Spin-Torque Nano-Oscillator: Phase Portrait

Drive & Field

Spin-torque field H_s (current) 120 Oe

In-plane bias field H_ext 800 Oe

Gilbert damping α 0.020

Output

Initializing…

Frequency

— GHz

Cone angle θ

0.0°

Output power

m_z

1.00

How it works

The free layer of the nanopillar is a single macrospin, unit vector m, obeying the Landau-Lifshitz-Gilbert-Slonczewski equation:

dm/dt = -γ(m×H_eff) - αγ[m×(m×H_eff)] - γH_s[m×(m×p)]

H_eff = H_ext x̂ - 4πM_s·m_z ẑ   (in-plane bias + out-of-plane demag)
p = ẑ                            (fixed-layer spin polarizer)
γ/2π ≈ 2.8 GHz/kOe               (electron gyromagnetic ratio)

This 2D view drops the camera entirely and instead plots the physically real projection of m onto the film plane, (m_x, m_y) — exactly the orbit a real STNO's polarizer "sees" edge-on. Radius from the centre equals sin θ (0 at the pole, 1 at the equator); a spiral collapsing inward means damping is winning, a spiral growing outward means the spin torque is winning, and a closed ring at fixed radius is the self-sustained limit cycle — the microwave tone the device emits. Drag inside the portrait to pan, scroll/pinch to zoom — the trail keeps recording underneath.

H_s below threshold (|H_s| < αH_eff, roughly) — net damping wins, the orbit spirals into the pole. Damped.
H_s above threshold — the spin torque injects more energy per cycle than damping removes, so the orbit grows until nonlinear demag terms balance it at a fixed radius. Auto-oscillating.

Output power (bottom-left scope, orange) is read out via 1 − m_z²; m_z itself (blue) is the raw precession waveform. The bottom-right panel builds a live Hs → frequency characteristic as you move the drive slider — real STNOs (Kiselev et al. 2003) show the same red-shift: frequency drops as drive current increases.

Precession phase portrait — (m_x, m_y)

polarizer axis (⊥ page, centre) current m projection orbit trail

m_z / power vs time

Frequency vs H_s (live)