Opposite pressure effects on magnetic phase transitions in NiBr2

This study reveals that hydrostatic pressure exerts opposite effects on the magnetic phases of NiBr2 compared to NiI2, where pressure suppresses the helimagnetic order while steeply enhancing the collinear antiferromagnetic order due to the dominant role of interlayer exchange interactions.

The Gist

Imagine a tiny, microscopic world made of layers of atoms, like a stack of pancakes. In this specific stack, called NiBr₂ (Nickel Bromide), the atoms inside each "pancake" are magnets that like to dance in a spiral pattern. This is called a helimagnetic order. However, if you heat them up a bit, they stop dancing in spirals and line up in neat, straight rows. This is called collinear antiferromagnetic order.

Scientists wanted to know: What happens if we squeeze this stack of magnetic pancakes?

Usually, when you squeeze a material, you expect the magnets to get "stronger" and hold their order at higher temperatures. But in this paper, the researchers found something surprising: Squeezing NiBr₂ does two opposite things at once.

Here is the breakdown of their discovery using simple analogies:

1. The Two Different "Dances"

Think of the magnetic atoms in NiBr₂ as a group of dancers.

• The Spiral Dance (Helimagnetic): At low temperatures, the dancers twist and turn in a spiral. This is the "cool" state where the material has special properties (multiferroicity).
• The Line Dance (Collinear Antiferromagnetic): At slightly higher temperatures, the dancers stop twisting and stand in straight, alternating lines.

2. The Squeeze Test (Hydrostatic Pressure)

The researchers put this material in a machine that applies hydrostatic pressure (squeezing it equally from all sides, like a deep-sea diver being crushed by the ocean).

• The Result for the "Line Dance": As they squeezed harder, the dancers loved the line formation. The temperature at which they could stay in a straight line shot up dramatically. It went from 44 K (very cold) to nearly 100 K with just a little bit of pressure. It's as if the pressure gave them a super-boost of energy to stay organized.
• The Result for the "Spiral Dance": The spiral dancers hated the squeeze. As soon as the pressure got a tiny bit higher (around 0.8 GPa), the spiral dance completely stopped. The dancers couldn't twist anymore; they were forced to snap into the straight line formation.

3. The "Twin" Comparison (NiBr₂ vs. NiI₂)

The scientists compared this to a very similar material called NiI₂ (Nickel Iodide). Think of NiBr₂ and NiI₂ as twins who look almost identical but have different personalities.

• The Twin (NiI₂): When you squeeze NiI₂, both the spiral dance and the line dance get stronger. They both survive the pressure.
• The Subject (NiBr₂): When you squeeze NiBr₂, the spiral dance dies immediately, while the line dance gets super strong.

This difference is unique. Usually, pressure helps everything get stronger. Here, it helps one thing while killing the other.

4. Why Does This Happen? (The Secret Sauce)

To understand why, the researchers used powerful computers to look at the invisible "glue" holding the atoms together. This glue is called exchange interaction.

• The Glue Between Layers: Imagine the layers of pancakes are held together by weak glue (van der Waals forces). When you squeeze the stack, you push the pancakes closer together, making that glue much stronger.
• The Discovery: The computer simulations showed that in NiBr₂, this "inter-layer glue" (specifically a second-nearest neighbor connection) is the key.
  • When the pressure squeezes the layers together, this specific glue gets so strong that it forces the atoms to line up in straight rows.
  • This strong glue is too heavy for the delicate "spiral dance" to survive. The spiral is too fragile for the pressure, so it collapses.
  • In the twin material (NiI₂), the internal rules are different, so the spiral dance is tough enough to survive the squeeze.

Summary

The paper tells us that pressure is a powerful switch for NiBr₂.

• It kills the special spiral magnetic state very quickly (at low pressure).
• It supercharges the straight-line magnetic state, making it survive at much higher temperatures.

The scientists concluded that the difference between NiBr₂ and its twin NiI₂ comes down to the specific strength of the "glue" between the layers. In NiBr₂, that glue is just right to crush the spiral but perfect for building a strong straight line. This helps us understand how to control magnetic materials by simply squeezing them.

