Pressure and doping control of magnetic order and metallization in Ruddlesden-Popper La2NiO4

Using density functional theory with Hubbard corrections, this study reveals that hydrostatic pressure drives an insulator-to-metal transition in La$_2$NiO$_4$ while preserving robust magnetic order up to 75 GPa, whereas Sr doping systematically alters the magnetic ground state from G-type to ferromagnetic order and induces metallization, offering key insights into the mechanisms of nickelate superconductivity.

The Gist

Imagine a microscopic world made of tiny, spinning magnets arranged in a grid. This is the world of La₂NiO₄, a material scientists are studying to understand why some materials conduct electricity perfectly (superconductivity) while others do not. Think of this material as a "single-layer" version of a family of similar materials, some of which have recently been found to superconduct under high pressure.

Here is a simple breakdown of what the researchers discovered, using everyday analogies:

1. The Starting Point: A Quiet, Spinning Grid

At normal room pressure, the atoms in La₂NiO₄ are like a crowd of people standing in a checkerboard pattern.

• The Spin: Each person (a Nickel atom) is spinning. If one spins "up," the person next to them spins "down." This is called G-type antiferromagnetism. It's a very orderly, quiet dance where neighbors are always opposite.
• The Layers: The material is made of flat sheets stacked on top of each other. In this specific material, the sheets don't really talk to each other; the magnetic "conversation" happens mostly within the sheet itself.
• The Insulator: Right now, electricity cannot flow through this material. It's like a road blocked by a wall (an energy gap). The electrons are stuck in their spots, unable to move freely.

2. Squeezing the Material (Pressure)

The researchers put this material under extreme pressure, like a hydraulic press squeezing a sponge.

• The Squeeze: As they squeezed it harder (up to 50 gigapascals, which is about 500,000 times normal atmospheric pressure), the "wall" blocking the electricity started to crumble.
• The Result: At 50 GPa, the wall disappeared, and the material turned into a metal. Electricity could finally flow.
• The Surprise: Usually, when you squeeze a magnet, it stops being magnetic. But here, the "spinning dance" of the atoms remained strong and orderly even as the material became a metal. It was only when the pressure got really high (above 75 GPa) that the magnetic order started to weaken.
• Comparison: This is different from its "cousin" material (La₃Ni₂O₇), which loses its magnetic order very quickly when squeezed. La₂NiO₄ is much more stubborn and keeps its magnetic personality even under pressure.

3. Mixing in New Ingredients (Doping)

Instead of just squeezing the material, the researchers also tried changing its recipe. They swapped some of the Lanthanum atoms for Strontium atoms. Think of this as adding a new type of player to the dance floor who changes the rhythm.

• Changing the Dance: As they added more Strontium, the orderly "checkerboard" dance (G-type) broke down.
  • First, it changed to a different pattern (A-type).
  • Then, it formed stripes (like stripes on a shirt) where some areas were magnetic and others weren't.
  • Finally, with enough Strontium, everyone started spinning in the same direction (Ferromagnetism), like a crowd all cheering for the same team.
• The Metal Connection: This mixing also helped turn the material into a metal, but it did so by creating a complex pattern of "stripes" where charge and magnetism were unevenly distributed, rather than just by squeezing.

4. The Big Picture: Why This Matters

The researchers found that La₂NiO₄ is unique.

• Pressure vs. Recipe: Squeezing the material (pressure) and changing its recipe (doping) both turn it into a metal, but they do it in very different ways. Pressure keeps the magnetic order strong for a long time, while doping breaks the magnetic order and creates new, complex patterns.
• The Superconductivity Question: The ultimate goal in this field is to find materials that superconduct (conduct electricity with zero resistance) at high temperatures. While the researchers didn't find superconductivity in this specific single-layer material in this study, they found that its magnetic behavior is very different from its multi-layer cousins.
• The Lesson: To get superconductivity in this specific "single-layer" material, you might need more than just pressure. You might need to engineer the material's layers or interfaces in very specific ways, because its natural magnetic "stubbornness" makes it hard to switch to a superconducting state.

In summary: The paper shows that La₂NiO₄ is a magnetic material that is very hard to break. It stays magnetic even when squeezed until it becomes a metal. Changing its chemical recipe breaks the magnetism and creates new patterns. Understanding these specific behaviors helps scientists figure out the "rules of the game" for why some nickel-based materials become superconductors and others don't.

Technical Summary

Technical Summary: Pressure and Doping Control of Magnetic Order and Metallization in Ruddlesden-Popper La2NiO4

Problem and Motivation
The recent discovery of high-pressure superconductivity in multilayer Ruddlesden-Popper (RP) nickelates ($La_{n+1}Ni_nO_{3n+1}$) has spurred interest in understanding the intrinsic electronic and magnetic properties of the single-layer parent compound, $La_2NiO_4$ ($n=1$). Unlike its cuprate analogue $La_{2-x}Sr_xCuO_4$, which exhibits superconductivity upon doping, the parent phase $La_2NiO_4$ and its Sr-doped variants have not shown superconductivity at ambient pressure. A fundamental question remains regarding the electronic and magnetic nature of $La_2NiO_4$ and how it compares to the bilayer ($La_3Ni_2O_7$) and trilayer ($La_4Ni_3O_{10}$) systems. Specifically, it is unclear whether the magnetic interactions in $La_2NiO_4$ follow a simple Néel-type antiferromagnetic order similar to cuprates or if the multi-orbital nature of nickelates leads to more complex ground states that differ under pressure and doping.

