Magnetic compressibility of layered ferromagnet under pressure Open Access

The magnetic properties of low-dimensional magnets under pressure have garnered significant research interest due to their tunable behavior arising from structural compressibility.^1–3 These materials often exhibit novel magnetic phenomena when subjected to external pressure.^4,5 For instance, in two-dimensional (2D) van der Waals (vdW) materials, even a fractional change of a lattice constant between adjacent layers can result in profound alternations in their physical properties.^6,7 In magnetic vdW materials, such changes can alter interlayer exchange pathways, modifying both the magnitude and sign of the interlayer exchange coupling.^8–10 

In intermetallic compounds with three-dimensional (3D) crystal structures, layered magnetic elements are often separated by non-magnetic layers, providing an analog for studying magnetism in reduced dimensions.^11,12 The discovery of ferromagnetism in 2D vdW systems such as Cr₂Ge₂Te₆ and Fe₃GeTe₂ has opened new avenues for controlling and manipulating magnetism and spin transport phenomena.^13–16 Unlike conventional 3D magnetic systems, these 2D magnets exhibit pronounced responses to external stimuli, including magnetic fields, electric fields, light, strain, and pressure.^17,18 This makes them ideal candidates for applications in spintronics, straintronics, and quantum computation.^19,20 Pressure can be used as a clean tool for modulating the magnetic properties without changing the chemical composition.²¹ For example, theoretical predictions suggest that tensile strain can increase the Curie temperature and coercivity of Fe–Ge–Te materials, a prediction confirmed by experimental studies. Conversely, high-pressure conditions strongly suppress ferromagnetism and Curie temperature in the Fe–Ge–Te family.^22,23 This suppression has been attributed to a reduction in exchange interactions and magnetocrystalline anisotropy under pressure.²⁴ Despite their potential, Mn-based 2D ferromagnetic materials have been scarcely investigated. In Mn-based magnetic systems, the Mn–Mn interatomic distances play a critical role in determining the magnetic ordering. For example, in topological Kagome magnetic compounds such as RMn₆Ge₆ (R = heavy lanthanide elements or Y), the Mn–Mn distances significantly influence the nature of magnetic interactions.^25,26 Longer Mn–Mn distances generally favor ferromagnetic ordering and high saturation magnetic moments, whereas shorter distances tend to stabilize antiferromagnetic interactions.

Thus, we investigated the layered ferromagnetic compound MnPt₅As, which crystallizes in a tetragonal structure with the space group P4/mmm (No. 123).²⁷ In this structure, the Mn atoms exhibit distinct interatomic distances: the nearest Mn–Mn separation within the ab-plane is 3.93 Å, while the interlayer Mn–Mn distance along the c-axis is significantly larger, measuring 7.09 Å. High-pressure x-ray diffraction experiments were performed on MnPt₅As, revealing that no phase transition occurs up to 11.5 GPa. Notably, the c-axis lattice parameter is more compressible compared to the a lattice parameter, indicating anisotropic structural compression under pressure. Complementary neutron diffraction measurements under low pressure (up to ∼4.9 GPa) confirmed that MnPt₅As retains its ferromagnetic ordering within this pressure range. However, even at these modest pressures, the magnetic anisotropy was observed to decrease, suggesting sensitivity of the magnetic alignment to the structural changes induced by external pressure.

Polycrystalline MnPt₅As was synthesized using a high-temperature arc-melting technique, distinct from the previously reported solid-state pellet synthesis methods, to produce sufficient material for neutron scattering experiments.²⁷ Stoichiometric amounts of Mn, Pt, and As powders, in an atomic ratio of Mn:Pt:As = 1:5:1.1, were homogenized and pelletized in an argon-filled glovebox to mitigate the toxicity of arsenic. The pellet was then heated to 600 °C at a controlled rate of 30 °C per hour and maintained at this temperature overnight to minimize arsenic volatilization. Subsequently, the sample was subjected to two cycles of arc-melting under an argon atmosphere to ensure compositional homogeneity. To confirm the phase information of the synthesized samples, high-pressure phase analysis on selected crystals was conducted using synchrotron powder x-ray diffraction at the 13BM-C beamline (PX²) of the Advanced Photon Source (APS) at Argonne National Laboratory (ANL), employing a wavelength of 0.434 Å. A BX-90 diamond anvil cell,²⁸ equipped with one pair of anvils of 200 μm diameter culet, was utilized to apply pressure. A 4:1 (volume ratio) methanol–ethanol mixture was used as the pressure-transmitting medium.²⁹ The two-dimensional diffraction images were integrated using Dioptas software,³⁰ and Rietveld refinement of the data set was conducted with GSAS II.^31,32

