Microscopic origin of the internal fields and temperature-dependent ordered structure in the chiral organic ferromagnet DNPNN

The purely organic radical ferromagnet 3,5-dinitrophenyl nitronyl nitroxide (DNPNN), an achiral molecule that crystallizes as two mirror-image chiral enantiomorphs (tetragonal P4 $_3$ and P4 $_1$ ), orders ferromagnetically below 1.10(1) K. Muon-spin rotation ( $\mu$ SR) 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 ( $S=1/2$ ) 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 $\mu_B$ , 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 P4 $_3$ and P4 $_1$ ), 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 $2J/k_B = 12$ K) with weak interchain coupling ( $2zJ'/k_B \approx 1$ K) that drive three-dimensional order at $T_C \approx 1.1$ K.

Muon-spin rotation ( $\mu$ SR) 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 $B$ at the muon stopping site, producing oscillatory signals with frequency $\nu = \gamma_\mu B/2\pi$ ( $\gamma_\mu/2\pi = 135.5$ MHz T $^{-1}$ ). In a magnet the internal field at a muon site is dominated by the dipolar sum over the surrounding molecular moments, $B^\alpha_{dip}(\mathbf{r}_\mu) = \sum_i D_i^{\alpha\beta} m_i^\beta$ , plus the macroscopic Lorentz field ( $\mu_0 M/3$ ) and a demagnetizing field ( $-NM$ , with $N$ the sample-dependent demagnetizing factor). In $\mu$ SR 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 $\mu$ SR study of DNPNN (Blundell et al., Magnetochemistry 2021) confirmed bulk long-range order below $T_C = 1.10(1)$ K with critical exponents $\beta = 0.41(1)$ and $0.37(1)$ for the two frequencies, close to the three-dimensional Heisenberg value ( $0.369$ ). It also revealed two unexplained features. First, two distinct precession frequencies appear, both approaching $\approx 1$ MHz as $T \to 0$ ; 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 $f(T)$ , 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 $T \to 0$ , 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 $\nu_1(0) = 1.21(2)$ MHz and $\nu_2(0) = 1.37(2)$ MHz, both vanishing at a common $T_C = 1.10(1)$ 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 $\nu_1(T)$ and $\nu_2(T)$ 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

S. J. Blundell, T. Lancaster, P. J. Baker, F. L. Pratt, D. Shiomi, K. Sato, T. Takui, "The Internal Field in a Ferromagnetic Crystal with Chiral Molecular Packing of Achiral Organic Radicals", Magnetochemistry 7(5), 71 (2021). DOI: 10.3390/magnetochemistry7050071, https://doi.org/10.3390/magnetochemistry7050071
D. Shiomi, Y. Kanzaki, S. Okada, R. Arima, Y. Miyazaki, A. Inaba, R. Tanaka, K. Sato, T. Takui, "An Enantiopair of Organic Ferromagnet Crystals Based on Helical Molecular Packing of Achiral Organic Radicals", J. Phys. Chem. Lett. 2(24), 3036–3039 (2011). DOI: 10.1021/jz2014105, https://doi.org/10.1021/jz2014105
M. Tamura, Y. Nakazawa, D. Shiomi, K. Nozawa, Y. Hosokoshi, M. Ishikawa, M. Takahashi, M. Kinoshita, "Bulk ferromagnetism in the β-phase crystal of the p-nitrophenyl nitronyl nitroxide radical", Chemical Physics Letters 186(4–5), 401–404 (1991). DOI: 10.1016/0009-2614(91)90198-i, https://doi.org/10.1016/0009-2614(91)90198-i
S. J. Blundell, P. A. Pattenden, F. L. Pratt, R. M. Valladares, T. Sugano, W. Hayes, "μ+SR of the organic ferromagnet p-NPNN: diamagnetic and paramagnetic states", Europhysics Letters 31(9), 573–578 (1995). DOI: 10.1209/0295-5075/31/9/012, https://doi.org/10.1209/0295-5075/31/9/012
E. V. Tretyakov, V. I. Ovcharenko, A. O. Terent'ev, I. B. Krylov, T. V. Magdesieva, D. G. Mazhukin, N. P. Gritsan, "Conjugated nitroxides", Russian Chemical Reviews 91(2), RCR5025 (2022). DOI: 10.1070/rcr5025, https://doi.org/10.1070/rcr5025
A. S. Budnikov, I. B. Krylov, I. E. Ushakov, I. R. Subbotina, F. K. Monin, G. I. Nikishin, N. N. Efimov, D. E. Gorbunov, N. P. Gritsan, E. V. Tretyakov, B. Yu, A. O. Terent'ev, "Two Discoveries in One Crystal: σ-Type Oxime Radical as an Unforeseen Building Block in Molecular Magnetics and Its Spatial Structure", Inorganic Chemistry 62(28), 10965–10972 (2023). DOI: 10.1021/acs.inorgchem.3c00947, https://doi.org/10.1021/acs.inorgchem.3c00947
L. Martin, S. S. Turner, J. D. Wallis, H. Akutsu, C. J. Gómez-García, "Perspectives on Molecular Materials—A Tribute to Professor Peter Day", Magnetochemistry 7(12), 152 (2021). DOI: 10.3390/magnetochemistry7120152, https://doi.org/10.3390/magnetochemistry7120152
A. K. Mondal, N. Brown, S. Mishra, P. Makam, D. Wing, S. Gilead, Y. Wiesenfeld, G. Leitus, L. J. W. Shimon, R. Carmieli, D. Ehre, G. Kamieniarz, J. Fransson, O. Hod, L. Kronik, E. Gazit, R. Naaman, "Long-Range Spin-Selective Transport in Chiral Metal–Organic Crystals with Temperature-Activated Magnetization", ACS Nano 14(12), 16624–16633 (2020). DOI: 10.1021/acsnano.0c07569, https://doi.org/10.1021/acsnano.0c07569
R. Tanimoto, S. Suzuki, M. Kozaki, D. Shiomi, K. Sato, T. Takui, K. Okada, "Synthesis and Magnetic Properties of Nitronyl Nitroxides with an Adjacent Chiral Group", Bulletin of the Chemical Society of Japan 87(2), 314–322 (2014). DOI: 10.1246/bcsj.20130264, https://doi.org/10.1246/bcsj.20130264
S. J. Blundell, T. Lancaster, "DFT + μ: Density functional theory for muon site determination", Applied Physics Reviews 10(2), 021316 (2023). DOI: 10.1063/5.0149080, https://doi.org/10.1063/5.0149080
S. Vaidya, S. P. M. Curley, P. Manuel, J. Ross Stewart, M. Duc Le, A. Hernández-Melián, T. J. Hicken, C. Wang, H. Luetkens, J. Krieger, S. J. Blundell, T. Lancaster, K. A. Wheeler, D. Y. Villa, Z. E. Manson, J. A. Villa, J. L. Manson, J. Singleton, R. D. Johnson, P. A. Goddard, "Single-ion anisotropy driven chiral magnetic order in a spin-1 antiferromagnetic chain", Physical Review B 114(9), 094402 (2026). DOI: 10.1103/2gnf-lrdx, https://doi.org/10.1103/2gnf-lrdx (preprint: arXiv:2509.07173, https://arxiv.org/abs/2509.07173)