Methodology
The authors employ density functional theory with Hubbard corrections (DFT+U) using the Vienna Ab initio Simulation Package (VASP) and projector-augmented wave pseudopotentials. The study systematically investigates the magnetic ground state, electronic structure evolution, and Sr-doping effects in $La_2NiO_4$.

• Pressure: Hydrostatic pressure is applied from ambient conditions up to 100 GPa to tune electronic bandwidth and orbital overlap without introducing chemical disorder.
• Doping: Ordered substitution patterns are used to model $La_{2-x}Sr_xNiO_4$ with doping levels $x = 0.5, 1.0, 1.5$. Structural relaxations are performed to ensure thermodynamic stability.
• Parameters: The Hubbard $U$ parameter for Ni 3d orbitals is varied from 2 eV to 5 eV, with Hund's coupling $J = 0.1U$.
• Analysis: The study evaluates total energy differences among various magnetic configurations (Non-magnetic, Ferromagnetic, A-type AFM, G-type AFM, and Double Spin Stripe), calculates local magnetic moments, and analyzes exchange interactions via a Heisenberg model. Electronic properties are examined through band structures, partial density of states (PDOS), and Bader charge analysis.

Key Results

1. Ambient Pressure Ground State:

   • At ambient pressure, tetragonal $La_2NiO_4$ exhibits a robust G-type antiferromagnetic (G-AFM) order. This state is energetically favored over other configurations (including A-AFM and double spin stripe) across the entire range of $U$ values studied.
   • The system displays negligible interlayer magnetic coupling, consistent with its quasi-two-dimensional nature. The nearest-neighbor in-plane exchange coupling ($J_1$) is robustly antiferromagnetic (36.2–61.2 meV), while the next-nearest-neighbor coupling ($J_2$) is weak.
   • Local magnetic moments on Ni ions are approximately 1.40–1.75 $\mu_B$, showing weak dependence on the correlation strength $U$.

2. Pressure-Induced Evolution:

   • Under hydrostatic pressure, the system undergoes a continuous insulator-to-metal transition (IMT) at approximately 50 GPa. The insulating gap, initially ~1 eV, narrows and closes smoothly without abrupt structural phase transitions.
   • Crucially, the magnetic order remains robust up to 75 GPa, with Ni magnetic moments decreasing only slightly from 1.6 $\mu_B$ to 1.4 $\mu_B$.
   • Unlike the bilayer $La_3Ni_2O_7$, which shows rapid suppression of magnetic order and metallization near 10 GPa, $La_2NiO_4$ maintains strong magnetism. This is attributed to the dominance of in-plane $d_{x^2-y^2}$ orbital character and the absence of pressure-enhanced interlayer $d_{z^2}$ hybridization.
   • No charge or orbital ordering is observed in the pressured parent phase up to 100 GPa; the system remains in a uniform spin-density-wave phase.

3. Sr-Doping Effects:

   • Sr doping induces a systematic evolution of magnetic order distinct from the pressure response. As doping increases ($x = 0.5 \to 1.0 \to 1.5$), the ground state transitions from G-AFM to A-type AFM, then to a striped antiferromagnetic order, and finally to ferromagnetic (FM) order.
   • Metallization: The $x=0.5$ system becomes metallic, while the $x=1.0$ system ($LaSrNiO_4$) remains insulating with a gap of 0.27 eV.
   • Charge and Orbital Order: In $LaSrNiO_4$ ($x=1.0$), the substitution of $La^{3+}$ by $Sr^{2+}$ creates two inequivalent Ni sites. The system exhibits weak charge ordering ($n_{Ni-1} - n_{Ni-2} \approx 0.08$) and weak orbital ordering ($n_{x^2-y^2} - n_{3z^2} \approx 0.08$ on Ni-1). This is accompanied by a site-selective Mott-like scenario where one Ni site becomes non-magnetic ($S=0$) while the other retains a moment ($S=1$).
   • Local magnetic moments are progressively suppressed with doping, reflecting the oxidation of $Ni^{2+}$ ($d^8$) toward $Ni^{3+}$ ($d^7$).

Significance and Claims
The paper claims to provide a comprehensive magnetic and electronic phase diagram for the single-layer RP nickelate $La_2NiO_4$ as a function of pressure and doping. Key contributions include:

• Establishing that the G-AFM ground state of $La_2NiO_4$ is remarkably sensitive to doping but less so to pressure compared to multilayer counterparts.
• Demonstrating that the robust magnetism in $La_2NiO_4$ persists up to high pressures (75 GPa), contrasting sharply with the rapid magnetic suppression seen in $La_3Ni_2O_7$. This suggests that achieving superconductivity in the 214 phase may require mechanisms beyond simple hydrostatic pressure, such as strain engineering or interfacial effects.
• Revealing that Sr doping drives a complex sequence of magnetic transitions and induces weak charge/orbital orders in $LaSrNiO_4$, offering insights into the interplay between magnetism and superconductivity in the RP family.
• Providing a benchmark for understanding the fundamental properties of 214 nickelates and the role of dimensionality in determining electronic correlations.

The authors conclude that while $La_2NiO_4$ shares a similar crystal field environment with multilayer nickelates, its isolated $NiO_2$ planes result in distinct pressure responses and magnetic robustness, highlighting the critical role of dimensionality in these correlated systems.