Suppression of ferromagnetism in van der Waals insulator due to pressure-induced layer stacking variation

Technical Summary: Pressure-induced structure transformation and collapse of ferromagnetism in van der Waals insulator CrBr₃

Problem Statement
Van der Waals (vdW) magnetic insulators, such as CrBr₃, exhibit intrinsic ferromagnetism (FM) that is highly sensitive to structural modifications. While previous studies established that CrBr₃ undergoes a structural transition from a high-temperature monoclinic phase to a low-temperature rhombohedral ($R\bar{3}$) phase, the behavior of its crystal structure and magnetic order under hydrostatic pressure remained a subject of debate. Specifically, while Curie temperature ($T_C$) was observed to decrease with pressure, the mechanism behind this suppression was unclear. Theoretical expectations suggested that compressive strain should ideally enhance FM interactions by optimizing the Cr-Br-Cr bond angle toward 90°, yet experimental data showed a rapid collapse of ferromagnetism, a phenomenon more typical of itinerant metallic ferromagnets than localized insulators. Furthermore, prior literature suggested a critical pressure for the loss of ferromagnetism around 8.4 GPa based on linear extrapolations, and the existence of a high-pressure structural phase remained unresolved due to the limitations of powder X-ray diffraction.

Methodology
The authors employed a comprehensive multi-modal approach combining experimental characterization with first-principles theoretical modeling:

• Experimental:
  • Single-crystal X-ray diffraction (XRSCD): Performed at ambient pressure and under high pressure (up to 21.5 GPa) using a diamond anvil cell (DAC) to resolve structural phases and stacking sequences. Reciprocal-space mapping was utilized to analyze layer stacking and domain sizes.
  • Magnetization: Direct measurements of magnetization isotherms and thermomagnetic curves were conducted on single crystals under pressure (up to ~6.24 GPa) using a SQUID magnetometer with a miniature DAC.
  • Raman Spectroscopy: High-pressure phonon excitations were mapped to track structural evolution and phase coexistence.
• Theoretical:
  • Ab initio DFT: Electronic structure calculations were performed using VASP with GGA+U and vdW corrections to determine exchange interactions ($J_1$, $J_L$) and magnetic anisotropy for different stacking configurations (ABC vs. AA).
  • Atomistic Simulations: Finite-temperature Monte Carlo (MC) and spin dynamics simulations (using UppASD) were used to model the magnetic behavior of mixed-phase systems, incorporating the calculated exchange parameters.

Key Contributions and Results

1. Discovery of Intrinsic Trimorphism and a New Trigonal Phase:
   Ambient-pressure single-crystal diffraction revealed that CrBr₃ is not purely rhombohedral ($R\bar{3}$) but exhibits intrinsic trimorphism. A previously unreported trigonal phase with space group $P\bar{3}m1$ coexists with the $R\bar{3}$ phase. The $P\bar{3}m1$ phase is characterized by AA stacking of layers and a 2/3 occupancy of the Cr 1a site. The coexistence of these phases at ambient conditions is well-described by a paracrystal model, indicating a random sequence of structural blocks.

2. Pressure-Induced Structural Transformation:
   Increasing hydrostatic pressure drives a gradual transformation from the dominant $R\bar{3}$ phase to the $P\bar{3}m1$ phase. The $R\bar{3}$ phase becomes undetectable above 8.4 GPa, while the $P\bar{3}m1$ phase remains stable even after decompression from 21.5 GPa, suggesting it is a metastable phase stabilized at high pressure. This transition involves the randomization of Cr occupancies and a shift from ABC to AA stacking sequences.

3. Direct Evidence of Ferromagnetism Collapse:
   Magnetization measurements provided the first direct experimental proof of the pressure-induced suppression of ferromagnetism in CrBr₃. Both the Curie temperature ($T_C$) and the saturated magnetization ($M_{sat}$) decrease continuously with pressure. The rate of suppression accelerates above 3 GPa, leading to a complete collapse of the ferromagnetic signal at a critical pressure ($p_c$) of approximately 5.8 GPa. This value is significantly lower than the 8.4 GPa predicted by previous linear extrapolations.

4. Mechanism of Magnetic Collapse:
   The paper attributes the loss of ferromagnetism not to the delocalization of electrons (as the material remains an insulator with a calculated band gap of 1.39 eV at 10 GPa) but to the emergence of antiferromagnetic (AFM) interlayer coupling. DFT calculations indicate that while the intralayer FM coupling ($J_1$) remains robust, the interlayer coupling ($J_L$) changes sign from FM (in ABC stacking) to AFM (in AA stacking) under pressure. As the pressure increases, the volume fraction of the AFM-favoring AA-stacked ($P\bar{3}m1$) phase grows, introducing competing AFM interactions that suppress the bulk $T_C$.

5. Validation via Simulation:
   Atomistic simulations of mixed systems (containing varying fractions of ABC and AA stacked layers) successfully reproduced the experimental trend of $T_C$ suppression. The results confirm that the introduction of AFM-coupled AA layers into an FM matrix is sufficient to explain the observed rapid decline in magnetic order.

Significance and Claims
The authors claim that this work resolves the long-standing puzzle of why $T_C$ in CrBr₃ decreases so rapidly with pressure despite the material being a localized insulator. The significance lies in:

• Establishing CrBr₃ as a model platform for studying pressure-driven structural and magnetic transformations in layered vdW systems.
• Providing the first direct experimental evidence that the collapse of ferromagnetism in this system is driven by a structural phase transition that introduces AFM interlayer coupling, rather than a change in electronic itinerancy.
• Demonstrating that the "critical pressure" for magnetic collapse is determined by the kinetics of the structural phase transition (the growth of the AA-stacked phase) rather than a simple thermodynamic limit of the FM state.
• Highlighting the sensitivity of vdW magnets to mechanical manipulation, where minor structural perturbations (stacking faults) can fundamentally alter magnetic ground states.

The paper concludes that the magnetic order in CrBr₃ is a delicate balance between FM intralayer and interlayer interactions, which can be tipped toward AFM ordering simply by altering the stacking sequence via external pressure.