow down in a way that doesn't make sense, or they might get stuck in a gridlock that changes depending on how hard you push them.

This paper is about a specific type of "city" made of Nickelate (a material containing nickel and oxygen) that scientists are studying because it can become a superconductor (a material where electricity flows with zero resistance, like a car driving on a frictionless highway).

The Mystery: Two Different Personalities

Scientists have been trying to figure out what happens inside these Nickelate cities when they are "overdoped" (meaning they have extra electrical carriers, like adding more cars to the road).

Usually, when a material is a "strange metal," it shows two weird signs:

1. Temperature: As it gets colder, the traffic resistance drops in a straight line (Linear).
2. Magnetic Field: When you apply a magnetic field, the resistance goes up in a straight line (Linear).

The researchers in this paper wanted to see if their Nickelate samples were "Strange Metals" or "Normal Metals." They tested three different samples with slightly different amounts of doping.

The Experiment: The Ultimate Traffic Test

To see how the cars behave, the scientists did two things:

1. The Heat Test: They cooled the samples down to near absolute zero (very cold) to see how the traffic moved without a magnetic field.
2. The Siren Test: They used a massive, pulsed magnetic field (up to 62 Tesla—imagine a magnetic field strong enough to lift a small car) to see how the traffic reacted to a huge "police presence."

The Surprising Results: A Split Personality

The results were confusing but fascinating. The material didn't act like just one thing; it acted like two different things at the same time.

1. The "Normal" Side (The Temperature Test)
When they looked at how the resistance changed with temperature, the material acted like a perfectly normal, well-behaved city.

• The Analogy: As the temperature dropped, the traffic resistance slowed down exactly like a standard car engine cooling down. It followed a "square law" (if you double the coldness, the resistance drops by four).
• The Verdict: This is the signature of a Fermi Liquid—a normal, predictable metal.

2. The "Strange" Side (The Magnetic Field Test)
However, when they turned on the giant magnetic field, the material suddenly acted like a Strange Metal.

• The Analogy: When the "police sirens" (magnetic field) turned on, the cars didn't just slow down a little; they slowed down in a straight line, regardless of how fast they were going. They ignored the standard traffic laws (Kohler's Rule) that normal metals follow.
• The Verdict: This is the signature of a Strange Metal, a state usually associated with quantum weirdness and high-temperature superconductivity.

Why This Matters: The "Split-Brain" Discovery

The most exciting part of this paper is that they found both behaviors in the same material at the same time.

• Think of it like a chameleon: Most materials are either a "normal lizard" or a "color-changing chameleon." This Nickelate material is like a lizard that has a normal body but a color-changing tail.
• The Implication: This suggests that the "Strange Metal" behavior (which is often linked to the magic of superconductivity) might not require the entire material to be weird. It seems the "weirdness" lives in how the electrons react to magnetic fields, while the "normalcy" lives in how they react to heat.

The "Rare Earth" Twist

The paper also compares their Nickelate (made with Lanthanum) to a similar one made with Neodymium.

• The Neodymium version is like a city with a chaotic, noisy background (magnetic atoms that are constantly flipping), making everything messy.
• The Lanthanum version (this study) is like a quiet city without that background noise.
• The Lesson: By removing the "noise" of the rare-earth magnets, the scientists could see the true nature of the Nickel atoms. They found that even without the noise, the material still has this split personality. This helps scientists understand that the "strangeness" comes from the Nickel atoms themselves, not just the messy background.

Summary in One Sentence

This paper discovered that in certain superconducting nickel materials, the electrons act like normal, predictable cars when it comes to temperature, but turn into unpredictable, rule-breaking racers when a magnetic field is applied, revealing a unique mix of normal and "strange" physics that could help us understand how superconductivity works.

Technical Summary

1. Problem Statement and Motivation

The nature of the normal ground state in infinite-layer nickelates (specifically La$_{1-x}$Sr$_x$NiO$_2$ or LSNO) remains a subject of debate. While these materials are considered analogs to high-$T_c$ cuprates, their transport properties near the quantum critical point (QCP) are not fully understood.

• The Conflict: Conventional Fermi liquids exhibit quadratic temperature dependence in resistivity ($\rho \propto T^2$) and follow Kohler's rule for magnetoresistance (MR). In contrast, "strange metals" near a QCP often display linear-in-$T$ resistivity and linear-in-$H$ magnetoresistance (H-linear MR) that violates Kohler's rule.
• The Gap: Previous studies on Nd-based nickelates (NSNO) showed signatures of strange metallicity ($T$-linear $\rho$), but these were complicated by rare-earth magnetism. Recent hints of a QCP in La-based LSNO (e.g., sign changes in Hall/Seebeck coefficients) suggested a similar strange metal state, but a systematic study of the normal-state transport in the $T \to 0$ limit was lacking.
• Objective: To determine whether the overdoped regime of high-crystallinity LSNO films hosts a strange metal state (characterized by $T$-linear $\rho$ and H-linear MR) or a conventional Fermi liquid, and to disentangle the effects of rare-earth magnetism from the intrinsic NiO$_2$ physics.

2. Methodology

The authors conducted a systematic magnetotransport study on high-quality thin films of LSNO with overdoped compositions ($x = 0.20, 0.22, 0.24$).

