Magnetic super-structure and active surface role in the onset of magnetic excitons revealed in TbCu₂ nanoparticles

The study explores whether complex antiferromagnetic (AF) super-structures persist at the nanoscale and how surface symmetry breaking influences magnetic excitations and crystalline electric field (CEF) levels. While AF materials are promising for spintronic applications and can host complex non-collinear structures, it remains unclear if such long-range correlations survive in nanoparticle ensembles where inter-particle interactions and surface disorder can induce supermagnetic states. The authors investigate TbCu₂ in bulk and nanoparticles (~7–8 nm) to: (1) determine the presence of a magnetic helix-like super-structure using small-angle neutron scattering (SANS), and (2) resolve CEF schemes and magnetic excitons using inelastic neutron scattering (INS), thereby assessing core versus surface roles in nanoscale magnetic dynamics relevant to spintronics and topological spin textures.

AF materials have unique advantages for spintronics and host complex structures (helix, non-collinear/noncoplanar), potentially yielding topological spin textures. Prior work revisited AF structures for exotic phenomena but did not address their stability in nanoparticle ensembles, where reduced dimensionality and interactions drive supermagnetic states (superparamagnetic, super-ferromagnetic, super spin glass). For TbCu₂, previous studies reported a commensurate AF core maintained in nanoparticles with a surface spin-glass-like state leading to superantiferromagnetism, but did not probe possible longer-period magnetic super-structures. INS is well established for single crystals, less so for polycrystalline materials, and rare for nanoparticles, especially 4f AFs. Size reduction modifies energy level schemes and collective excitations due to microstrain, disorder, and interfaces, necessitating remodeled CEF and magnon descriptions. Related nanoparticle systems (e.g., NdCu₂) showed surface-driven magnons and CEF shifts, suggesting interfaces can actively influence excitation propagation.

- Materials and fabrication: Polycrystalline TbCu₂ synthesized by arc melting under Ar (99.99%). Nanoparticles produced by high-energy planetary ball milling under Ar (99.99%), with milling times t = 2 h and 5 h yielding D ≈ 8(1) nm and 7(1) nm, respectively; total mass ~12 g MNPs prepared for INS. - Transmission electron microscopy (TEM): Jeol 2100 at 200 kV on milled powders; quasi-spherical morphology; size histogram mean 7.4(1.6) nm. - Small-angle neutron scattering (SANS): SANS2D (ISIS, UK), time-of-flight mode with 1.75 Å < λ < 16.5 Å, temperatures 5–285 K, fields μ0H = 0–6 T, 0.5 h per pattern. Analyses targeted low-q power-law behavior and high-q magnetic Bragg features. Field geometries H_parallel and H_perp assessed. Experiment DOI: 10.5286/ISIS.E.RB1910077. - Inelastic neutron scattering (INS): IN4 (ILL, France) on Tb₀.₁Y₀.₉Cu₂ (non-magnetic proxy for CEF analysis) and TbCu₂ (bulk and ~7 nm NPs). Incident energies Ei = 8.74, 16.9, and 67.6 meV at Q = 1.75 Å⁻¹; temperature range 1.5–100 K across PM and AF states. Additional IN6 measurements at Ei = 3.1 meV. Corrections for background, absorption, self-shielding; normalized to vanadium. - Heat capacity: Relaxation method (no external field), 2–300 K, to estimate magnetic entropy and infer higher-lying CEF levels. - Modeling: CEF analysis using McPhase (Searchspace, Sumanfit, Simann) starting from literature parameters; compared calculated level schemes with experimental transitions. Considered molecular field effects below TN to account for level shifts and Zeeman splitting. Supplementary notes include detailed CEF state compositions and calculations.

