Applications / Experiments read through FDT
One carrier in a patterned magnetic circuit
Superconducting resonators patterned over a 100 nm garnet film bring microwave photons and propagating spin waves to one frequency, and the two split into hybrid modes. FDT reads the photon and the magnon as two regimes of one carrier: the avoided crossing is two regime modes of that carrier hybridising, with nothing mediated.
The record
What was measured
Li and colleagues grow a 100 nm film of yttrium iron garnet on a rare-earth-free Y₃Sc₂Ga₃O₁₂ substrate, cover it with 10 nm of silicon nitride, and pattern 30 nm niobium nitride resonators on top. A quarter-wave resonator carries a 2 µm or a 0.5 µm signal line; a meander resonator carries a 1 µm line folded three times. The microwave field under a narrow line drives propagating spin waves, not only the film’s uniform Kittel mode, at wavelengths the line geometry selects: 2.8, 5.2 and 6.5 µm for the 0.5 µm line, the meander and the 2 µm line.
Sweeping the in-plane field moves the spin-wave frequency through the resonator’s. Where the two meet, the transmission spectrum shows an avoided crossing, which the source fits with the coupled-mode equation
With the field along the line, the Damon–Eshbach configuration, the 2 µm quarter-wave device gives g/2π = 115 MHz against a magnon damping of 70 MHz. The meander gives 150 MHz in the Damon–Eshbach configuration and 100 MHz in the backward-volume configuration, against 34 MHz. The photon damping is 1.1 MHz for both devices. The meander meets the strong-coupling criterion, g above both damping rates. For the quarter-wave device the lower-field branch near 0.15 T is wider than the model, and the source leaves it uncertain whether g strictly exceeds the magnon damping.
| Device | Spin wave | Wavelength | g/2π | κm/2π | κc/2π | g²/(κcκm) |
|---|---|---|---|---|---|---|
| Quarter-wave, 2 µm line | Damon–Eshbach | 6.5 µm | 115 MHz | 70 MHz | 1.1 MHz | not printed |
| Meander, 1 µm line | Damon–Eshbach | 5.2 µm | 150 MHz | 34 MHz | 1.1 MHz | 662 |
| Meander, 1 µm line | backward-volume | 5.2 µm | 100 MHz | 34 MHz | 1.1 MHz | 294 |
A second, weaker anticrossing shows at lower field: the first perpendicular standing spin wave, a mode with a node across the film’s thickness, 80 mT from the main mode. The source’s exchange-field formula, μ₀Hex = (2Aex/Ms)(π/t)² with Aex = 2.6 pJ/m, gives 37 mT for free surfaces and 74 mT with the interface to the substrate pinned.
A detection line 5 µm from the resonator picks up the spin waves the hybrid mode radiates. At negative field the lower hybrid branch transmits more strongly from the resonator to the detection line, S21, than back, S12; reversing the field reverses the order. The power isolation at the hybrid peak is 4 dB at both polarities, with the modes degenerate at −0.171 T and +0.187 T.
The FDT reading
I-2 One carrier, P-5 magnetism is geometry, P-2 nodal architecture
Photon, graviton, gluon, phonon and magnon are one spin-one density excitation of the omnium, read in different density and geometry regimes (I-2). The chain gives them one medium and one propagation speed. The resonator mode is that carrier as a stroke along a superconducting line; the spin wave is the same carrier as a stroke through the film’s helical density gradient (P-5).
Where the two strokes reach one frequency, they hybridise. Each hybrid branch changes its reading continuously across the crossing: far from it, one branch reads as the photon and the other as the spin wave, and at zero detuning each reads half of each. The splitting 2g is a fitted response of the circuit, not a force. Nothing travels between the film and the resonator as a separate particle, and the source’s coupled-mode equation, run on its own inputs, returns its spectra unchanged.
The bias field is a helical density gradient of the omnium along the field axis (P-5). The magnon is the carrier’s stroke through it, and the precession sense and the sense of the antenna’s field read the gradient’s hand. Reversing the field reverses the hand, and the stronger direction of transmission reverses with it.
The perpendicular standing spin waves are nodal patterns of the driven density field across the film thickness (P-2). Their geometry is set by the boundary conditions at the two surfaces, the clamps, not by the medium. Free surfaces put the first standing mode 37 mT above the main mode, one pinned surface 74 mT, two pinned surfaces 111 mT, and the observed 80 mT sits closest to one pinned surface. That closer agreement fixes neither the surface anisotropy nor a local density profile. The reading is in-sample, X-1, and no prediction rests on it.