The high-pressure neutron diffraction experiments on MnPt₅As were conducted on a SNAP diffractometer at the Spallation Neutron Source at Oak Ridge National Laboratory. The detectors were positioned at 50° and 90° with respect to the direct beam, enabling access to a d-spacing range of up to about 8 Å. To conduct these experiments, a powder sample of ∼1 g was loaded into a null-scattering Ti–Zr alloy encapsulated gasket, and pressure was applied using a gas cell. The press was installed at the beamline with the load axis in the vertical direction. The sample temperature was controlled by liquid nitrogen flow in the copper channels closely attached to both anvils. Pressure was incrementally increased in steps of 0.2–1.1 GPa, followed by data collection, to a maximum pressure of ∼4.9 GPa. Data reduction was performed using the Mantid package (Workbench version 6.2),³³ and Rietveld refinements were conducted using FullProf Suite.³⁴ The refined parameters for MnPt₅As consisted of lattice parameters, atomic coordinates, and thermal displacements.

Density functional theory (DFT) calculations were performed using version 7.3.1 of the Quantum ESPRESSO code to analyze the band structure, density of states (DOS), and Fermi surface of MnPt₅As.³⁵ The calculations utilized projector augmented-wave (PAW) pseudopotentials in conjunction with the Perdew–Burke–Ernzerhof (PBE) exchange-correlation functional.^36,37 A wavefunction cutoff energy of 300 Ry and a charge density cutoff set to 12 times this value were employed. An 11 × 11 × 6 Monkhorst–Pack k-point mesh was employed in the reciprocal space.³⁸ Convergence tests were conducted to ensure the change of total energy smaller than 1 meV/atom. The Davidson diagonalization algorithm was applied, and the convergence threshold for self-consistency is set to 10^–9Ry.³⁹ The high-symmetry path for the Brillouin zone was generated using the Spglib library and visualized using the XCrySDen software package.^40–42 

MnPt₅As crystallizes in the tetragonal P4/mmm space group, exhibiting an isostructural relationship with MgPt₅As. The previously reported crystal structure is depicted in Fig. 1(a). Phase purity and structural evolution under pressure were investigated through Rietveld refinement of synchrotron powder x-ray diffraction (XRD) data, as shown in Fig. 1(b). High-pressure XRD experiments conducted at room temperature up to 11.5 GPa revealed that the tetragonal layered structure is preserved under compression. The evolution of the unit cell volume and the lattice parameters, determined from Rietveld refinements, is presented in Fig. S1 in the supplementary material. A continuous reduction in lattice parameters was observed, with a and b decreasing from 3.889(1) Å at 0.4 GPa to 3.838(1) Å at 11.5 GPa and c decreasing from 6.846(1) Å at 0.4 GPa to 6.745(1) Å at 11.5 GPa. This confirms the absence of any structural phase transition within the studied pressure range. Fitting the volume vs pressure data using the second-order Birch–Murnaghan equation of state (EOS) in Fig. S2 in the supplementary material yielded an isothermal bulk modulus B₀ = 256(7) GPa, indicating that MnPt₅As is highly incompressible.

Temperature-dependent neutron powder diffraction measurements were conducted at a series of temperatures (100, 125, 150, 180, 220, 250, 270, and 320 K) to investigate the magnetic evolution of MnPt₅As under pressures up to ∼4.9 GPa. The nuclear structure determined at high pressure was consistent with the previous findings from single-crystal x-ray diffraction (XRD) and high-pressure powder XRD, as shown in Fig. 1(b). Changes in the intensity, width, and positions of magnetic diffraction peaks were observed in the data sets collected between 320 and 100 K. Considering the pressure-temperature phase diagram of MnPt₃ and using Pb as a pressure indicator, contributions from both MnPt₃ and Pb phases were incorporated into the refinement process. This approach yielded improved agreement between the observed and calculated diffraction patterns. Notably, only trace amounts of MnPt₃ [∼5.0(2) at. %] were identified as a minor impurity from the synthesis. The refinements of pressure- and temperature-dependent neutron diffraction patterns reveal that the magnetic moments are localized exclusively on the Mn atoms. As the temperature decreases, the magnetic moments under pressure exhibit an increasing trend, ranging from 0.1 to 4.9 GPa, consistent with the observations at ambient pressure. Notably, the refined magnetic moments at 270 K display anomalous behavior, potentially associated with a magnetic transition near 300 K. However, no definitive trend in magnetic moments with respect to pressure variations is observed, which may be attributed to the relatively small incremental changes in pressure during the measurements (Fig. 2).