- SANS identification of a magnetic super-structure: - Clear incommensurate magnetic Bragg peak at q = 1.15(1) nm⁻¹ below ~40 K (T < TN) in bulk and nanoparticles, corresponding to a real-space spacing of 54.6(1) Å; not commensurate with the crystallographic unit cell. - Field dependence follows known metamagnetic transitions along the a-axis; the incommensurate peak vanishes for μ0H ≥ 2 T (bulk), with stronger robustness for H_parallel than H_perp. - Magnetic moment associated with the super-structure ~14 μB at 40 K; projections along crystallographic axes estimated at ~1.12, 1.77, and 1.90 μB/Tb³⁺; consistent with a helix in the bc-plane. - Proposed incommensurate propagation vector τ ≈ 1/12 (reduced units) and helical turn angle ~30°; supported by strong six-order CEF anisotropy. - On cooling to 5 K, peak intensity diminishes consistent with the decrease of τβ/τα reported previously; no peak in the paramagnetic region. - Nanoparticle robustness: peak persists in ~7–8 nm MNPs but is broader, less field-robust (remains only for μ0H ≤ 0.5 T), and slightly shifts to q = 1.13(1) nm⁻¹. Low-q intensity of MNPs follows power-law ∝ q⁻⁴.³, indicative of sharp interfaces. - INS and CEF scheme: - Tb₀.₁Y₀.₉Cu₂ (PM, Ei = 8.74 meV): observed CEF transitions at 5.3 and 6.1(±0.1) meV; thermally activated features at ~3.5 and ~4.3 meV from 20 K; levels nearly T-independent up to ~40 K; slight softening at 100 K; resolution-limited widths up to 20 K. - CEF modeling (McPhase) matches observed low-energy levels (I–IV) and predicts higher-energy states (up to ~70 meV) with low matrix elements; weak hints near 12–15 meV (possibly V–VIII convolution) and ~25 meV (phonons) at Ei = 67.6 meV. - TbCu₂ (PM, 100 K): spectra similar to Tb₀.₁Y₀.₉Cu₂; nanoparticles exhibit a downshift of ~−0.5 meV, consistent with CEF softening at interfaces. - Ordered state (T < TN ≈ 48 K): - Molecular field effects: a ~5 meV level is shifted to ~7 meV at low T by an internal molecular field ~60 T (equal-moment structure), with possible Zeeman splitting up to ~5 meV for θy ≈ 50 K. - Additional excitations: “VA” at 11.9(1) meV (assigned to splitting of a higher-lying level) and “M” at 6.7(1) meV (magnetic excitation not present in PM region) emerge and decrease in intensity as T approaches TN. - In nanoparticles, ordered-state energy transfers closely match bulk, indicating an additional surface molecular field counteracts the negative CEF softening observed in the PM state; surface thus actively contributes to the propagation and onset of magnetic excitons at 6.7(1) meV. - Near TN, a −0.4(1) meV negative shift reappears in NPs, consistent with pure CEF softening as surface-contributed molecular field fades. - Transition probabilities (areas) decrease and broaden in NPs; relative areas to II transition: bulk r(M/II) ≈ 0.96, r(III/II) ≈ 0.7; NPs r(M/II) ≈ 0.6, r(III/II) ≈ 0.3, indicating altered dipolar matrix elements due to surface-modified RKKY interactions. - A new NP excitation at 4.8(1) meV (“I”) appears, attributed to RKKY-induced splitting of a ground-state quasi-doublet, whose transition gains probability in reduced dimensionality. - Heat capacity: Magnetic entropy at 300 K Sexp ≈ 10 J/K²·mol is well below Stheo = R ln(2J+1) ≈ 21.3 J/K²·mol for J = 6, implying additional CEF levels at energies above room temperature. - Microstructure: TEM shows quasi-spherical MNPs with mean size 7.4(1.6) nm; SANS low-q behavior consistent with sharp interfaces and spin-misalignment contributions from surface disorder.

The work demonstrates that TbCu₂ hosts an incommensurate helix-like magnetic super-structure that persists down to nanoparticle sizes of ~7–8 nm, answering the open question about the stability of complex AF order in nanoparticle ensembles. SANS evidences a robust helical component with τ ≈ 1/12 and ~30° pitch; despite surface-induced disorder, long-range correlations survive, though broadened and less robust against field in NPs. INS resolves the CEF level scheme in the paramagnetic state and shows that, below TN, a strong molecular field (~60 T) shifts and splits levels, giving rise to magnetic excitations (e.g., at 6.7 meV). Crucially, nanoparticles do not simply follow PM CEF softening trends in the ordered state; instead, a surface-induced molecular field compensates the CEF downshift, preserving bulk-like excitation energies and enabling the onset of magnetic excitons at low energies. The altered transition probabilities and emergence of a 4.8 meV mode in NPs point to significant modifications of dipolar matrix elements and RKKY-mediated interactions at interfaces. These findings support a dual-spin dynamics picture (core vs surface) and highlight the active role of nanoparticle surfaces in excitation propagation. Overall, the results are significant for spintronics and the exploration of topological spin textures, as they underline the nanoscale robustness of incommensurate AF structures and reveal how surface symmetry breaking modulates both single-ion CEF and collective (RKKY-driven) excitations, potentially enabling engineered interfacial control of magnetic dynamics.

- The study reports an incommensurate, helix-like magnetic super-structure in polycrystalline TbCu₂ with τ ≈ 1/12 and ~30° pitch, evidenced by a SANS peak at q ≈ 1.15 nm⁻¹ (real-space ~54.6 Å). This super-structure remains robust in nanoparticles (~7–8 nm), though broadened and slightly shifted, demonstrating that complex AF order can persist at the nanoscale. - The CEF energy level scheme of Tb³⁺ in TbCu₂ is established using Tb₀.₁Y₀.₉Cu₂ and validated by INS and modeling; below TN, a molecular field (~60 T) shifts and splits levels, yielding magnetic excitations (e.g., 6.7 and 11.9 meV). In nanoparticles, an additional surface molecular field counterbalances CEF softening in the ordered state and triggers the onset of magnetic excitons, while modifying transition probabilities via altered RKKY interactions. - These insights substantiate a dual core–surface spin dynamics framework and suggest routes to harness interfacial effects in spintronic and topological applications. Future directions: Improve definition of energy levels and dispersion with single crystals and polarized INS to determine whether the observed excitons can be classified as magnons; extend combined SANS/INS studies to other nanoscale compounds to generalize the role of surface geometry and topology in excitation propagation.

- SANS form factor could not be extracted due to powder nature, small particle size, and size distribution; satellite peaks for the incommensurate structure were not resolved at large q. - INS sensitivity and instrumental resolution limited reliable identification of higher-energy (>12 meV) CEF transitions; hints at 12–15 and 25 meV lack sufficient intensity for firm assignment. - Use of polycrystalline samples precludes full directional dispersion mapping; single-crystal measurements would better resolve anisotropic excitations and distinguish magnons vs excitons. - Increased disorder in nanoparticles broadens and reduces peak intensities, complicating precise deconvolution of overlapping modes and quantitative matrix element extraction.