Same physics as the 3D version, recomputed as a 2D parameter map instead of an orbiting nanoparticle ensemble. Each nanoparticle's magnetic moment lags an oscillating field H(t) = H0cos(2πft) through two parallel relaxation channels:
1/τ = 1/τ_N + 1/τ_B
Néel (internal spin flip): τ_N = τ0·exp(K_a·V_core / k_B·T)
Brownian (particle rotates): τ_B = 3·η·V_hyd / k_B·T
SAR (Rosensweig, 2002):
χ0 = μ0·Md²·V_core·φ / (3·k_B·T)
P = μ0·π·χ0·H0²·f · (2πfτ) / (1 + (2πfτ)²)
SAR = P / (ρ·φ)
The left panel is a phase map: every pixel is an independent (core diameter, carrier viscosity) pair, colored by which channel wins there — this is what actually decides where the crossover between fast-Néel and fast-Brownian regimes sits, without needing to watch any single particle rotate. The top-right oscilloscope replays H(t) and the phase-lagged M(t) at a slowed, visible rate (the true 50–600 kHz drive can't be watched directly) using the real δ computed at your current settings. The bottom-right loop is the resulting M–H hysteresis loop; its enclosed area is exactly the heat delivered per field cycle.
- Core diameter — below ≈9 nm Néel relaxation is essentially instant and dominates (bright blue region); above ≈15 nm the anisotropy barrier makes Néel flips astronomically slow and Brownian rotation takes over (orange region) — trace the marker across the map as you drag the slider.
- Frequency & amplitude — SAR scales with f·H0² near resonance-free linear response; the phase map itself doesn't depend on either, since τ_N and τ_B never involve f or H0 — only τ_eff's phase lag against a given drive does.
- Medium — moving up the phase map (higher viscosity) slows Brownian rotation and pushes the crossover toward smaller diameters, which is why tumor-embedded particles are usually sized so Néel relaxation carries most of the heating.