The effects of pressure and temperature on the magnetic intensities and peak positions of MnPt₅As are shown in Figs. 3(a) and 3(b), respectively. At 100 K [Fig. 3(a)], the intensities of the magnetic peaks in MnPt₅As increase as the pressure is raised from 0.1 to 1.1 GPa but, subsequently, decrease with further pressure increases up to 700 bar. Additionally, the d-spacings of the magnetic peaks shift toward smaller values over the pressure range of 0.1 to 4.9 GPa, indicating a contraction of the magnetic unit cell and revealing the presence of magnetic anisotropic compressibility under pressure. To exclude temperature effects on the observed magnetic unit cell contraction, temperature-dependent measurements of magnetic intensities and peak positions were conducted at 4.9 GPa, as shown in Fig. 3(b). The results indicate a significant increase in magnetic intensity at lower temperatures, consistent with the temperature-dependent evolution of magnetic moments at ambient pressure. However, the d-spacing of the magnetic peaks remains unchanged with decreasing temperature at 4.9 GPa. This behavior is further supported by non-magnetic peaks, such as the peak with a d-spacing of approximately 2.98 Å, which exhibits a similar trend to the magnetic peak at a d-spacing of ∼3.9 Å. These findings confirm that the magnetic anisotropic compressibility in MnPt₅As is pressure dependent but temperature-independent.

The crystal structures of MnPt₅As were optimized under applied pressures of 0, 1.112, 2.657, 3.741, and 4.874 GPa, with full relaxation of both lattice parameters and atomic positions. The optimized structural parameters, detailed in Table S1 in the supplementary material and depicted in Figs. 4(a)–4(c), exhibit a slight anisotropy in lattice contraction, with linear compressibility k_a = 0.0014 GPa⁻¹ and k_c = 0.0019 GPa⁻¹. Spin polarization was incorporated using the Local Spin Density Approximation (LSDA),⁴³ and the corresponding magnetic moments, derived from DFT-optimized lattice parameters, are summarized in Table S2 in the supplementary material. A pressure-induced reduction in the ordered magnetic moment of the Mn atoms is observed, as shown in Fig. 4(d). The ferromagnetic behavior is predominantly attributed to the Mn atoms, consistent with the previously reported findings.

Figure S4(b) in the supplementary material illustrates the Brillouin zone, and the high-symmetry path utilized for the band structure and density of states (DOS) calculations of MnPt₅As under pressures of 0 and 4.874 GPa, with the results presented in Figs. S4(c) and S4(d) in the supplementary material. The compound exhibits metallic behavior, consistent with the experimental resistivity measurements. The band structure reveals spin splitting, corroborating the ferromagnetic nature observed experimentally. The electronic structures under the two pressure conditions show negligible differences, reflecting minimal changes in the relaxed lattice parameters. At both pressure conditions, a pseudogap is observed approximately 1.28 eV above the Fermi level, and a Van Hove singularity is identified around −0.19 eV. The atomic-projected density of states (DOS) of MnPt₅As at 0 and 4.874 GPa, shown in Fig. S5(a) and S5(b) in the supplementary material, reveals that the DOS below the Fermi level is predominantly contributed by the Pt d-states, with a slight predominance of up-spin states. Above the Fermi level, the Mn d-states dominate, with a notable prevalence of down-spin states.

The band structures and projected density of states (PDOS) of MnPt₅As were computed to assess the impact of spin polarization (SP) and spin–orbit coupling (SOC), as shown in Fig. S6 in the supplementary material. The SOC calculations were performed based on the spin-polarized results, where the initial magnetization aligns with the calculated magnetic orientation from the spin-polarized case. Even with SOC included, the spin density retains a directional bias, predominantly aligned along the projection of the total angular momentum, with a magnitude of approximately 4.55 μ_B, consistent with the spin-polarized case. Although the spins deviate from purely “up” or “down” states, they remain oriented along the resultant angular momentum direction. When neither SP nor SOC is included, a Van Hove singularity originating from the Mn–d orbitals appears near the Fermi level (E_F), as shown in Fig. S6(a) in the supplementary material. This result is consistent with earlier studies.^27,44 Upon introducing SP, the bands near E_F are no longer fully occupied, leading to the absence of a pronounced peak in the density of states (DOS) at E_F [Fig. S6(b) in the supplementary material]. Additionally, the spin-polarized calculation reduces the presence of flatbands near E_F compared to the non-spin-polarized scenario [Fig. S6(a) in the supplementary material] and the SOC-included scenario [Fig. S6(c) in the supplementary material]. The inclusion of SOC [Fig. S6(c) in the supplementary material] further modifies the electronic structure. The strong DOS peak near E_F splits into smaller peaks, and a saddle point at the Γ point near E_F, visible in the absence of SOC, is disrupted. SOC also introduces bandgaps at other high-symmetry points in the band structure, highlighting its significant influence on the electronic properties.

