The purely organic radical ferromagnet 3,5-dinitrophenyl nitronyl nitroxide (DNPNN), an achiral molecule that crystallizes as two mirror-image chiral enantiomorphs (tetragonal P43_3 and P41_1), orders ferromagnetically below 1.10(1) K. Muon-spin rotation (μ\muSR) shows two spontaneous precession frequencies whose temperature dependences differ — impossible for a static magnetic structure — and dipolar-field calculations at the candidate muon sites overshoot the measured fields by factors of ~1.5–5 even after accounting for a muon-induced local singlet and macroscopic Lorentz and demagnetizing fields. The unresolved problem is to determine the ordered-state magnetic structure of DNPNN and the microscopic interactions that produce it: the spin-density distribution and muon perturbation needed to reproduce the measured local fields, the temperature-dependent (plausibly noncollinear or helical) structure behind the two distinct frequency evolutions, the magnitude of symmetry-allowed anisotropic (Dzyaloshinskii–Moriya) exchange, and the role of the chiral molecular packing in selecting the ordered state. The problem remains open.

Background

Purely organic ferromagnets — magnets built only from light s- and p-block elements (C, H, N, O) with no d or f electrons — were long thought impossible on the basis of Heisenberg's theory of ferromagnetism, and were first realized in the nitronyl nitroxide radical p-NPNN (Tamura et al., Chem. Phys. Lett. 1991). A nitronyl nitroxide is a stable organic molecule carrying one unpaired electron (S=1/2S=1/2) whose spin density is delocalized mainly over the O–N–C–N–O fragment; in the crystal each molecule carries a magnetic moment of order 1 μB\mu_B, and magnetic order appears only below ~1 K, driven by weak intermolecular exchange. DNPNN (3,5-dinitrophenyl nitronyl nitroxide) is a particularly interesting member of this family: although the molecule itself is achiral, it crystallizes spontaneously as an enantiopair — two mirror-image chiral tetragonal crystals (space groups P43_3 and P41_1), in which radicals stack in a helical arrangement along the fourfold screw axes (Shiomi et al., J. Phys. Chem. Lett. 2011). Its susceptibility is well described by ferromagnetic one-dimensional chains (intrachain 2J/kB=122J/k_B = 12 K) with weak interchain coupling (2zJ′/kB≈12zJ'/k_B \approx 1 K) that drive three-dimensional order at TC≈1.1T_C \approx 1.1 K.

Muon-spin rotation (μ\muSR) is a volume-sensitive probe of local magnetism: spin-polarized positive muons are implanted throughout a sample, and below an ordering transition their spins precess in the internal field BB at the muon stopping site, producing oscillatory signals with frequency ν=γμB/2π\nu = \gamma_\mu B/2\pi (γμ/2π=135.5\gamma_\mu/2\pi = 135.5 MHz T−1^{-1}). In a magnet the internal field at a muon site is dominated by the dipolar sum over the surrounding molecular moments, Bdipα(rμ)=∑iDiαβmiβB^\alpha_{dip}(\mathbf{r}_\mu) = \sum_i D_i^{\alpha\beta} m_i^\beta, plus the macroscopic Lorentz field (μ0M/3\mu_0 M/3) and a demagnetizing field (−NM-NM, with NN the sample-dependent demagnetizing factor). In μ\muSR studies of p-NPNN it was found that the implanted muon can bind the electron of the nearest radical into a spin singlet, switching off that molecule's moment — the muon is not a passive spectator, and any field calculation must model this perturbation.

A μ\muSR study of DNPNN (Blundell et al., Magnetochemistry 2021) confirmed bulk long-range order below TC=1.10(1)T_C = 1.10(1) K with critical exponents β=0.41(1)\beta = 0.41(1) and 0.37(1)0.37(1) for the two frequencies, close to the three-dimensional Heisenberg value (0.3690.369). It also revealed two unexplained features. First, two distinct precession frequencies appear, both approaching ≈1\approx 1 MHz as T→0T \to 0; density-functional-theory muon-site calculations combined with dipolar-field sums (including a nearest-molecule singlet and Lorentz/demagnetizing corrections) give fields that are still too large — roughly 4.6–4.8 MHz, 3–4 MHz, and 1.5–3 MHz for the three candidate muon sites. Second, the two frequencies follow different temperature dependences: since each precession frequency should simply scale with a single order parameter f(T)f(T), differing evolutions require the magnetic structure itself (the arrangement of the moments) to change with temperature. The authors suggest possible sources — a temperature-dependent noncollinear or helical component from competing interchain couplings, Dzyaloshinskii–Moriya (DM) exchange (the antisymmetric, spin–orbit-driven part of the exchange interaction that favors spin canting and is symmetry-allowed in chiral crystals, though expected to be weak in a light-element magnet), or the chiral packing itself — but none is established, and the magnetic structure of DNPNN has never been directly determined.

Problem Statement

Provide a quantitative microscopic account of the ordered state of the chiral organic ferromagnet DNPNN that explains the internal fields measured by μSR. This comprises: (i) the magnetic moment distribution in the ordered state and the degree to which the implanted muon perturbs nearby molecular spin density (e.g., through muon-induced singlet formation), such that calculated dipolar fields at the muon stopping sites — with Lorentz and demagnetizing corrections — quantitatively reproduce the measured precession frequencies (both ≈1 MHz as T→0T \to 0, versus calculated values of 1.5–4.8 MHz for existing models); (ii) the ordered magnetic structure and its temperature evolution, which must be noncollinear or otherwise temperature dependent to generate the two observed precession frequencies with different temperature dependences (fitted zero-temperature magnitudes ν1(0)=1.21(2)\nu_1(0) = 1.21(2) MHz and ν2(0)=1.37(2)\nu_2(0) = 1.37(2) MHz, both vanishing at a common TC=1.10(1)T_C = 1.10(1) K) — establishing whether the proposed helical/noncollinear component driven by competing interchain couplings, or another mechanism, is correct; (iii) the magnitude and role of anisotropic (Dzyaloshinskii–Moriya) exchange, which is symmetry-allowed by the chiral crystal structure but unassessed for this light-element (C, H, N, O) magnet; and (iv) whether and how the chiral packing of the achiral radicals selects the ordered state and its temperature evolution. These strands jointly support one objective: a microscopic model of DNPNN's ordered state that reproduces the measured local fields ν1(T)\nu_1(T) and ν2(T)\nu_2(T) and identifies the mechanism behind them. The problem is open as stated; no narrowing to a particular technique, temperature range, or model class is implied.

References

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