• Sample Synthesis: Films were grown via Pulsed Laser Deposition (PLD) followed by topotactic reduction using CaH$_2$ to convert the perovskite precursor (La$_{1-x}$Sr$_x$NiO$_3$) into the infinite-layer phase. High crystallinity was confirmed via X-ray diffraction.
• Experimental Conditions:
  • Magnetic Fields: Transport measurements were performed up to 62 Tesla using pulsed magnetic fields at the Dresden High Magnetic Field Laboratory (HLD-EMFL). Low-field measurements (<9 T) were done using a PPMS.
  • Temperature Range: Measurements extended down to ~2 K, well below the superconducting critical temperatures ($T_c$) of the samples.
  • Geometry: Current was applied in the $ab$-plane, with magnetic fields perpendicular to the plane (parallel to the $c$-axis).
• Data Analysis:
  • Kohler's Rule Test: Plotting fractional MR ($\Delta\rho/\rho_0$) vs. $\mu_0 H / \rho_0$.
  • Scaling Analysis: Plotting $\Delta\rho/T$ vs. $\mu_0 H/T$ to test for H-linear scaling behavior.
  • Power-Law Fitting: Fitting zero-field resistivity $\rho(T)$ below 30 K to the form $\rho(T) = \rho_0 + A T^n$ to extract the exponent $n$.

3. Key Contributions and Results

A. Violation of Kohler's Rule and H-Linear Magnetoresistance

The study revealed that the normal-state magnetoresistance in overdoped LSNO does not follow Kohler's rule.

• Functional Form: Instead of the expected quadratic dependence ($\Delta\rho \propto H^2$) for Fermi liquids, the MR exhibits a distinct H-linear behavior in the high $H/T$ limit.
• Scaling: The data collapses onto a single curve when plotted as $\Delta\rho/T$ versus $\mu_0 H/T$. This scaling is consistent with the unconventional MR functional form:
  $$\rho(H, T) = F(T) + \sqrt{(\alpha T)^2 + (\gamma \mu_0 H)^2}$$
  This behavior is typically associated with strange metals and quantum critical systems.

B. Coexistence with Fermi-Liquid Resistivity ($T^2$)

Contrary to the expectation that H-linear MR implies $T$-linear resistivity (a hallmark of strange metals), the authors found a dichotomy:

• Resistivity Behavior: The zero-field normal-state resistivity $\rho(T)$ below 30 K consistently follows a $T^2$ power law ($n \approx 2$) for all three overdoped samples ($x=0.20, 0.22, 0.24$).
• Fitting Results:
  • $x=0.20$: $n = 2.16 \pm 0.20$
  • $x=0.22$: $n = 1.88 \pm 0.18$
  • $x=0.24$: $n = 2.07 \pm 0.16$
• Significance: This confirms a Fermi-liquid ground state for the charge transport in the zero-field limit, despite the presence of unconventional H-linear MR.

C. Independence from Doping and $T_c$

The slope of the H-linear MR ($\gamma$) was found to be largely independent of the Sr doping level ($x$) and the superconducting critical temperature ($T_c$). This contrasts with some other strange metal systems where the MR slope correlates strongly with $T_c$, suggesting the mechanism driving the H-linear MR in LSNO may be distinct or decoupled from the superconducting pairing strength in the overdoped regime.

D. Role of Rare-Earth Magnetism

The authors compare their LSNO results with Nd-based nickelates (NSNO).

• NSNO exhibits $T$-linear resistivity and H-linear MR (strange metal behavior).
• LSNO exhibits $T^2$ resistivity and H-linear MR (Fermi liquid + unconventional MR).
• Conclusion: The difference is attributed to the absence of rare-earth magnetism in La-based compounds. The magnetic ground state of Nd (spin glass) likely drives the strange metal behavior in NSNO, whereas the La-based system reveals the intrinsic physics of the NiO$_2$ lattice, which appears to be a Fermi liquid in the overdoped regime.

4. Significance and Implications

• Resolution of the "Strange Metal" Debate: The study demonstrates that the infinite-layer nickelates are not universally strange metals. The "strange metal" signatures observed in Nd-based compounds may be extrinsic to the NiO$_2$ plane, driven by rare-earth magnetic fluctuations.
• New Transport Paradigm: The coexistence of H-linear magnetoresistance (typically a signature of Planckian dissipation or quantum criticality) with $T^2$ resistivity (the hallmark of a Fermi liquid) presents a unique and intriguing transport regime. It challenges the standard view that H-linear MR strictly requires a breakdown of the Fermi liquid description in the zero-field resistivity.
• Intrinsic Physics: By utilizing La-based compounds, the authors provide the cleanest view to date of the intrinsic electronic transport of infinite-layer nickelates, suggesting that the parent state of superconductivity in these materials is a Fermi liquid, not a strange metal.
• Theoretical Challenge: The results pose a challenge to theoretical models. While Boltzmann transport theory with anisotropic scattering can explain H-linear MR, the specific combination of H-linear MR and $T^2$ resistivity in this system requires further theoretical investigation to understand the interplay between elastic and inelastic scattering channels.

In summary, this paper establishes that overdoped La$_{1-x}$Sr$_x$NiO$_2$ is a Fermi liquid that exhibits unconventional H-linear magnetoresistance, decoupling the strange metal phenomenology from the intrinsic NiO$_2$ physics and highlighting the critical role of rare-earth magnetism in previous observations.