Pressure-induced charge orders and their postulated coupling to magnetism in hexagonal multiferroic LuFe₂O₄

The study addresses how charge order (CO) and spin order couple in hexagonal multiferroic LuFe₂O₄, a material exhibiting mixed-valence Fe³⁺/Fe²⁺ ordering with high transition temperatures. Prior measurements established a 3D CO below T_CO ≈ 320 K and a quasi-2D CO persisting up to ~525 K, alongside ferrimagnetic order below T_N ≈ 240 K. The interplay of charge and magnetism in the frustrated triangular bilayers is central to its multiferroicity, yet the coupling mechanism remains debated. Pressure is proposed as a clean tuning parameter to probe this interplay. Previous pressure studies on powders suggested reduced ferrimagnetic moments up to ~3 GPa and hinted at structural transitions, but powder averaging obscured details of superlattice evolution; a high-pressure polymorph (LuFe₂O₄-hp) above ~12 GPa with a rectangular Fe lattice is known but not directly relevant to the ambient triangular lattice. This work aims to elucidate pressure-driven evolution of charge orders and their coupling to magnetism in single-crystalline LuFe₂O₄.

Earlier XRD and TEM studies reported 3D CO in LuFe₂O₄ at ambient pressure, with periodic Fe²⁺/Fe³⁺ ordering and possible CO-driven ferroelectricity, though the ferroelectric origin is debated. Above T_CO, quasi-2D charge correlations persist to ~525 K. Neutron diffraction revealed ferrimagnetism below T_N ≈ 240 K. Prior high-pressure neutron powder diffraction indicated ~30% reduction of ferrimagnetic ordered moment up to ~3 GPa. X-ray powder diffraction suggested pressure-induced structural transitions, but superlattice peak evolution was non-systematic due to poor powder averaging. A high-pressure polymorph (LuFe₂O₄-hp) above ~12 GPa, retaining structure after decompression, adopts a rectangular Fe lattice and differs from the frustrated triangular lattice of the ambient phase. Competing charge orders have been observed in related RFe₂O₄ systems (R = Y, Yb), including (1/4,1/4) type modulations at ambient pressure in YFe₂O₄ by TEM, later reinterpreted by XRD as (1/4,1/2,1/4) with an enlarged triclinic supercell along c.

Sample preparation: Single crystals of LuFe₂O₄ were grown by floating-zone in a CO/CO₂ (~2.7:1) atmosphere to control oxygen stoichiometry; EPMA showed Lu₁.₀₁(1)Fe₂O₃.₉₇(4). High-pressure single-crystal X-ray diffraction (HP-SXD): Conducted at APS 13BM-C using 0.434 Å monochromatic X-rays. Pressure range: 0.8–14.5 GPa. Scans included 1° step, wide-step, and whole-range over ±35°. Symmetry analysis used SARAh and the Bilbao Crystallographic Server; refinements used FULLPROF. Ruby fluorescence determined pressure with <5% uncertainty; offline ruby used before/after pressure changes at ambient T. High-pressure XMCD: Fe K-edge XAS/XMCD at APS 4ID-D with circular polarization from a diamond phase retarder. Helicity modulated at 13.1 Hz and detected with lock-in; scans repeated with opposite magnetic fields to remove artifacts. Measurements at T = 100 K, H = ±5 T, at P = 1.9, 4.3, and 9.5 GPa. XAS collected simultaneously as helicity average. Online membrane and ruby systems used for pressure control/measurement at low T. Density functional theory: VASP with PAW and PBE GGA; plane-wave cutoff 500 eV. Correlations treated with GGA+U (U_eff = 4 eV; results robust for U_eff ~3.1–5.5 eV). Two-step procedure: initial optimization at larger U_eff (7.5 eV) to stabilize desired CO, followed by re-optimization at U_eff = 4 eV using converged charges. Forces converged <0.01 eV Å⁻¹. Enthalpy H = U − PV computed; atomic positions relaxed while lattice constants were constrained to experimental pressure-dependent values.