The projections of the primary orbitals of MnPt₅As are illustrated in Fig. 5. In the absence of both spin polarization and spin–orbit coupling (SOC), as shown in Fig. 5(a), and with SOC included [Fig. 5(b)], the d-orbitals of Mn and Pt2 atoms dominate the electronic states near the Fermi level (E_F) through hybridization. When only spin polarization is considered, as depicted in Figs. 5(c) and 5(d), the d-orbitals of Pt2 atoms contribute significantly to the electronic states below E_F, while for the spin-down states, the d-orbitals of Mn atoms become the primary contributors above E_F. Experimentally, the c-axis of the crystal structure compresses more easily than the ab-plane under pressure. This behavior corresponds to changes in the Brillouin zone, particularly from the Γ-point to the Z-point, which is dominated by the d-orbitals of Pt2 atoms under the influence of SOC and spin polarization. Theoretical simulations indicate that the compressibility of MnPt₅As is closely linked to the Pt d-orbitals. Furthermore, these orbitals significantly affect the magnetic anisotropy of the material, even though the magnetic moments are primarily localized on the Mn atoms. The three-dimensional Fermi surface of MnPt₅As, depicted in Fig. S7 in the supplementary material, illustrates the intersections of energy bands with the Fermi level within the first Brillouin zone (BZ). Upon incorporating spin–orbit coupling (SOC), the Fermi surface undergoes significant modifications, including the emergence of pronounced pockets and sharp edges. These changes indicate that SOC induces or shifts energy gaps at specific high-symmetry points within the BZ. Such alterations in the Fermi surface topology imply the potential for anisotropic transport properties and spin-polarized currents.

The magnetic properties of the layered ferromagnet MnPt₅As were systematically investigated under pressure using a combination of experimental measurements and theoretical simulations. MnPt₅As exhibits a ferromagnetic transition at ∼301 K. Neutron diffraction measurements performed up to ∼4.9 GPa across a temperature range of 320–100 K reveal that the Mn atoms maintain ferromagnetic ordering under low applied pressures, though magnetic anisotropy is significantly suppressed. X-ray diffraction under pressure indicates that the c-axis undergoes more pronounced compression compared to the ab-plane, correlating with the suppression of Mn ferromagnetic ordering along the c-axis. Theoretical simulations confirm minimal changes in magnetic ordering under an applied pressure, consistent with the experimental findings. These results highlight the role of Pt d-orbitals, spin–orbit coupling, and pressure-induced structural changes in governing the magnetic and electronic properties of MnPt₅As. The insights gained underscore the potential of MnPt₅As for strain-engineered magnetic devices and applications requiring control of the spin-dependent transport properties.

The supplementary material file contains additional analysis and data that support the results obtained in the manuscript: lattice parameters refined from PXRD under high pressure; second-order Birch-–Murnaghan EOS fit; Rietveld refinement on the magnetic structure of MnPt5As; neutron scattering and DFT relaxed lattice parameters and unit cell volumes; magnetic moments of MnPt5As unit cell from DFT relaxations; band structures and total DOS of MnPt5As under pressure; projected density of states (PDOS) of MnPt5As under pressure; band structures and PDOS calculated for MnPt5As; and Fermi surface of MnPt5As in the first Brillouin zone.

The work at Michigan State University was supported by the U.S. DOE-BES under Contract No. DE-SC0023648. W.B. was supported by the National Science Foundation (NSF) Career (Award No. DMR-2045760). This research used resources of the Advanced Photon Source (APS); a U.S. Department of Energy (DOE) Office of Science User Facility operated for the U.S. DOE Office of Science by Argonne National Laboratory (ANL) under Contract No. DE-AC02-06CH11357. A portion of this research used resources at the Spallation Neutron Source, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory.

The authors have no conflicts to disclose.

Matt Boswell: Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Writing – review & editing (lead). Cheng Peng: Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Validation (equal); Writing – original draft (equal); Writing – review & editing (equal). Wenli Bi: Data curation (lead); Formal analysis (lead); Funding acquisition (equal); Investigation (lead); Methodology (lead); Supervision (supporting); Writing – review & editing (lead). Antonio F. Moreira dos Santos: Data curation (lead); Formal analysis (lead); Methodology (lead); Supervision (equal); Writing – review & editing (equal). Weiwei Xie: Conceptualization (lead); Funding acquisition (lead); Project administration (lead); Supervision (lead); Validation (equal); Writing – original draft (lead); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.