Energy budget along the lattice
How it Works
Every atom in the lattice below carries a local magnetic moment — a tiny arrow pointing (mostly) along the film's easy axis. Driving one edge tips those moments slightly off-axis at frequency ω; exchange coupling to their neighbours passes that tip along, so a transverse precession wave — a magnon — ripples through the lattice while the underlying atoms themselves stay fixed in place. Only spin angular momentum and energy travel; no net charge moves at all.
The dispersion relation above is the long-wavelength (exchange-dominated) approximation for a ferromagnetic magnon: raising the applied field H shifts the whole band up (a higher drive frequency is needed before any wave can propagate at all), while the exchange stiffness D sets how fast wavelength shrinks as drive frequency climbs. When the source frequency sits below γH there is no real wavenumber solution — the perturbation is evanescent and dies within a few sites instead of propagating. Gilbert damping α controls how quickly the travelling wave's amplitude decays with distance; real magnetic insulators like YIG can reach α as low as 10⁻⁴–10⁻⁵, letting spin waves travel millimetres with very little loss.
Flip to charge-current mode and the same lattice instead carries electrons nudged along by an electric field. Every carrier constantly scatters off phonons and lattice defects, converting kinetic energy into heat (Joule/Ohmic heating, I²R) — a loss mechanism that has nothing to do with damping and cannot be tuned away by any of the sliders here. That contrast is the core promise of spintronics and magnonics: information can be carried by a spin current or a coherent spin wave with dramatically lower dissipation than pushing the same information down a wire as charge.
Frequently Asked Questions
Why does raising the applied field stop the wave from propagating?
The dispersion relation ω(k) = γH + Dk² has a minimum value of γH at k=0. If the drive frequency ω is below γH, there is no real k that solves the equation, so the disturbance cannot form a travelling wave — it decays away within a few lattice sites instead (an evanescent mode), which is exactly what the "Regime" readout reports as non-propagating.
What does the Gilbert damping slider actually change?
It sets α, the phenomenological damping constant in the Landau-Lifshitz-Gilbert equation that governs how fast precessing moments relax back toward equilibrium. Higher α shortens the attenuation length κ⁻¹ = v_g/(αω), so the wave's amplitude envelope decays over fewer lattice sites before reaching the far edge.
Why doesn't the spin-current lane generate heat the way the charge lane does?
A magnon transports angular momentum and energy through collective precession without any net displacement of charge or mass — there is no current-carrying particle scattering off impurities the way a conduction electron does. Some energy is still lost to damping (a magnon has a finite lifetime), but that loss is intrinsically much smaller and, in low-damping materials, can be pushed close to zero — unlike Ohmic heating, which is unavoidable in any real charge-carrying wire.
What is the difference between spintronics and magnonics here?
Spintronics broadly covers using the electron's spin (in addition to or instead of its charge) for information; magnonics is the more specific sub-field that encodes and processes information purely in the collective spin-wave excitations (magnons) of a magnetic medium, with no charge current involved at all — which is the mechanism this simulator's spin-current mode visualises directly.
Why does the exchange stiffness make the wavelength shrink as I raise the drive frequency?
From ω = γH + Dk², k grows as √((ω−γH)/D) — so above threshold, a higher drive frequency demands a larger wavenumber k, and since wavelength λ = 2π/k, the wave packs in tighter as ω increases. Materials with a larger exchange stiffness D need a bigger frequency step to shrink the wavelength by the same amount.