Long-range propagating paramagnon-polaritons in organic free radicals

Abstract

Materials are commonly distinguished by their magnetic response into diamagnetic, paramagnetic, and magnetically ordered (ferro-, ferri-, and antiferromagnetic) phases. Diamagnets and paramagnets lack spontaneous long-range order, whereas ordered magnets develop such order below their Curie or Néel temperature and support single spin-wave excitations (magnons). Magnons have found applications in radio-frequency technologies and computation, magneto-optics, and foundational quantum experiments. Above the Curie/Néel temperature, long-range order is lost and the material transitions to a paramagnetic phase, with localised spin alignment in small patches, producing paramagnons with only short-range propagation. Here we show that long-range coherence is preserved in the organic free radical 2,2,6,6-tetramethylpiperidin-1-oxyl above the Néel temperature using all-electrical propagating spin-wave spectroscopy in external magnetic fields. We observe coherently excited low-energy paramagnon-polaritons up to $\mathbf{23\,\mathrm{GHz}}$ , propagating over $\mathbf{8\,\mathrm{mm}}$ at supersonic group velocities exceeding $\mathbf{100\,\mathrm{km\,s^{-1}}}$. Using free radicals as magnon carriers integrates organic materials with spintronics and opens the way to organic electronics, dense information storage, and quantum technologies.

Figures (4)

• Figure 1: TEMPO characterisation and propagation demonstration:a, Sample schematic for all-electrical propagating spin-wave spectroscopy of paramagnon-polaritons. The microwave signal is applied on port 1 (antenna 1), exciting paramagnon-polaritons in a TEMPO-filled glass capillary and detected on port 2 (antenna 2), under an external field (B$_{\perp}$ or B$_{\parallel}$). Inset: Chemical diagram of the aminoxyl radical C$_9$H$_{18}$NO (TEMPO). It is characterised by its NO-group, with one unpaired electron delocalised over the nitrogen-oxygen bond. b, Magnetisation of TEMPO with respect to the magnetic field for different temperatures, using vibrating sample magnetometry. The signal saturates for high magnetic fields and low temperatures at about 24 $\mathrm{kA/m}$. c, Brillouin fit of the 2 K measurement (in b,) and extrapolation for 50 mK. For example, at 500 mT an effective magnetisation of around 2.2 $\mathrm{kA/m}$ can be estimated (dashed line). d, Magnetisation with respect to temperature. The curves flatten below about 3 K (inset), indicating the phase transition between paramagnetic and antiferromagnetic states. The black dashed line indicates the $T_{\mathrm{N}}=2.4\,\mathrm{K}$ literature value. e, Electron paramagnetic resonance (EPR) absorption measurements of TEMPO comparing room, kelvin and millikelvin temperatures, taken at 500 mT. The linewidth increases from 42 MHz at 297 K to about 67 MHz at 750 mK, while the frequency shifts from 14.066 GHz to 14.014 GHz (fit errors negligible). At lower temperatures, the linewidth broadens. A single Lorentz fit is used at room temperature, and a double Lorentz fit is used at cryogenic temperatures (see main text for more details). f, Demonstration of all-electrical propagating spin-wave spectroscopy transmission signal (S$'_{21}$) in the paramangetic state of TEMPO at 3.55 K and at B$_{\parallel}=$ 500 mT (paramagnon-polariton). The linear magnitude (black), real (red), and imaginary part (blue) of the transmission signal are shown. The phase of the propagation is preserved, as indicated by the $\pi/2$-phase relation between the real and imaginary parts.
• Figure 2: Temperature- and field-dependent AEPSWS of TEMPO.a, Background corrected real part of S$'_{21}$ at different temperatures and fixed external magnetic field of $B_{\parallel}=500\mathrm{mT}$. The temperature is swept from 85 to 3550 mK, and a reference measurement at 297 K is taken. A coherent signal is visible for the cryogenic temperatures. The signal amplitude increases by one order of magnitude as the Néel point is approached (note different amplitude on abscissa), while the signal is not visible at room temperature. The SNR ratio is largest around the Néel point for the propagating paramagnon-polaritons, possibly due to the protection from temperature broadening near the quantum critical point (see main text). b, Background corrected real part of part of S$'_{21}$ at different external magnetic fields, measured at 85 mK. The propagating signal shifts as the magnetic field increases. An amplitude increase is observed with increased field due to the increased effective magnetisation.
• Figure 3: Time-resolved measurements.a, Continuous-frequency measurement (real part) for $B_{\mathrm{\perp}}=500\,\mathrm{mT}$ and 55 mK, at 4 mm antenna spacing. b, Inverse fast Fourier transformation (IFFT) of the continuous-frequency signal in a. The first peak at 45 ns is due to electromagnetic delay/leakage in the setup. The signal is visible until about 85 ns, resulting in a spin-wave propagation time of about 40 ns. c, Pulsed measurement with absolute measured amplitudes for comparing resonant and off-resonant excitation of the spin wave, as shown in a. A 100 ns pulse at a repetition rate of 1 ms is used. Consistent with the IFFT, a propagation time of approximately 9 ns is observed when comparing on-resonant and off-resonant signals. From the phase periodicity in the continuous-frequency data and from time-of-flight, we estimate $v_{\mathrm g}\!\approx\!100$–$440\,\mathrm{km\,s^{-1}}$.
• Figure 4: Theoretical dispersion calculation.a, Close-up view of hybridised magnon-polariton dispersion curves (solid green lines); uncoupled magnon and polariton dispersions are shown in dashed (blue, red). b, Corresponding group velocity of paramagnons (dashed) and coupled magnon-polaritons (solid). The inset shows a full-scale view of the dispersions. Data are for $B_\bot = 500\,$mT and $M_s = 2.2\,$kA/m. Calculation details are given in Supplementary Section II.