- Identification of three pressure-induced charge-ordered phases in single-crystal LuFe₂O₄: 1) CO-AP: centrosymmetric, incommensurate 3D CO with k ≈ (1/3, 1/3, 3/2) at low pressure; ferrimagnetic ground state. 2) CO-2D: non-centrosymmetric, incommensurate quasi-2D CO with k ≈ (1/3, 1/3, 0) emerging under pressure up to ~5.5 GPa; ferrimagnetic with reduced net magnetization. 3) CO-HP: centrosymmetric, commensurate 3D CO with k = (1/4, 1/4, 0) stabilized for 6.0–12.6 GPa; antiferromagnetic with zero net magnetization. - HP-SXD shows progressive broadening along L for the (1/3,1/3,L) superlattice as pressure increases to 5.0 GPa and a shift of L maxima from half-integer (L = n + 1/2) to integer (L = n), indicating emergent interplane polarization in the Q2D phase. Above 6.0 GPa, sharp peaks at (1/4,1/4,0) indicate restored robust 3D order. - In-plane incommensurability δ evolves from κ_AP = (1/3+δ,1/3+δ,3/2) and κ_2 = (1/3−δ,1/3−δ,0) at 0.8 GPa, increasing with pressure and reaching the commensurate κ_HP = (1/4,1/4,0) at ≥6.0 GPa; twin-related peaks trace spiral-like trajectories in reciprocal space. - Lattice compression from 0.8 to 12.6 GPa: monoclinic (C2/m) parameters change from a = 5.957(2) Å, b = 3.434(4) Å, c = 8.642(3) Å, β = 103.28(2)° to a = 5.809(5) Å, b = 3.339(16) Å, c = 8.374(11) Å, β = 103.39(9)°, with an 8.2(6)% volume reduction. - Transport: Resistivity exhibits a kink near ~6 GPa, consistent with the (1/3,1/3) → (1/4,1/4) CO transition. - HP-XMCD at Fe K-edge (T = 100 K, H = 5 T): finite dichroic peaks at 7114.0 eV (pre-edge) and 7129.0 eV at 1.9 GPa indicate net ferrimagnetism; signals weaken at 4.3 GPa (reduced net magnetization) and vanish at 9.5 GPa, indicating zero net magnetization (AFM). XAS pre-edge/leading-edge positions do not shift with pressure, implying an unchanged Fe²⁺/Fe³⁺ ratio. - DFT finds 2:1 ferrimagnetic ground states for CO-AP and CO-2D, and an antiferromagnetic ground state for CO-HP. Enthalpy calculations versus pressure reproduce the experimental phase sequence (3D ferri → Q2D ferri → 3D AFM). Calculated interlayer-to-intralayer Coulomb ratio V_CNNN/V_abNN remains nearly constant for 1–5 GPa and drops sharply above 6 GPa where the (1/4,1/4,0) CO is favored.

The results reveal strong coupling between charge order and magnetism in LuFe₂O₄ under pressure. Pressure-driven compression of the frustrated [Fe₂O₄] double layers redistributes charge density and tunes effective Fe–Fe Coulomb interactions, especially the balance among nearest, second-nearest, and third-nearest neighbors. This tuning destabilizes the frustrated (1/3,1/3) CO and stabilizes a less frustrated, charge-neutral-layer (1/4,1/4,0) CO. The interlayer-to-intralayer Coulomb interaction ratio decreases beyond ~6 GPa, aligning with the emergence of the commensurate 3D CO-HP phase. Because charge and spin correlations are coupled, the charge reorganization modifies exchange interactions, driving a magnetic transition from a 2:1 ferrimagnetic state (in CO-AP and CO-2D) to an antiferromagnetic state (in CO-HP). The disappearance of XMCD at 9.5 GPa corroborates the zero net magnetization expected for the AFM state. The DFT enthalpy landscape under experimentally constrained lattice parameters matches the observed sequence of 3D–2D–3D CO and ferrimagnetic-to-antiferromagnetic transitions, reinforcing that lattice compression is the control knob linking charge order topology and magnetic ground state.

In situ high-pressure single-crystal X-ray diffraction and Fe K-edge XMCD, combined with DFT, reveal a pressure-driven sequence of coupled spin–charge phases in LuFe₂O₄: a centrosymmetric 3D CO with 2:1 ferrimagnetism, a non-centrosymmetric quasi-2D CO with ferrimagnetism, and a centrosymmetric commensurate 3D CO with antiferromagnetism. The transitions are driven by pressure-enhanced Fe–Fe Coulomb interactions that favor a less frustrated (1/4,1/4,0) charge pattern and concomitant AFM order. These findings elucidate the coupling among charge, spin, and lattice degrees of freedom and demonstrate hydrostatic pressure as an effective, controllable means to tune spin–charge orders in frustrated layered ferrites. Future work could map full temperature–pressure phase diagrams and explore analogous pressure- or doping-induced (1/3,1/3,0) or (1/4,1/4,0) CO states in related RFe₂O₄ (R = Y, Yb, etc.) systems.

Magnetic structures under pressure are inferred from Fe K-edge XMCD net magnetization and DFT rather than directly determined by high-pressure neutron diffraction; thus the AFM configuration is proposed based on indirect evidence. XMCD measurements were performed at 100 K and 5 T at discrete pressures (1.9, 4.3, 9.5 GPa), and SXD at room temperature, so the full temperature–pressure phase space was not mapped. Structural and CO characterizations extend to 12.6 GPa; behavior beyond this range, including potential transitions to the known high-pressure polymorph with a different Fe lattice, was not the focus of this study.