Technical Summary

Technical Summary: Opposite Pressure Effects on Magnetic Phase Transitions in NiBr₂

Problem Statement
NiBr₂ and NiI₂ are archetypal van der Waals (vdW) triangular-lattice multiferroics that exhibit complex magnetic ordering, transitioning from a collinear antiferromagnetic (AFM) state at higher temperatures to an incommensurate helimagnetic (HM) state at lower temperatures. While high hydrostatic pressure has been shown to significantly enhance the stability of both magnetic phases in NiI₂, previous studies on NiBr₂ suggested a contradictory behavior where the HM phase is suppressed under pressure. However, existing theoretical calculations for NiBr₂ failed to reproduce this suppression, predicting only HM order across a wide pressure range (0–15 GPa). This discrepancy between experimental observations and theoretical predictions, alongside the contrasting pressure responses of the isostructural NiBr₂ and NiI₂, motivated a comprehensive re-investigation of the pressure-dependent magnetic phase transitions in NiBr₂.

Methodology
The study employed an integrated approach combining experimental measurements and first-principles theoretical simulations:

• Experimental: High-quality single crystals of NiBr₂ were grown via chemical vapor transport. The magnetic properties under hydrostatic pressure (up to ~3 GPa) were investigated using AC magnetic susceptibility measurements with a custom-built piston-cylinder pressure cell. Specific heat measurements were also performed at ambient pressure to characterize thermodynamic anomalies.
• Theoretical: The researchers utilized ab initio density functional theory (DFT) calculations employing the r2SCAN meta-generalized gradient approximation combined with a nonlocal rVV10 van der Waals functional and DFT+U (U = 2.5 eV) to account for electron correlation. Exchange interactions were mapped from DFT energies of broken-symmetry magnetic configurations to an isotropic Heisenberg Hamiltonian.
• Simulation: Finite-temperature magnetism was modeled using atomistic spin dynamics simulations (UppASD framework) based on the calculated exchange parameters. Monte Carlo simulations were used to determine transition temperatures and ground-state spin configurations under varying pressures.

Key Results

1. Opposite Pressure Trends: The experiments revealed a stark contrast in the pressure response of the two magnetic transitions in NiBr₂:
   • The Néel temperature ($T_{N1}$) of the collinear AFM phase increases steeply with pressure at a rate of ~20 K/GPa, reaching ~100 K at 3 GPa without signs of saturation. This represents the highest pressure coefficient observed in known vdW AFM compounds.
   • Conversely, the transition temperature to the helimagnetic phase ($T_{N2}$) decreases rapidly with pressure, and the HM phase is completely suppressed above a critical pressure of ~0.8 GPa.
2. Theoretical Validation: The ab initio calculations successfully reproduced the experimental trend, predicting a transition from HM to collinear AFM order between 0 and 1 GPa. The simulations identified the second-nearest interlayer exchange interaction ($j_2'$) as the primary driver stabilizing the collinear AFM phase.
3. Mechanism of Suppression: Analysis of the exchange parameters showed that while the in-plane exchange ratio ($|j_3/j_1|$) remains relatively constant, the interlayer coupling ($j_2'$) increases significantly (by >150% up to 5 GPa). The study demonstrates that the HM order in NiBr₂ is fragile because its stability relies on a delicate balance of in-plane and interlayer interactions; the rapid strengthening of $j_2'$ under pressure shifts the ground state preference toward the collinear AFM order.
4. Comparison with NiI₂: The paper attributes the divergent behavior between NiBr₂ and NiI₂ to the different ratios of intralayer couplings. In NiI₂, the ratio $|j_3/j_1|$ is much higher (0.81 vs. ~0.25 in NiBr₂), making the helimagnetic order inherently more stable against the pressure-induced strengthening of interlayer interactions.

Significance and Claims
The paper claims to provide the first comprehensive pressure-dependent study of NiBr₂ up to 3 GPa, resolving previous contradictions between experimental data and theoretical models. The primary significance lies in identifying the dominant role of interlayer interactions in governing the distinct pressure responses of magnetic phases in these closely related vdW magnets. By establishing that subtle differences in exchange coupling values dictate whether a material's magnetic phases are enhanced or suppressed by pressure, the work offers a refined understanding of magnetic phase stability in triangular-lattice multiferroics. The study underscores that while pressure generally strengthens magnetic order in vdW materials, the specific evolution of exchange parameters can lead to unique, phase-selective suppression, as observed in the rapid disappearance of the helimagnetic phase in NiBr₂.