One carrier, two regimes. In Avoided crossing, choose a device and set the resonator frequency: the window follows the crossing, and the inset shows where it sits in the whole sweep. The hybrid branches shade from the photon’s colour to the spin wave’s as their shares change; hover to read the shares. The rates are the source’s fits and the dispersions its equations; the resonator frequency is a control because the source prints none. Standing waves sets the mode profiles across the film for three surface conditions against the observed 80 mT. Direction shows the measured degeneracy fields and the 4 dB isolation; the drawn waves are schematic.
I-2, P-5, P-2
What FDT predicts
Tests the record does not yet contain
Each test compares independently prepared samples or paths, so the conventional response cancels or sits in a measured comparator. T-1 adds a source; T-2 to T-4 change a constitutive input, the density response to isotope substitution (I-7), and each reads its sign through sensitivities measured independently on the same films.
- T-1Twist and the degeneracy field. Clamp the 2 µm quarter-wave chip at both ends, 5.0 mm apart, and twist it about the bias axis at ±0.10 rad/m, at 2.0 K in the same magnet. Measure the field of zero detuning at both bias polarities and both hands, and form the double contrast Dtw = ¼(H++ − H−+ − H+− + H−−). A static twist is even under time reversal, and magnetoelastic and strain responses act on both polarities alike, so the conventional contrast is zero. Under P-5 the twist establishes a field along its axis that reverses with the hand, and FDT reads a nonzero contrast. P-5 fixes the axis and the reversal; a magnitude needs a declared kernel, so the test is one of existence. Twelve cooldowns of eight cycles detect 0.7 µT above a 0.3 µT systematic bound.
- T-2Iron isotopes and the meander splitting. Grow films whose iron is 5 % and 95 % 56Fe, the rest 54Fe, on the same substrate, anneal, spacer and niobium nitride stack, and fit the meander’s Damon–Eshbach coupling g at 2.0 K. The heavier film’s higher density raises its magnetic energy density (I-7). At the declared test point FDT reads a log change Δln g = 0.012 against a comparator of 1.9 × 10⁻⁵, above a detection threshold of 0.0013.
- T-3Oxygen isotopes and the standing-wave separation. Replace the air anneal with 16O and 18O anneals on the source’s schedule, 850 °C for 3 hours, cooled at 30 °C per hour at 1.0 bar, and assay the exchanged depth profile. Record the field separation Y between the first standing mode and the main Damon–Eshbach mode at a fixed 7.4 GHz, 71 mT at the baseline. FDT reads the denser film as a stiffer exchange: Δln Y = 0.015 against a comparator of 0.00088, above a threshold of 0.0013.
- T-4Nitrogen isotopes and the superconducting transition. Sputter the 30 nm niobium nitride layer with 14N and 15N gases at identical pressure, power and thickness, and measure its transition on a witness bar at half the normal-state resistance. The pairing and volume comparator gives Δln Tc = −0.016; adding the density input, FDT reads +0.0095. The difference, 0.025, clears the 0.012 threshold.
Readings declined
Use 6 Data yes, interpretation not necessarily
Standard reading
Magnons and photons are two kinds of quasiparticle, and the coupling transfers excitations between two systems.
FDT reading
One spin-one density excitation read in two regimes; the avoided crossing is two regime modes of that carrier hybridising (I-2).
Spin waves mediate interactions, such as the entanglement of spin qubits.
Nothing is mediated: mediation is a coordinate artefact, and correlated patterns share a bivector grade (I-2, I-4).
The bias field is an independent entity about which the magnetisation precesses.
The field is a helical density gradient of the omnium; the magnon is the carrier’s stroke through it, and its precession sense reads the gradient’s hand (P-5).
Convergence
Use 2 Same source, same data
Set the twist source and the isotope density response to their conventional limits, and the source’s coupled-mode, dispersion, linewidth, exchange-field and escape-time equations stand unchanged. On the same inputs they return its fitted couplings, its magnon and photon damping rates, its frequency offsets against the estimated wavenumbers, its radiation-damping estimates of 26.5, 11.5 and 6.6 MHz, and, in sample, the meander’s linewidth curve. They keep what the record keeps: the 80 mT standing-wave separation beside the 37 and 74 mT estimates, the quarter-wave linewidth excess near 0.15 T, and the printed cooperativities beside their recomputation.
FDT departs from the consensus prediction only where it adds a source, the twist field of T-1, or a constitutive input, the isotope density response of T-2 to T-4. The splittings, linewidths and transmissions are accepted in full and recovered by the identical response calculation.