Multiple magnetic orders in LaFeAs_1-xP_xO uncover universality of iron-pnictide superconductors

Since the 2008 discovery of superconductivity in LaFeAsO1−xFx (1111 family), related iron-pnictide families such as hole-doped and electron-doped 122s, 111, and 1144 have exhibited proximity between antiferromagnetism and superconductivity, suggesting unconventional pairing. Parent compounds generally display in-plane stripe antiferromagnetic order with two-fold rotational symmetry (C2^M). Subsequent studies uncovered additional magnetic states: a re-entrant tetragonal out-of-plane collinear double-Q phase (C4^AM) in hole-doped 122s and an in-plane non-collinear double-Q spin-vortex crystal “hedgehog” phase (C4^A, often labeled C_ab) in 1144 compounds, and possibly in Ba1−xNaxFe2As2. Theoretical proposals attribute the multiplicity of magnetic orders to factors such as Fermi surface nesting quality, spin–orbit coupling, disorder, and quantum fluctuations. The RFePnO (1111) family has a rich phase diagram; however, magnetic order on the Fe sublattice had been definitively determined only in LaFeAsO (C2^M), while other LaFeAs1−xPxO compositions showed indications of unknown magnetism via non-structural probes. LaFeAs1−xPxO uniquely exhibits two disconnected superconducting domes amid multiple magnetic states. Fluorine substitution merges these domes by suppressing magnetism, hinting that separated superconductivity arises from competition with diverse magnetic orders. This study addresses whether multiple distinct magnetic orders can be realized within a single 1111 system, enabling a unified comparison across iron-pnictide families.

Prior work established superconductivity in several iron-pnictide families (1111, 122, 111, 1144), with parent compounds typically exhibiting stripe antiferromagnetism (C2^M). Novel magnetic orders were identified subsequently: the tetragonal C4^AM double-Q phase in hole-doped Ba/Sr/Ca 122s, and the in-plane non-collinear C4^A (spin-vortex crystal, “hedgehog”) order in CaKFe4As4. µSR and NMR studies suggested additional magnetic states in LaFeAs1−xPxO beyond low-x C2^M, but magnetic structures on the Fe sublattice were not resolved except in LaFeAsO. Theoretical frameworks (Landau theory with spin–orbit coupling, effects of nesting degradation, quantum fluctuations, and disorder) predict possible degeneracy and competition among C2^M, C4^A, and C4^AM. In LaFeAs1−xPxO, two separated superconducting domes had been observed, merging under fluorine doping, indicating magnetic competition underlies the split domes. These findings motivated a comprehensive structural and magnetic determination across the 1111 series.

Samples: Polycrystalline LaFeAs1−xPxO spanning x = 0 to 1 were synthesized in an Ar-atmosphere glovebox (<5 ppm O2, <0.1 ppm H2O) from LaAs, La2O3 (pre-dried at 900 °C), LaP, Fe, Fe2O3, FeAs, Fe2As, FeP, and Fe2P. Powders were ground, loaded into alumina crucibles, flame-sealed under vacuum in quartz tubes, and annealed at 1100 °C for up to 40 h with iterative regrinding/annealing (final optimized procedure achieved phase purity after two cycles). Sample quality was monitored by laboratory XRD; magnetic susceptibility was measured in 10 Oe using a Quantum Design MPMS.

Diffraction and µSR: High-resolution synchrotron x-ray powder diffraction was performed on beamline 11-BM-B (APS, Argonne) for x = 0–0.6. High-resolution neutron diffraction was performed on POWGEN (SNS, ORNL) for x = 0.23–1.0, and high-flux neutron diffraction on WISH (ISIS, RAL) for x = 0–0.8. Muon spin relaxation (µSR) was carried out on EMU (ISIS, RAL) for x = 0.23–1.0. µSR asymmetry data were fitted with a flat background plus a stretched exponential G2(t) = A_g + A_1 exp[−(λ t)^β] using Mantidplot; magnetic transition temperatures T_N were extracted from the inflection point in the second derivative of the temperature-dependent asymmetry.

Structural and magnetic analysis: Rietveld refinements used GSAS/EXPGUI and GSAS-II. Nuclear refinements determined phase fractions; magnetic refinements on difference patterns (below minus above T_N) determined magnetic structures and ordered moments. Lattice parameters across x were refined; Vegard’s law adherence was checked via the c-axis linearity.

Theoretical modeling: Magnetism was modeled via two order parameters M1 and M2 at wave-vectors Q1=(π,0) and Q2=(0,π) in a Landau free-energy expansion F = F^(2)+F^(4). The quadratic term included spin-isotropic part a(M1^2+M2^2) and spin-anisotropic terms with coefficients α_i selecting moment direction; quartic terms involved coefficients μ, g, and w controlling single-Q vs double-Q order and relative orientation (parallel vs perpendicular). Microscopic coefficients were obtained from a k·p-based multiband model (after Cvetkovic & Vafek; Christensen et al.), incorporating spin–orbit coupling. Isovalent P-for-As substitution was modeled as increasing electron and hole Fermi surface sizes (Δk_F/k_F), reflecting reduced electronic correlations (DMFT/DFT indicate LaFeAsO more correlated than LaFePO). Computed evolutions of g and α_i vs Δk_F/k_F identify stability regions for C2^M (g>0), C4^A (g<0 with in-plane easy axis), and C4^AM (g<0 with out-of-plane easy axis).

• LaFeAs1−xPxO hosts three distinct magnetic orders within a single compositional phase diagram: orthorhombic single-Q C2^M at low x; a narrow tetragonal in-plane double-Q C4^A (spin-vortex crystal, “hedgehog”) region near x ≈ 0.45; and a wide tetragonal out-of-plane double-Q C4^AM region spanning approximately 0.5 ≤ x ≤ 0.8.
• All three magnetic phases compete strongly with superconductivity; the superconducting domain splits into two domes separated by magnetic order, and merges into a single dome upon fluorine doping that suppresses magnetism.
• µSR indicates bulk magnetism for all compositions with x ≤ 0.8; compositions x ≥ 0.9 show no bulk magnetism.
• Structural evolution: The system transforms from orthorhombic (C2^M region) to tetragonal by x ≥ 0.35, consistent with high-resolution synchrotron data; the c-axis follows Vegard’s law across x, confirming continuous P-for-As substitution.
• Neutron diffraction unambiguously distinguishes the magnetic structures via characteristic magnetic Bragg peak positions/intensities (e.g., for C2^M most intense peaks at ~4.05 Å and 5.4 Å; for C4^A at ~3.43 Å and 4.73 Å; for C4^AM at ~4.71 Å and 5.63 Å), with Rietveld refinements indexing correct peaks and intensities.
• Ordered magnetic moments refined from neutron diffraction: ~0.6 μB at x = 0 in the C2^M phase, decreasing continuously to ~0.2 μB for x ≥ 0.3 and remaining roughly constant through tetragonal double-Q phases; finite moments persist when a=b, indicating four-fold symmetric magnetic order onset.
• Theoretical modeling reproduces the sequential stabilization of magnetic orders with increasing Fermi surface size (proxy for increasing x): small Fermi surfaces favor C2^M; larger ones yield C4^A; further increase favors C4^AM due to a change in spin anisotropy (α_3 becoming smallest). Spin–orbit coupling is essential to select between tetragonal phases.
• The phase diagram exhibits symmetry around x ≈ 0.5 disorder maximum: SC domes peak near x ≈ 0.27 and x ≈ 0.8; disorder from isovalent substitution suppresses both T_N and T_c, with magnetism suppressed more rapidly, enabling SC emergence between magnetic regions.
• LaFePO (x = 1) lacks long-range magnetic order, consistent with a more metallic, less correlated state and a relatively robust SC dome on the P-rich side.

The study resolves the magnetic structures throughout LaFeAs1−xPxO, demonstrating that a single 1111 system can realize the same three magnetic orders previously observed separately in 122 and 1144 families. This addresses the open question of whether diverse magnetic orders across iron-pnictides are system-specific or reflect a universal behavior: the results support underlying universality, with the sequence C2^M → C4^A → C4^AM controlled by changes in Fermi surface size and spin anisotropy. The experimental phase diagram shows strong competition among the three magnetic states and superconductivity, explaining the split superconducting domes that recombine under electron doping (F substitution) when magnetic order is suppressed. Theoretical Landau analysis linked to a k·p model captures the evolution of quartic (g) and anisotropy (α_i) coefficients with increasing Fermi surface size due to reduced correlations under P substitution, reproducing the observed reorientation of magnetic moments and phase sequence. Disorder from isovalent substitution further shapes the phase diagram by suppressing T_N and T_c, with magnetism more sensitive than s± superconductivity, accounting for the emergence of SC between magnetic domes and the observed symmetry around x ≈ 0.5.

A comprehensive x-ray, neutron diffraction, and µSR study of LaFeAs1−xPxO establishes a phase diagram hosting all three key magnetic states of iron-pnictides—C2^M, C4^A (hedgehog), and C4^AM—within a single system, clarifying their competition with superconductivity and revealing a universal framework across distinct crystal structures and chemistries. Theoretical modeling based on changes in Fermi surface size and spin–orbit-induced anisotropy corroborates the sequential stabilization of magnetic orders with P substitution. These results unify our understanding of magnetism–superconductivity interplay in iron-pnictides. Future work could include µSR and Mössbauer studies with higher time resolution to identify muon stopping sites and local field distributions in tetragonal magnetic phases, as well as further probes of disorder and correlation effects controlling the phase boundaries.

• µSR measurements at EMU could not access the short time scales necessary to determine muon stopping sites and fully resolve the bimodal local field distributions in tetragonal magnetic phases.
• The theoretical model simplifies P substitution primarily as an increase in Fermi surface size due to reduced correlations; other effects (e.g., detailed band-structure changes, orbital selectivity, impurity scattering specifics) may also contribute and are not fully ruled out.
• Measurements were performed on polycrystalline samples; single-crystal studies could provide directional resolution for subtle anisotropies and domain effects.
• Minor impurity phases (e.g., La(OH)3, LaOH at ~1 wt%) were present in some samples, though accounted for in refinements.